%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW312+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:25:55 EDT 2023

% Result   : Theorem 1.62s 2.45s
% Output   : Proof 1.62s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW312+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.33  % Computer : n015.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Thu May 18 22:44:07 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 1.62/2.45  
% 1.62/2.45  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 1.62/2.45  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.62/2.45  %-----------------------------------------------------
% 1.62/2.45  ncf(matrix, plain, [(52215 ^ _784416) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts))], (2 ^ _784416) ^ [_784446] : [-(_784446 = _784446)], (4 ^ _784416) ^ [_784469, _784471] : [_784471 = _784469, -(_784469 = _784471)], (10 ^ _784416) ^ [_784542, _784544, _784546] : [-(_784546 = _784542), _784546 = _784544, _784544 = _784542], (20 ^ _784416) ^ [_784679, _784681, _784683, _784685, _784687, _784689, _784691, _784693, _784695, _784697, _784699, _784701] : [-(c_Predicate_Oinv__imagep(_784699, _784695, _784691, _784687, _784683, _784679)), c_Predicate_Oinv__imagep(_784701, _784697, _784693, _784689, _784685, _784681), _784701 = _784699, _784697 = _784695, _784693 = _784691, _784689 = _784687, _784685 = _784683, _784681 = _784679], (50 ^ _784416) ^ [_785224, _785226, _785228, _785230, _785232, _785234, _785236, _785238, _785240, _785242, _785244, _785246] : [-(c_Nitpick_Ofold__graph_H(_785244, _785240, _785236, _785232, _785228, _785224)), c_Nitpick_Ofold__graph_H(_785246, _785242, _785238, _785234, _785230, _785226), _785246 = _785244, _785242 = _785240, _785238 = _785236, _785234 = _785232, _785230 = _785228, _785226 = _785224], (80 ^ _784416) ^ [_785769, _785771, _785773, _785775, _785777, _785779, _785781, _785783] : [-(c_Partial__Function_Omk__less(_785781, _785777, _785773, _785769)), c_Partial__Function_Omk__less(_785783, _785779, _785775, _785771), _785783 = _785781, _785779 = _785777, _785775 = _785773, _785771 = _785769], (102 ^ _784416) ^ [_786122, _786124, _786126, _786128, _786130, _786132] : [-(c_Orderings_Oorder__class_Ostrict__mono(_786130, _786126, _786122)), c_Orderings_Oorder__class_Ostrict__mono(_786132, _786128, _786124), _786132 = _786130, _786128 = _786126, _786124 = _786122], (120 ^ _784416) ^ [_786391, _786393, _786395, _786397, _786399, _786401, _786403, _786405, _786407, _786409, _786411, _786413] : [-(c_Equiv__Relations_Ocongruent2(_786411, _786407, _786403, _786399, _786395, _786391)), c_Equiv__Relations_Ocongruent2(_786413, _786409, _786405, _786401, _786397, _786393), _786413 = _786411, _786409 = _786407, _786405 = _786403, _786401 = _786399, _786397 = _786395, _786393 = _786391], (150 ^ _784416) ^ [_786936, _786938, _786940, _786942] : [-(c_Nitpick_Orefl_H(_786940, _786936)), c_Nitpick_Orefl_H(_786942, _786938), _786942 = _786940, _786938 = _786936], (164 ^ _784416) ^ [_787129, _787131, _787133, _787135] : [-(c_Equiv__Relations_Oequivp(_787133, _787129)), c_Equiv__Relations_Oequivp(_787135, _787131), _787135 = _787133, _787131 = _787129], (178 ^ _784416) ^ [_787322, _787324, _787326, _787328, _787330, _787332, _787334, _787336] : [-(c_Finite__Set_Ofolding__idem(_787334, _787330, _787326, _787322)), c_Finite__Set_Ofolding__idem(_787336, _787332, _787328, _787324), _787336 = _787334, _787332 = _787330, _787328 = _787326, _787324 = _787322], (200 ^ _784416) ^ [_787675, _787677, _787679, _787681, _787683, _787685, _787687, _787689, _787691, _787693, _787695, _787697] : [-(c_Finite__Set_Ofolding__image__simple(_787695, _787691, _787687, _787683, _787679, _787675)), c_Finite__Set_Ofolding__image__simple(_787697, _787693, _787689, _787685, _787681, _787677), _787697 = _787695, _787693 = _787691, _787689 = _787687, _787685 = _787683, _787681 = _787679, _787677 = _787675], (230 ^ _784416) ^ [_788220, _788222, _788224, _788226, _788228, _788230, _788232, _788234, _788236, _788238] : [-(c_Finite__Set_Ofolding__image(_788236, _788232, _788228, _788224, _788220)), c_Finite__Set_Ofolding__image(_788238, _788234, _788230, _788226, _788222), _788238 = _788236, _788234 = _788232, _788230 = _788228, _788226 = _788224, _788222 = _788220], (256 ^ _784416) ^ [_788665, _788667, _788669, _788671, _788673, _788675] : [-(c_Big__Operators_Osemilattice__big(_788673, _788669, _788665)), c_Big__Operators_Osemilattice__big(_788675, _788671, _788667), _788675 = _788673, _788671 = _788669, _788667 = _788665], (274 ^ _784416) ^ [_788934, _788936, _788938, _788940, _788942, _788944, _788946, _788948, _788950, _788952] : [-(c_Big__Operators_Ocomm__monoid__big(_788950, _788946, _788942, _788938, _788934)), c_Big__Operators_Ocomm__monoid__big(_788952, _788948, _788944, _788940, _788936), _788952 = _788950, _788948 = _788946, _788944 = _788942, _788940 = _788938, _788936 = _788934], (300 ^ _784416) ^ [_789379, _789381] : [-(class_Rings_Odivision__ring__inverse__zero(_789379)), _789381 = _789379, class_Rings_Odivision__ring__inverse__zero(_789381)], (310 ^ _784416) ^ [_789504, _789506] : [-(class_Rings_Odivision__ring(_789504)), _789506 = _789504, class_Rings_Odivision__ring(_789506)], (320 ^ _784416) ^ [_789629, _789631, _789633, _789635] : [-(c_Int_Oiszero(_789633, _789629)), c_Int_Oiszero(_789635, _789631), _789635 = _789633, _789631 = _789629], (334 ^ _784416) ^ [_789822, _789824] : [-(class_Fields_Ofield__inverse__zero(_789822)), _789824 = _789822, class_Fields_Ofield__inverse__zero(_789824)], (344 ^ _784416) ^ [_789947, _789949, _789951, _789953, _789955, _789957] : [-(c_Orderings_Oorder__class_Omono(_789955, _789951, _789947)), c_Orderings_Oorder__class_Omono(_789957, _789953, _789949), _789957 = _789955, _789953 = _789951, _789949 = _789947], (362 ^ _784416) ^ [_790216, _790218] : [-(class_Fields_Ofield(_790216)), _790218 = _790216, class_Fields_Ofield(_790218)], (372 ^ _784416) ^ [_790341, _790343] : [-(c_Nat__Transfer_Ois__nat(_790341)), _790343 = _790341, c_Nat__Transfer_Ois__nat(_790343)], (382 ^ _784416) ^ [_790466, _790468] : [-(class_Fields_Olinordered__field__inverse__zero(_790466)), _790468 = _790466, class_Fields_Olinordered__field__inverse__zero(_790468)], (392 ^ _784416) ^ [_790591, _790593, _790595, _790597, _790599, _790601, _790603, _790605] : [-(c_Wellfounded_Omax__extp(_790603, _790599, _790595, _790591)), c_Wellfounded_Omax__extp(_790605, _790601, _790597, _790593), _790605 = _790603, _790601 = _790599, _790597 = _790595, _790593 = _790591], (414 ^ _784416) ^ [_790944, _790946, _790948, _790950] : [-(c_FunDef_Oreduction__pair(_790948, _790944)), c_FunDef_Oreduction__pair(_790950, _790946), _790950 = _790948, _790946 = _790944], (428 ^ _784416) ^ [_791137, _791139, _791141, _791143] : [-(c_Predicate_Oreflp(_791141, _791137)), c_Predicate_Oreflp(_791143, _791139), _791143 = _791141, _791139 = _791137], (442 ^ _784416) ^ [_791330, _791332, _791334, _791336] : [-(c_Nitpick_Owf_H(_791334, _791330)), c_Nitpick_Owf_H(_791336, _791332), _791336 = _791334, _791332 = _791330], (456 ^ _784416) ^ [_791523, _791525] : [-(c_Nitpick_Ounknown(_791523)), _791525 = _791523, c_Nitpick_Ounknown(_791525)], (466 ^ _784416) ^ [_791648, _791650, _791652, _791654, _791656, _791658, _791660, _791662] : [-(c_Equiv__Relations_Ocongruent(_791660, _791656, _791652, _791648)), c_Equiv__Relations_Ocongruent(_791662, _791658, _791654, _791650), _791662 = _791660, _791658 = _791656, _791654 = _791652, _791650 = _791648], (488 ^ _784416) ^ [_792001, _792003, _792005, _792007] : [-(c_Wellfounded_OwfP(_792005, _792001)), c_Wellfounded_OwfP(_792007, _792003), _792007 = _792005, _792003 = _792001], (502 ^ _784416) ^ [_792194, _792196, _792198, _792200] : [-(c_Relation_Oirrefl(_792198, _792194)), c_Relation_Oirrefl(_792200, _792196), _792200 = _792198, _792196 = _792194], (516 ^ _784416) ^ [_792387, _792389, _792391, _792393, _792395, _792397] : [-(c_Relation_Ototal__on(_792395, _792391, _792387)), c_Relation_Ototal__on(_792397, _792393, _792389), _792397 = _792395, _792393 = _792391, _792389 = _792387], (534 ^ _784416) ^ [_792656, _792658, _792660, _792662, _792664, _792666, _792668, _792670] : [-(c_Finite__Set_Ofolding(_792668, _792664, _792660, _792656)), c_Finite__Set_Ofolding(_792670, _792666, _792662, _792658), _792670 = _792668, _792666 = _792664, _792662 = _792660, _792658 = _792656], (556 ^ _784416) ^ [_793009, _793011, _793013, _793015, _793017, _793019] : [-(c_Finite__Set_Ofolding__one__idem(_793017, _793013, _793009)), c_Finite__Set_Ofolding__one__idem(_793019, _793015, _793011), _793019 = _793017, _793015 = _793013, _793011 = _793009], (574 ^ _784416) ^ [_793278, _793280, _793282, _793284, _793286, _793288] : [-(c_Finite__Set_Ofolding__one(_793286, _793282, _793278)), c_Finite__Set_Ofolding__one(_793288, _793284, _793280), _793288 = _793286, _793284 = _793282, _793280 = _793278], (592 ^ _784416) ^ [_793547, _793549, _793551, _793553, _793555, _793557] : [-(c_Relation_Osingle__valued(_793555, _793551, _793547)), c_Relation_Osingle__valued(_793557, _793553, _793549), _793557 = _793555, _793553 = _793551, _793549 = _793547], (610 ^ _784416) ^ [_793816, _793818, _793820, _793822, _793824, _793826, _793828, _793830, _793832, _793834, _793836, _793838] : [-(c_Finite__Set_Ofolding__image__simple__idem(_793836, _793832, _793828, _793824, _793820, _793816)), c_Finite__Set_Ofolding__image__simple__idem(_793838, _793834, _793830, _793826, _793822, _793818), _793838 = _793836, _793834 = _793832, _793830 = _793828, _793826 = _793824, _793822 = _793820, _793818 = _793816], (640 ^ _784416) ^ [_794361, _794363] : [-(c_Nat__Transfer_Onat__set(_794361)), _794363 = _794361, c_Nat__Transfer_Onat__set(_794363)], (650 ^ _784416) ^ [_794486, _794488, _794490, _794492, _794494, _794496] : [-(c_Enum_Oex__n__lists(_794494, _794490, _794486)), c_Enum_Oex__n__lists(_794496, _794492, _794488), _794496 = _794494, _794492 = _794490, _794488 = _794486], (668 ^ _784416) ^ [_794755, _794757, _794759, _794761, _794763, _794765] : [-(c_Enum_Oall__n__lists(_794763, _794759, _794755)), c_Enum_Oall__n__lists(_794765, _794761, _794757), _794765 = _794763, _794761 = _794759, _794757 = _794755], (686 ^ _784416) ^ [_795024, _795026, _795028, _795030, _795032, _795034] : [-(c_Equiv__Relations_Oequiv(_795032, _795028, _795024)), c_Equiv__Relations_Oequiv(_795034, _795030, _795026), _795034 = _795032, _795030 = _795028, _795026 = _795024], (704 ^ _784416) ^ [_795293, _795295, _795297, _795299, _795301, _795303, _795305, _795307, _795309, _795311] : [-(c_Typedef_Otype__definition(_795309, _795305, _795301, _795297, _795293)), c_Typedef_Otype__definition(_795311, _795307, _795303, _795299, _795295), _795311 = _795309, _795307 = _795305, _795303 = _795301, _795299 = _795297, _795295 = _795293], (730 ^ _784416) ^ [_795738, _795740, _795742, _795744, _795746, _795748, _795750, _795752] : [-(c_List_Olistrelp(_795750, _795746, _795742, _795738)), c_List_Olistrelp(_795752, _795748, _795744, _795740), _795752 = _795750, _795748 = _795746, _795744 = _795742, _795740 = _795738], (752 ^ _784416) ^ [_796091, _796093] : [-(class_Lattices_Oab__semigroup__idem__mult(_796091)), _796093 = _796091, class_Lattices_Oab__semigroup__idem__mult(_796093)], (762 ^ _784416) ^ [_796216, _796218, _796220, _796222, _796224, _796226] : [-(c_Finite__Set_Ofun__left__comm__idem(_796224, _796220, _796216)), c_Finite__Set_Ofun__left__comm__idem(_796226, _796222, _796218), _796226 = _796224, _796222 = _796220, _796218 = _796216], (780 ^ _784416) ^ [_796485, _796487] : [-(c_List_Onat__list(_796485)), _796487 = _796485, c_List_Onat__list(_796487)], (790 ^ _784416) ^ [_796610, _796612, _796614, _796616, _796618, _796620] : [-(c_Finite__Set_Ofun__left__comm(_796618, _796614, _796610)), c_Finite__Set_Ofun__left__comm(_796620, _796616, _796612), _796620 = _796618, _796616 = _796614, _796612 = _796610], (808 ^ _784416) ^ [_796879, _796881, _796883, _796885, _796887, _796889, _796891, _796893] : [-(c_Fun_Oinj__on(_796891, _796887, _796883, _796879)), c_Fun_Oinj__on(_796893, _796889, _796885, _796881), _796893 = _796891, _796889 = _796887, _796885 = _796883, _796881 = _796879], (830 ^ _784416) ^ [_797232, _797234, _797236, _797238] : [-(c_Wellfounded_Owf(_797236, _797232)), c_Wellfounded_Owf(_797238, _797234), _797238 = _797236, _797234 = _797232], (844 ^ _784416) ^ [_797425, _797427, _797429, _797431, _797433, _797435, _797437, _797439, _797441, _797443] : [-(c_List_Olist__all2(_797441, _797437, _797433, _797429, _797425)), c_List_Olist__all2(_797443, _797439, _797435, _797431, _797427), _797443 = _797441, _797439 = _797437, _797435 = _797433, _797431 = _797429, _797427 = _797425], (870 ^ _784416) ^ [_797870, _797872, _797874, _797876] : [-(c_List_Olinorder__class_Osorted(_797874, _797870)), c_List_Olinorder__class_Osorted(_797876, _797872), _797876 = _797874, _797872 = _797870], (884 ^ _784416) ^ [_798063, _798065] : [-(class_Rings_Oinverse(_798063)), _798065 = _798063, class_Rings_Oinverse(_798065)], (894 ^ _784416) ^ [_798188, _798190, _798192, _798194, _798196, _798198] : [-(c_Nitpick_Oless__frac(_798196, _798192, _798188)), c_Nitpick_Oless__frac(_798198, _798194, _798190), _798198 = _798196, _798194 = _798192, _798190 = _798188], (912 ^ _784416) ^ [_798457, _798459, _798461, _798463, _798465, _798467] : [-(c_Nitpick_Oless__eq__frac(_798465, _798461, _798457)), c_Nitpick_Oless__eq__frac(_798467, _798463, _798459), _798467 = _798465, _798463 = _798461, _798459 = _798457], (930 ^ _784416) ^ [_798726, _798728, _798730, _798732] : [-(c_FunDef_Ois__measure(_798730, _798726)), c_FunDef_Ois__measure(_798732, _798728), _798732 = _798730, _798728 = _798726], (944 ^ _784416) ^ [_798919, _798921, _798923, _798925, _798927, _798929, _798931, _798933] : [-(c_Nat__Transfer_Otransfer__morphism(_798931, _798927, _798923, _798919)), c_Nat__Transfer_Otransfer__morphism(_798933, _798929, _798925, _798921), _798933 = _798931, _798929 = _798927, _798925 = _798923, _798921 = _798919], (966 ^ _784416) ^ [_799272, _799274, _799276, _799278] : [-(c_Wellfounded_Oacyclic(_799276, _799272)), c_Wellfounded_Oacyclic(_799278, _799274), _799278 = _799276, _799274 = _799272], (980 ^ _784416) ^ [_799465, _799467] : [-(class_Fields_Olinordered__field(_799465)), _799467 = _799465, class_Fields_Olinordered__field(_799467)], (990 ^ _784416) ^ [_799590, _799592, _799594, _799596, _799598, _799600] : [-(c_Relation_Orefl__on(_799598, _799594, _799590)), c_Relation_Orefl__on(_799600, _799596, _799592), _799600 = _799598, _799596 = _799594, _799592 = _799590], (1008 ^ _784416) ^ [_799859, _799861, _799863, _799865, _799867, _799869] : [-(c_List_Olist__ex1(_799867, _799863, _799859)), c_List_Olist__ex1(_799869, _799865, _799861), _799869 = _799867, _799865 = _799863, _799861 = _799859], (1026 ^ _784416) ^ [_800128, _800130, _800132, _800134, _800136, _800138] : [-(c_List_Olist__all(_800136, _800132, _800128)), c_List_Olist__all(_800138, _800134, _800130), _800138 = _800136, _800134 = _800132, _800130 = _800128], (1044 ^ _784416) ^ [_800397, _800399, _800401, _800403, _800405, _800407] : [-(c_List_Olist__ex(_800405, _800401, _800397)), c_List_Olist__ex(_800407, _800403, _800399), _800407 = _800405, _800403 = _800401, _800399 = _800397], (1062 ^ _784416) ^ [_800666, _800668, _800670, _800672, _800674, _800676] : [-(c_List_Oall__interval__int(_800674, _800670, _800666)), c_List_Oall__interval__int(_800676, _800672, _800668), _800676 = _800674, _800672 = _800670, _800668 = _800666], (1080 ^ _784416) ^ [_800935, _800937] : [-(class_Lattices_Obounded__lattice(_800935)), _800937 = _800935, class_Lattices_Obounded__lattice(_800937)], (1090 ^ _784416) ^ [_801060, _801062] : [-(class_Rings_Olinordered__semiring__1__strict(_801060)), _801062 = _801060, class_Rings_Olinordered__semiring__1__strict(_801062)], (1100 ^ _784416) ^ [_801185, _801187] : [-(class_Groups_Oordered__ab__group__add__abs(_801185)), _801187 = _801185, class_Groups_Oordered__ab__group__add__abs(_801187)], (1110 ^ _784416) ^ [_801310, _801312] : [-(class_Groups_Olinordered__ab__group__add(_801310)), _801312 = _801310, class_Groups_Olinordered__ab__group__add(_801312)], (1120 ^ _784416) ^ [_801435, _801437] : [-(class_Rings_Oring__1__no__zero__divisors(_801435)), _801437 = _801435, class_Rings_Oring__1__no__zero__divisors(_801437)], (1130 ^ _784416) ^ [_801560, _801562] : [-(class_Rings_Olinordered__ring__strict(_801560)), _801562 = _801560, class_Rings_Olinordered__ring__strict(_801562)], (1140 ^ _784416) ^ [_801685, _801687] : [-(class_Rings_Oring__no__zero__divisors(_801685)), _801687 = _801685, class_Rings_Oring__no__zero__divisors(_801687)], (1150 ^ _784416) ^ [_801810, _801812] : [-(class_Rings_Olinordered__semiring__1(_801810)), _801812 = _801810, class_Rings_Olinordered__semiring__1(_801812)], (1160 ^ _784416) ^ [_801935, _801937] : [-(class_Groups_Oordered__ab__group__add(_801935)), _801937 = _801935, class_Groups_Oordered__ab__group__add(_801937)], (1170 ^ _784416) ^ [_802060, _802062] : [-(class_Rings_Oordered__ring__abs(_802060)), _802062 = _802060, class_Rings_Oordered__ring__abs(_802062)], (1180 ^ _784416) ^ [_802185, _802187] : [-(class_Rings_Olinordered__ring(_802185)), _802187 = _802185, class_Rings_Olinordered__ring(_802187)], (1190 ^ _784416) ^ [_802310, _802312] : [-(class_Rings_Olinordered__idom(_802310)), _802312 = _802310, class_Rings_Olinordered__idom(_802312)], (1200 ^ _784416) ^ [_802435, _802437] : [-(class_Groups_Oab__group__add(_802435)), _802437 = _802435, class_Groups_Oab__group__add(_802437)], (1210 ^ _784416) ^ [_802560, _802562] : [-(class_Rings_Oordered__ring(_802560)), _802562 = _802560, class_Rings_Oordered__ring(_802562)], (1220 ^ _784416) ^ [_802685, _802687] : [-(class_Rings_Ocomm__ring__1(_802685)), _802687 = _802685, class_Rings_Ocomm__ring__1(_802687)], (1230 ^ _784416) ^ [_802810, _802812] : [-(class_Groups_Ogroup__add(_802810)), _802812 = _802810, class_Groups_Ogroup__add(_802812)], (1240 ^ _784416) ^ [_802935, _802937] : [-(class_Divides_Oring__div(_802935)), _802937 = _802935, class_Divides_Oring__div(_802937)], (1250 ^ _784416) ^ [_803060, _803062] : [-(class_Int_Oring__char__0(_803060)), _803062 = _803060, class_Int_Oring__char__0(_803062)], (1260 ^ _784416) ^ [_803185, _803187] : [-(class_Int_Onumber__ring(_803185)), _803187 = _803185, class_Int_Onumber__ring(_803187)], (1270 ^ _784416) ^ [_803310, _803312] : [-(class_Groups_Osgn__if(_803310)), _803312 = _803310, class_Groups_Osgn__if(_803312)], (1280 ^ _784416) ^ [_803435, _803437] : [-(class_Groups_Oabs__if(_803435)), _803437 = _803435, class_Groups_Oabs__if(_803437)], (1290 ^ _784416) ^ [_803560, _803562] : [-(class_Rings_Oring__1(_803560)), _803562 = _803560, class_Rings_Oring__1(_803562)], (1300 ^ _784416) ^ [_803685, _803687] : [-(class_Rings_Oring(_803685)), _803687 = _803685, class_Rings_Oring(_803687)], (1310 ^ _784416) ^ [_803810, _803812] : [-(class_Rings_Oidom(_803810)), _803812 = _803810, class_Rings_Oidom(_803812)], (1320 ^ _784416) ^ [_803935, _803937] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_803935)), _803937 = _803935, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_803937)], (1330 ^ _784416) ^ [_804060, _804062] : [-(class_Orderings_Owellorder(_804060)), _804062 = _804060, class_Orderings_Owellorder(_804062)], (1340 ^ _784416) ^ [_804185, _804187] : [-(class_Complete__Lattice_Ocomplete__lattice(_804185)), _804187 = _804185, class_Complete__Lattice_Ocomplete__lattice(_804187)], (1350 ^ _784416) ^ [_804310, _804312] : [-(class_Lattices_Obounded__lattice__top(_804310)), _804312 = _804310, class_Lattices_Obounded__lattice__top(_804312)], (1360 ^ _784416) ^ [_804435, _804437] : [-(class_Lattices_Obounded__lattice__bot(_804435)), _804437 = _804435, class_Lattices_Obounded__lattice__bot(_804437)], (1370 ^ _784416) ^ [_804560, _804562] : [-(class_Lattices_Osemilattice__sup(_804560)), _804562 = _804560, class_Lattices_Osemilattice__sup(_804562)], (1380 ^ _784416) ^ [_804685, _804687] : [-(class_Lattices_Osemilattice__inf(_804685)), _804687 = _804685, class_Lattices_Osemilattice__inf(_804687)], (1390 ^ _784416) ^ [_804810, _804812] : [-(class_Lattices_Odistrib__lattice(_804810)), _804812 = _804810, class_Lattices_Odistrib__lattice(_804812)], (1400 ^ _784416) ^ [_804935, _804937] : [-(class_Lattices_Oboolean__algebra(_804935)), _804937 = _804935, class_Lattices_Oboolean__algebra(_804937)], (1410 ^ _784416) ^ [_805060, _805062] : [-(class_Lattices_Olattice(_805060)), _805062 = _805060, class_Lattices_Olattice(_805062)], (1420 ^ _784416) ^ [_805185, _805187] : [-(class_Orderings_Otop(_805185)), _805187 = _805185, class_Orderings_Otop(_805187)], (1430 ^ _784416) ^ [_805310, _805312] : [-(class_Orderings_Obot(_805310)), _805312 = _805310, class_Orderings_Obot(_805312)], (1440 ^ _784416) ^ [_805435, _805437] : [-(class_Groups_Ouminus(_805435)), _805437 = _805435, class_Groups_Ouminus(_805437)], (1450 ^ _784416) ^ [_805560, _805562] : [-(class_Lazy__Sequence_Osmall__lazy(_805560)), _805562 = _805560, class_Lazy__Sequence_Osmall__lazy(_805562)], (1460 ^ _784416) ^ [_805685, _805687] : [-(class_Finite__Set_Ofinite(_805685)), _805687 = _805685, class_Finite__Set_Ofinite(_805687)], (1470 ^ _784416) ^ [_805810, _805812] : [-(class_Smallcheck_Osmall(_805810)), _805812 = _805810, class_Smallcheck_Osmall(_805812)], (1480 ^ _784416) ^ [_805935, _805937] : [-(class_Enum_Oenum(_805935)), _805937 = _805935, class_Enum_Oenum(_805937)], (1490 ^ _784416) ^ [_806060, _806062] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_806060)), _806062 = _806060, class_Groups_Oordered__cancel__ab__semigroup__add(_806062)], (1500 ^ _784416) ^ [_806185, _806187] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_806185)), _806187 = _806185, class_Groups_Oordered__ab__semigroup__add__imp__le(_806187)], (1510 ^ _784416) ^ [_806310, _806312] : [-(class_Rings_Olinordered__comm__semiring__strict(_806310)), _806312 = _806310, class_Rings_Olinordered__comm__semiring__strict(_806312)], (1520 ^ _784416) ^ [_806435, _806437] : [-(class_Groups_Olinordered__ab__semigroup__add(_806435)), _806437 = _806435, class_Groups_Olinordered__ab__semigroup__add(_806437)], (1530 ^ _784416) ^ [_806560, _806562] : [-(class_Rings_Olinordered__semiring__strict(_806560)), _806562 = _806560, class_Rings_Olinordered__semiring__strict(_806562)], (1540 ^ _784416) ^ [_806685, _806687] : [-(class_Groups_Oordered__ab__semigroup__add(_806685)), _806687 = _806685, class_Groups_Oordered__ab__semigroup__add(_806687)], (1550 ^ _784416) ^ [_806810, _806812] : [-(class_Groups_Oordered__comm__monoid__add(_806810)), _806812 = _806810, class_Groups_Oordered__comm__monoid__add(_806812)], (1560 ^ _784416) ^ [_806935, _806937] : [-(class_Groups_Ocancel__ab__semigroup__add(_806935)), _806937 = _806935, class_Groups_Ocancel__ab__semigroup__add(_806937)], (1570 ^ _784416) ^ [_807060, _807062] : [-(class_Rings_Oordered__cancel__semiring(_807060)), _807062 = _807060, class_Rings_Oordered__cancel__semiring(_807062)], (1580 ^ _784416) ^ [_807185, _807187] : [-(class_Rings_Oordered__comm__semiring(_807185)), _807187 = _807185, class_Rings_Oordered__comm__semiring(_807187)], (1590 ^ _784416) ^ [_807310, _807312] : [-(class_Groups_Ocancel__semigroup__add(_807310)), _807312 = _807310, class_Groups_Ocancel__semigroup__add(_807312)], (1600 ^ _784416) ^ [_807435, _807437] : [-(class_Rings_Olinordered__semiring(_807435)), _807437 = _807435, class_Rings_Olinordered__semiring(_807437)], (1610 ^ _784416) ^ [_807560, _807562] : [-(class_Rings_Olinordered__semidom(_807560)), _807562 = _807560, class_Rings_Olinordered__semidom(_807562)], (1620 ^ _784416) ^ [_807685, _807687] : [-(class_Groups_Oab__semigroup__mult(_807685)), _807687 = _807685, class_Groups_Oab__semigroup__mult(_807687)], (1630 ^ _784416) ^ [_807810, _807812] : [-(class_Groups_Ocomm__monoid__mult(_807810)), _807812 = _807810, class_Groups_Ocomm__monoid__mult(_807812)], (1640 ^ _784416) ^ [_807935, _807937] : [-(class_Groups_Oab__semigroup__add(_807935)), _807937 = _807935, class_Groups_Oab__semigroup__add(_807937)], (1650 ^ _784416) ^ [_808060, _808062] : [-(class_Rings_Oordered__semiring(_808060)), _808062 = _808060, class_Rings_Oordered__semiring(_808062)], (1660 ^ _784416) ^ [_808185, _808187] : [-(class_Rings_Ono__zero__divisors(_808185)), _808187 = _808185, class_Rings_Ono__zero__divisors(_808187)], (1670 ^ _784416) ^ [_808310, _808312] : [-(class_Groups_Ocomm__monoid__add(_808310)), _808312 = _808310, class_Groups_Ocomm__monoid__add(_808312)], (1680 ^ _784416) ^ [_808435, _808437] : [-(class_Rings_Ocomm__semiring__1(_808435)), _808437 = _808435, class_Rings_Ocomm__semiring__1(_808437)], (1690 ^ _784416) ^ [_808560, _808562] : [-(class_Groups_Osemigroup__add(_808560)), _808562 = _808560, class_Groups_Osemigroup__add(_808562)], (1700 ^ _784416) ^ [_808685, _808687] : [-(class_Divides_Osemiring__div(_808685)), _808687 = _808685, class_Divides_Osemiring__div(_808687)], (1710 ^ _784416) ^ [_808810, _808812] : [-(class_Rings_Ocomm__semiring(_808810)), _808812 = _808810, class_Rings_Ocomm__semiring(_808812)], (1720 ^ _784416) ^ [_808935, _808937] : [-(class_Nat_Osemiring__char__0(_808935)), _808937 = _808935, class_Nat_Osemiring__char__0(_808937)], (1730 ^ _784416) ^ [_809060, _809062] : [-(class_Rings_Ozero__neq__one(_809060)), _809062 = _809060, class_Rings_Ozero__neq__one(_809062)], (1740 ^ _784416) ^ [_809185, _809187] : [-(class_Orderings_Opreorder(_809185)), _809187 = _809185, class_Orderings_Opreorder(_809187)], (1750 ^ _784416) ^ [_809310, _809312] : [-(class_Orderings_Olinorder(_809310)), _809312 = _809310, class_Orderings_Olinorder(_809312)], (1760 ^ _784416) ^ [_809435, _809437] : [-(class_Groups_Omonoid__mult(_809435)), _809437 = _809435, class_Groups_Omonoid__mult(_809437)], (1770 ^ _784416) ^ [_809560, _809562] : [-(class_Groups_Omonoid__add(_809560)), _809562 = _809560, class_Groups_Omonoid__add(_809562)], (1780 ^ _784416) ^ [_809685, _809687] : [-(class_Rings_Osemiring__1(_809685)), _809687 = _809685, class_Rings_Osemiring__1(_809687)], (1790 ^ _784416) ^ [_809810, _809812] : [-(class_Rings_Osemiring__0(_809810)), _809812 = _809810, class_Rings_Osemiring__0(_809812)], (1800 ^ _784416) ^ [_809935, _809937] : [-(class_Rings_Omult__zero(_809935)), _809937 = _809935, class_Rings_Omult__zero(_809937)], (1810 ^ _784416) ^ [_810060, _810062] : [-(class_Orderings_Oorder(_810060)), _810062 = _810060, class_Orderings_Oorder(_810062)], (1820 ^ _784416) ^ [_810185, _810187] : [-(class_Rings_Osemiring(_810185)), _810187 = _810185, class_Rings_Osemiring(_810187)], (1830 ^ _784416) ^ [_810310, _810312] : [-(class_Orderings_Oord(_810310)), _810312 = _810310, class_Orderings_Oord(_810312)], (1840 ^ _784416) ^ [_810435, _810437] : [-(class_Groups_Ominus(_810435)), _810437 = _810435, class_Groups_Ominus(_810437)], (1850 ^ _784416) ^ [_810560, _810562] : [-(class_Power_Opower(_810560)), _810562 = _810560, class_Power_Opower(_810562)], (1860 ^ _784416) ^ [_810685, _810687] : [-(class_Groups_Ozero(_810685)), _810687 = _810685, class_Groups_Ozero(_810687)], (1870 ^ _784416) ^ [_810810, _810812] : [-(class_Int_Onumber(_810810)), _810812 = _810810, class_Int_Onumber(_810812)], (1880 ^ _784416) ^ [_810935, _810937] : [-(class_Groups_Oone(_810935)), _810937 = _810935, class_Groups_Oone(_810937)], (1890 ^ _784416) ^ [_811060, _811062] : [-(class_HOL_Oequal(_811060)), _811062 = _811060, class_HOL_Oequal(_811062)], (1900 ^ _784416) ^ [_811185, _811187] : [-(class_Nat_Osize(_811185)), _811187 = _811185, class_Nat_Osize(_811187)], (1910 ^ _784416) ^ [_811310, _811312] : [-(hBOOL(_811310)), _811312 = _811310, hBOOL(_811312)], (1920 ^ _784416) ^ [_811431, _811433, _811435, _811437, _811439, _811441] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_811439, _811435, _811431)), c_Hoare__Mirabelle_Ohoare__derivs(_811441, _811437, _811433), _811441 = _811439, _811437 = _811435, _811433 = _811431], (1938 ^ _784416) ^ [_812465, _812467, _812469, _812471] : [-(c_Enum_Oenum__the(_812471, _812467) = c_Enum_Oenum__the(_812469, _812465)), _812471 = _812469, _812467 = _812465], (1948 ^ _784416) ^ [_812614, _812616, _812618, _812620, _812622, _812624] : [-(c_Partial__Function_Oflat__lub(_812624, _812620, _812616) = c_Partial__Function_Oflat__lub(_812622, _812618, _812614)), _812624 = _812622, _812620 = _812618, _812616 = _812614], (1962 ^ _784416) ^ [_812835, _812837, _812839, _812841] : [-(c_Inductive_Ocomplete__lattice__class_Ogfp(_812841, _812837) = c_Inductive_Ocomplete__lattice__class_Ogfp(_812839, _812835)), _812841 = _812839, _812837 = _812835], (1972 ^ _784416) ^ [_812984, _812986, _812988, _812990, _812992, _812994, _812996, _812998, _813000, _813002] : [-(c_Fun_Ooverride__on(_813002, _812998, _812994, _812990, _812986) = c_Fun_Ooverride__on(_813000, _812996, _812992, _812988, _812984)), _813002 = _813000, _812998 = _812996, _812994 = _812992, _812990 = _812988, _812986 = _812984], (1994 ^ _784416) ^ [_813373, _813375, _813377, _813379, _813381, _813383, _813385, _813387] : [-(c_Fun_Othe__inv__into(_813387, _813383, _813379, _813375) = c_Fun_Othe__inv__into(_813385, _813381, _813377, _813373)), _813387 = _813385, _813383 = _813381, _813379 = _813377, _813375 = _813373], (2012 ^ _784416) ^ [_813674, _813676, _813678, _813680] : [-(c_Option_Oset(_813680, _813676) = c_Option_Oset(_813678, _813674)), _813680 = _813678, _813676 = _813674], (2022 ^ _784416) ^ [_813823, _813825, _813827, _813829, _813831, _813833, _813835, _813837, _813839, _813841] : [-(c_Option_Ooption_Ooption__rec(_813841, _813837, _813833, _813829, _813825) = c_Option_Ooption_Ooption__rec(_813839, _813835, _813831, _813827, _813823)), _813841 = _813839, _813837 = _813835, _813833 = _813831, _813829 = _813827, _813825 = _813823], (2044 ^ _784416) ^ [_814212, _814214, _814216, _814218, _814220, _814222] : [-(c_SetInterval_Oord_OatMost(_814222, _814218, _814214) = c_SetInterval_Oord_OatMost(_814220, _814216, _814212)), _814222 = _814220, _814218 = _814216, _814214 = _814212], (2058 ^ _784416) ^ [_814433, _814435, _814437, _814439, _814441, _814443] : [-(c_SetInterval_Oord_OatLeast(_814443, _814439, _814435) = c_SetInterval_Oord_OatLeast(_814441, _814437, _814433)), _814443 = _814441, _814439 = _814437, _814435 = _814433], (2072 ^ _784416) ^ [_814654, _814656, _814658, _814660, _814662, _814664] : [-(c_SetInterval_Oord_OlessThan(_814664, _814660, _814656) = c_SetInterval_Oord_OlessThan(_814662, _814658, _814654)), _814664 = _814662, _814660 = _814658, _814656 = _814654], (2086 ^ _784416) ^ [_814875, _814877, _814879, _814881, _814883, _814885] : [-(c_SetInterval_Oord_OgreaterThan(_814885, _814881, _814877) = c_SetInterval_Oord_OgreaterThan(_814883, _814879, _814875)), _814885 = _814883, _814881 = _814879, _814877 = _814875], (2100 ^ _784416) ^ [_815096, _815098, _815100, _815102, _815104, _815106, _815108, _815110] : [-(c_SetInterval_Oord_OatLeastAtMost(_815110, _815106, _815102, _815098) = c_SetInterval_Oord_OatLeastAtMost(_815108, _815104, _815100, _815096)), _815110 = _815108, _815106 = _815104, _815102 = _815100, _815098 = _815096], (2118 ^ _784416) ^ [_815397, _815399, _815401, _815403, _815405, _815407, _815409, _815411] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_815411, _815407, _815403, _815399) = c_SetInterval_Oord_OgreaterThanLessThan(_815409, _815405, _815401, _815397)), _815411 = _815409, _815407 = _815405, _815403 = _815401, _815399 = _815397], (2136 ^ _784416) ^ [_815698, _815700, _815702, _815704, _815706, _815708, _815710, _815712, _815714, _815716] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_815716, _815712, _815708, _815704, _815700) = c_SetInterval_Oord_OgreaterThanAtMost(_815714, _815710, _815706, _815702, _815698)), _815716 = _815714, _815712 = _815710, _815708 = _815706, _815704 = _815702, _815700 = _815698], (2158 ^ _784416) ^ [_816087, _816089, _816091, _816093, _816095, _816097, _816099, _816101, _816103, _816105] : [-(c_SetInterval_Oord_OatLeastLessThan(_816105, _816101, _816097, _816093, _816089) = c_SetInterval_Oord_OatLeastLessThan(_816103, _816099, _816095, _816091, _816087)), _816105 = _816103, _816101 = _816099, _816097 = _816095, _816093 = _816091, _816089 = _816087], (2180 ^ _784416) ^ [_816476, _816478, _816480, _816482, _816484, _816486] : [-(c_Finite__Set_Ofold1Set(_816486, _816482, _816478) = c_Finite__Set_Ofold1Set(_816484, _816480, _816476)), _816486 = _816484, _816482 = _816480, _816478 = _816476], (2194 ^ _784416) ^ [_816697, _816699, _816701, _816703] : [-(c_Orderings_Oord__class_OLeast(_816703, _816699) = c_Orderings_Oord__class_OLeast(_816701, _816697)), _816703 = _816701, _816699 = _816697], (2204 ^ _784416) ^ [_816846, _816848, _816850, _816852, _816854, _816856] : [-(c_Option_Ooption_Ooption__size(_816856, _816852, _816848) = c_Option_Ooption_Ooption__size(_816854, _816850, _816846)), _816856 = _816854, _816852 = _816850, _816848 = _816846], (2218 ^ _784416) ^ [_817067, _817069, _817071, _817073, _817075, _817077, _817079, _817081] : [-(c_Sum__Type_OPlus(_817081, _817077, _817073, _817069) = c_Sum__Type_OPlus(_817079, _817075, _817071, _817067)), _817081 = _817079, _817077 = _817075, _817073 = _817071, _817069 = _817067], (2236 ^ _784416) ^ [_817368, _817370, _817372, _817374, _817376, _817378] : [-(c_Power_Opower_Opower(_817378, _817374, _817370) = c_Power_Opower_Opower(_817376, _817372, _817368)), _817378 = _817376, _817374 = _817372, _817370 = _817368], (2250 ^ _784416) ^ [_817589, _817591] : [_817591 = _817589, -(c_Nat_Onat_Onat__size(_817591) = c_Nat_Onat_Onat__size(_817589))], (2256 ^ _784416) ^ [_817674, _817676, _817678, _817680] : [-(c_SMT_Oz3div(_817680, _817676) = c_SMT_Oz3div(_817678, _817674)), _817680 = _817678, _817676 = _817674], (2266 ^ _784416) ^ [_817823, _817825, _817827, _817829] : [-(c_SMT_Oz3mod(_817829, _817825) = c_SMT_Oz3mod(_817827, _817823)), _817829 = _817827, _817825 = _817823], (2276 ^ _784416) ^ [_817972, _817974, _817976, _817978, _817980, _817982, _817984, _817986, _817988, _817990] : [-(c_Product__Type_Oprod_Oprod__size(_817990, _817986, _817982, _817978, _817974) = c_Product__Type_Oprod_Oprod__size(_817988, _817984, _817980, _817976, _817972)), _817990 = _817988, _817986 = _817984, _817982 = _817980, _817978 = _817976, _817974 = _817972], (2298 ^ _784416) ^ [_818361, _818363, _818365, _818367] : [-(c_Divides_Odivmod__nat(_818367, _818363) = c_Divides_Odivmod__nat(_818365, _818361)), _818367 = _818365, _818363 = _818361], (2308 ^ _784416) ^ [_818510, _818512, _818514, _818516] : [-(c_Divides_Odivmod__nat__rel(_818516, _818512) = c_Divides_Odivmod__nat__rel(_818514, _818510)), _818516 = _818514, _818512 = _818510], (2318 ^ _784416) ^ [_818659, _818661, _818663, _818665] : [-(c_Divides_Odivmod__int__rel(_818665, _818661) = c_Divides_Odivmod__int__rel(_818663, _818659)), _818665 = _818663, _818661 = _818659], (2328 ^ _784416) ^ [_818808, _818810, _818812, _818814, _818816, _818818, _818820, _818822] : [-(c_Nitpick_Oprod(_818822, _818818, _818814, _818810) = c_Nitpick_Oprod(_818820, _818816, _818812, _818808)), _818822 = _818820, _818818 = _818816, _818814 = _818812, _818810 = _818808], (2346 ^ _784416) ^ [_819109, _819111, _819113, _819115, _819117, _819119, _819121, _819123, _819125, _819127] : [-(c_Product__Type_Oprod_Oprod__rec(_819127, _819123, _819119, _819115, _819111) = c_Product__Type_Oprod_Oprod__rec(_819125, _819121, _819117, _819113, _819109)), _819127 = _819125, _819123 = _819121, _819119 = _819117, _819115 = _819113, _819111 = _819109], (2368 ^ _784416) ^ [_819498, _819500, _819502, _819504] : [-(c_Inductive_Ocomplete__lattice__class_Olfp(_819504, _819500) = c_Inductive_Ocomplete__lattice__class_Olfp(_819502, _819498)), _819504 = _819502, _819500 = _819498], (2378 ^ _784416) ^ [_819647, _819649, _819651, _819653] : [-(c_FunDef_Orp__inv__image(_819653, _819649) = c_FunDef_Orp__inv__image(_819651, _819647)), _819653 = _819651, _819649 = _819647], (2388 ^ _784416) ^ [_819796, _819798, _819800, _819802] : [-(c_Int_Onat__aux(_819802, _819798) = c_Int_Onat__aux(_819800, _819796)), _819802 = _819800, _819798 = _819796], (2398 ^ _784416) ^ [_819945, _819947, _819949, _819951, _819953, _819955] : [-(c_Nat_Onat_Onat__rec(_819955, _819951, _819947) = c_Nat_Onat_Onat__rec(_819953, _819949, _819945)), _819955 = _819953, _819951 = _819949, _819947 = _819945], (2412 ^ _784416) ^ [_820166, _820168] : [_820168 = _820166, -(c_Int_Osucc(_820168) = c_Int_Osucc(_820166))], (2418 ^ _784416) ^ [_820251, _820253] : [_820253 = _820251, -(c_Divides_Oadjust(_820253) = c_Divides_Oadjust(_820251))], (2424 ^ _784416) ^ [_820336, _820338, _820340, _820342] : [-(c_Divides_OnegDivAlg(_820342, _820338) = c_Divides_OnegDivAlg(_820340, _820336)), _820342 = _820340, _820338 = _820336], (2434 ^ _784416) ^ [_820485, _820487] : [_820487 = _820485, -(c_Int_Oring__1__class_OInts(_820487) = c_Int_Oring__1__class_OInts(_820485))], (2440 ^ _784416) ^ [_820570, _820572, _820574, _820576] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_820576, _820572) = c_Code__Numeral_Odiv__mod__code__numeral(_820574, _820570)), _820576 = _820574, _820572 = _820570], (2450 ^ _784416) ^ [_820719, _820721, _820723, _820725, _820727, _820729, _820731, _820733] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_820733, _820729, _820725, _820721) = c_Nat_Osemiring__1__class_Oof__nat__aux(_820731, _820727, _820723, _820719)), _820733 = _820731, _820729 = _820727, _820725 = _820723, _820721 = _820719], (2468 ^ _784416) ^ [_821020, _821022, _821024, _821026] : [-(c_Nat__Transfer_Otsub(_821026, _821022) = c_Nat__Transfer_Otsub(_821024, _821020)), _821026 = _821024, _821022 = _821020], (2478 ^ _784416) ^ [_821169, _821171] : [_821171 = _821169, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_821171) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_821169))], (2484 ^ _784416) ^ [_821254, _821256, _821258, _821260] : [-(c_Set_Othe__elem(_821260, _821256) = c_Set_Othe__elem(_821258, _821254)), _821260 = _821258, _821256 = _821254], (2494 ^ _784416) ^ [_821403, _821405] : [_821405 = _821403, -(c_Nat_Osemiring__1__class_ONats(_821405) = c_Nat_Osemiring__1__class_ONats(_821403))], (2500 ^ _784416) ^ [_821488, _821490, _821492, _821494] : [-(c_Orderings_Oord_Omax(_821494, _821490) = c_Orderings_Oord_Omax(_821492, _821488)), _821494 = _821492, _821490 = _821488], (2510 ^ _784416) ^ [_821637, _821639, _821641, _821643] : [-(c_Orderings_Oord_Omin(_821643, _821639) = c_Orderings_Oord_Omin(_821641, _821637)), _821643 = _821641, _821639 = _821637], (2520 ^ _784416) ^ [_821786, _821788] : [_821788 = _821786, -(c_Int_Opred(_821788) = c_Int_Opred(_821786))], (2526 ^ _784416) ^ [_821871, _821873] : [_821873 = _821871, -(c_SetInterval_Oord__class_OatLeast(_821873) = c_SetInterval_Oord__class_OatLeast(_821871))], (2532 ^ _784416) ^ [_821956, _821958, _821960, _821962, _821964, _821966, _821968, _821970] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_821970, _821966, _821962, _821958) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_821968, _821964, _821960, _821956)), _821970 = _821968, _821966 = _821964, _821962 = _821960, _821958 = _821956], (2550 ^ _784416) ^ [_822257, _822259, _822261, _822263] : [-(c_Divides_Odivmod__int(_822263, _822259) = c_Divides_Odivmod__int(_822261, _822257)), _822263 = _822261, _822259 = _822257], (2560 ^ _784416) ^ [_822406, _822408, _822410, _822412] : [-(c_Groups_Osgn__class_Osgn(_822412, _822408) = c_Groups_Osgn__class_Osgn(_822410, _822406)), _822412 = _822410, _822408 = _822406], (2570 ^ _784416) ^ [_822555, _822557, _822559, _822561] : [-(c_Divides_Opdivmod(_822561, _822557) = c_Divides_Opdivmod(_822559, _822555)), _822561 = _822559, _822557 = _822555], (2580 ^ _784416) ^ [_822704, _822706, _822708, _822710] : [-(c_Divides_OposDivAlg(_822710, _822706) = c_Divides_OposDivAlg(_822708, _822704)), _822710 = _822708, _822706 = _822704], (2590 ^ _784416) ^ [_822853, _822855, _822857, _822859] : [-(c_Nitpick_Onat__gcd(_822859, _822855) = c_Nitpick_Onat__gcd(_822857, _822853)), _822859 = _822857, _822855 = _822853], (2600 ^ _784416) ^ [_823002, _823004, _823006, _823008] : [-(c_Nitpick_Onat__lcm(_823008, _823004) = c_Nitpick_Onat__lcm(_823006, _823002)), _823008 = _823006, _823004 = _823002], (2610 ^ _784416) ^ [_823151, _823153] : [_823153 = _823151, -(c_Wellfounded_Omeasure(_823153) = c_Wellfounded_Omeasure(_823151))], (2616 ^ _784416) ^ [_823236, _823238] : [_823238 = _823236, -(c_Wellfounded_Ofinite__psubset(_823238) = c_Wellfounded_Ofinite__psubset(_823236))], (2622 ^ _784416) ^ [_823321, _823323, _823325, _823327, _823329, _823331] : [-(c_Wellfounded_Omlex__prod(_823331, _823327, _823323) = c_Wellfounded_Omlex__prod(_823329, _823325, _823321)), _823331 = _823329, _823327 = _823325, _823323 = _823321], (2636 ^ _784416) ^ [_823542, _823544, _823546, _823548] : [-(c_Wellfounded_Omin__ext(_823548, _823544) = c_Wellfounded_Omin__ext(_823546, _823542)), _823548 = _823546, _823544 = _823542], (2646 ^ _784416) ^ [_823691, _823693] : [_823693 = _823691, -(c_Int_Oint__ge__less__than(_823693) = c_Int_Oint__ge__less__than(_823691))], (2652 ^ _784416) ^ [_823776, _823778] : [_823778 = _823776, -(c_Int_Oint__ge__less__than2(_823778) = c_Int_Oint__ge__less__than2(_823776))], (2658 ^ _784416) ^ [_823861, _823863, _823865, _823867, _823869, _823871, _823873, _823875] : [-(c_Recdef_Osame__fst(_823875, _823871, _823867, _823863) = c_Recdef_Osame__fst(_823873, _823869, _823865, _823861)), _823875 = _823873, _823871 = _823869, _823867 = _823865, _823863 = _823861], (2676 ^ _784416) ^ [_824162, _824164] : [_824164 = _824162, -(c_Nitpick_Ozero__frac(_824164) = c_Nitpick_Ozero__frac(_824162))], (2682 ^ _784416) ^ [_824247, _824249] : [_824249 = _824247, -(c_Nitpick_Oone__frac(_824249) = c_Nitpick_Oone__frac(_824247))], (2688 ^ _784416) ^ [_824332, _824334, _824336, _824338] : [-(c_Nitpick_Onumber__of__frac(_824338, _824334) = c_Nitpick_Onumber__of__frac(_824336, _824332)), _824338 = _824336, _824334 = _824332], (2698 ^ _784416) ^ [_824481, _824483, _824485, _824487] : [-(c_Nitpick_Onorm__frac(_824487, _824483) = c_Nitpick_Onorm__frac(_824485, _824481)), _824487 = _824485, _824483 = _824481], (2708 ^ _784416) ^ [_824630, _824632, _824634, _824636, _824638, _824640, _824642, _824644] : [-(c_Product__Type_Oapfst(_824644, _824640, _824636, _824632) = c_Product__Type_Oapfst(_824642, _824638, _824634, _824630)), _824644 = _824642, _824640 = _824638, _824636 = _824634, _824632 = _824630], (2726 ^ _784416) ^ [_824931, _824933, _824935, _824937, _824939, _824941, _824943, _824945] : [-(c_Product__Type_Oapsnd(_824945, _824941, _824937, _824933) = c_Product__Type_Oapsnd(_824943, _824939, _824935, _824931)), _824945 = _824943, _824941 = _824939, _824937 = _824935, _824933 = _824931], (2744 ^ _784416) ^ [_825232, _825234, _825236, _825238, _825240, _825242] : [-(c_FunDef_Oin__rel(_825242, _825238, _825234) = c_FunDef_Oin__rel(_825240, _825236, _825232)), _825242 = _825240, _825238 = _825236, _825234 = _825232], (2758 ^ _784416) ^ [_825453, _825455, _825457, _825459] : [-(c_Predicate_OPowp(_825459, _825455) = c_Predicate_OPowp(_825457, _825453)), _825459 = _825457, _825455 = _825453], (2768 ^ _784416) ^ [_825602, _825604, _825606, _825608, _825610, _825612] : [-(c_Predicate_ODomainP(_825612, _825608, _825604) = c_Predicate_ODomainP(_825610, _825606, _825602)), _825612 = _825610, _825608 = _825606, _825604 = _825602], (2782 ^ _784416) ^ [_825823, _825825, _825827, _825829, _825831, _825833] : [-(c_Predicate_ORangeP(_825833, _825829, _825825) = c_Predicate_ORangeP(_825831, _825827, _825823)), _825833 = _825831, _825829 = _825827, _825825 = _825823], (2796 ^ _784416) ^ [_826044, _826046, _826048, _826050, _826052, _826054, _826056, _826058] : [-(c_Hilbert__Choice_Oinv__into(_826058, _826054, _826050, _826046) = c_Hilbert__Choice_Oinv__into(_826056, _826052, _826048, _826044)), _826058 = _826056, _826054 = _826052, _826050 = _826048, _826046 = _826044], (2814 ^ _784416) ^ [_826345, _826347, _826349, _826351] : [-(c_Wellfounded_Omax__ext(_826351, _826347) = c_Wellfounded_Omax__ext(_826349, _826345)), _826351 = _826349, _826347 = _826345], (2824 ^ _784416) ^ [_826494, _826496, _826498, _826500, _826502, _826504, _826506, _826508] : [-(c_Random_Oiterate(_826508, _826504, _826500, _826496) = c_Random_Oiterate(_826506, _826502, _826498, _826494)), _826508 = _826506, _826504 = _826502, _826500 = _826498, _826496 = _826494], (2842 ^ _784416) ^ [_826795, _826797, _826799, _826801] : [-(c_Random_Olog(_826801, _826797) = c_Random_Olog(_826799, _826795)), _826801 = _826799, _826797 = _826795], (2852 ^ _784416) ^ [_826944, _826946, _826948, _826950, _826952, _826954] : [-(c_Random_Ominus__shift(_826954, _826950, _826946) = c_Random_Ominus__shift(_826952, _826948, _826944)), _826954 = _826952, _826950 = _826948, _826946 = _826944], (2866 ^ _784416) ^ [_827165, _827167, _827169, _827171] : [-(c_Random_Oinc__shift(_827171, _827167) = c_Random_Oinc__shift(_827169, _827165)), _827171 = _827169, _827167 = _827165], (2876 ^ _784416) ^ [_827314, _827316, _827318, _827320] : [-(c_Relation_OId__on(_827320, _827316) = c_Relation_OId__on(_827318, _827314)), _827320 = _827318, _827316 = _827314], (2886 ^ _784416) ^ [_827463, _827465] : [_827465 = _827463, -(c_Nat_Ofunpow(_827465) = c_Nat_Ofunpow(_827463))], (2892 ^ _784416) ^ [_827548, _827550, _827552, _827554] : [-(c_Transitive__Closure_Otrancl(_827554, _827550) = c_Transitive__Closure_Otrancl(_827552, _827548)), _827554 = _827552, _827550 = _827548], (2902 ^ _784416) ^ [_827697, _827699] : [_827699 = _827697, -(c_Relation_OId(_827699) = c_Relation_OId(_827697))], (2908 ^ _784416) ^ [_827782, _827784, _827786, _827788, _827790, _827792] : [-(c_Finite__Set_Ofold__image(_827792, _827788, _827784) = c_Finite__Set_Ofold__image(_827790, _827786, _827782)), _827792 = _827790, _827788 = _827786, _827784 = _827782], (2922 ^ _784416) ^ [_828003, _828005] : [_828005 = _828003, -(c_Set_OBall(_828005) = c_Set_OBall(_828003))], (2928 ^ _784416) ^ [_828088, _828090] : [_828090 = _828088, -(c_SetInterval_Oord__class_OgreaterThan(_828090) = c_SetInterval_Oord__class_OgreaterThan(_828088))], (2934 ^ _784416) ^ [_828173, _828175] : [_828175 = _828173, -(c_Relation_OField(_828175) = c_Relation_OField(_828173))], (2940 ^ _784416) ^ [_828258, _828260, _828262, _828264] : [-(c_Relation_ODomain(_828264, _828260) = c_Relation_ODomain(_828262, _828258)), _828264 = _828262, _828260 = _828258], (2950 ^ _784416) ^ [_828407, _828409, _828411, _828413] : [-(c_Relation_ORange(_828413, _828409) = c_Relation_ORange(_828411, _828407)), _828413 = _828411, _828409 = _828407], (2960 ^ _784416) ^ [_828556, _828558, _828560, _828562, _828564, _828566] : [-(c_Set_Ovimage(_828566, _828562, _828558) = c_Set_Ovimage(_828564, _828560, _828556)), _828566 = _828564, _828562 = _828560, _828558 = _828556], (2974 ^ _784416) ^ [_828777, _828779] : [_828779 = _828777, -(c_Equiv__Relations_Oquotient(_828779) = c_Equiv__Relations_Oquotient(_828777))], (2980 ^ _784416) ^ [_828862, _828864] : [_828864 = _828862, -(c_HOL_OAll(_828864) = c_HOL_OAll(_828862))], (2986 ^ _784416) ^ [_828947, _828949, _828951, _828953, _828955, _828957, _828959, _828961, _828963, _828965] : [-(c_Finite__Set_Ofold__graph(_828965, _828961, _828957, _828953, _828949) = c_Finite__Set_Ofold__graph(_828963, _828959, _828955, _828951, _828947)), _828965 = _828963, _828961 = _828959, _828957 = _828955, _828953 = _828951, _828949 = _828947], (3008 ^ _784416) ^ [_829336, _829338, _829340, _829342, _829344, _829346] : [-(c_Relation_Orel__comp(_829346, _829342, _829338) = c_Relation_Orel__comp(_829344, _829340, _829336)), _829346 = _829344, _829342 = _829340, _829338 = _829336], (3022 ^ _784416) ^ [_829557, _829559, _829561, _829563, _829565, _829567] : [-(c_Smallcheck_Oorelse(_829567, _829563, _829559) = c_Smallcheck_Oorelse(_829565, _829561, _829557)), _829567 = _829565, _829563 = _829561, _829559 = _829557], (3036 ^ _784416) ^ [_829778, _829780, _829782, _829784, _829786, _829788] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(_829788, _829784, _829780) = c_Smallcheck_Ofull__small__class_Ofull__small(_829786, _829782, _829778)), _829788 = _829786, _829784 = _829782, _829780 = _829778], (3050 ^ _784416) ^ [_829999, _830001, _830003, _830005, _830007, _830009] : [-(c_Smallcheck_Ofull__small_H(_830009, _830005, _830001) = c_Smallcheck_Ofull__small_H(_830007, _830003, _829999)), _830009 = _830007, _830005 = _830003, _830001 = _829999], (3064 ^ _784416) ^ [_830220, _830222, _830224, _830226, _830228, _830230] : [-(c_Smallcheck_Osmall_H(_830230, _830226, _830222) = c_Smallcheck_Osmall_H(_830228, _830224, _830220)), _830230 = _830228, _830226 = _830224, _830222 = _830220], (3078 ^ _784416) ^ [_830441, _830443] : [_830443 = _830441, -(c_Smallcheck_Osmall__class_Osmall(_830443) = c_Smallcheck_Osmall__class_Osmall(_830441))], (3084 ^ _784416) ^ [_830526, _830528, _830530, _830532, _830534, _830536, _830538, _830540, _830542, _830544, _830546, _830548] : [-(c_Map_Omap__comp(_830548, _830544, _830540, _830536, _830532, _830528) = c_Map_Omap__comp(_830546, _830542, _830538, _830534, _830530, _830526)), _830548 = _830546, _830544 = _830542, _830540 = _830538, _830536 = _830534, _830532 = _830530, _830528 = _830526], (3110 ^ _784416) ^ [_831011, _831013] : [_831013 = _831011, -(c_Set_OPow(_831013) = c_Set_OPow(_831011))], (3116 ^ _784416) ^ [_831096, _831098, _831100, _831102, _831104, _831106] : [-(c_Map_Oran(_831106, _831102, _831098) = c_Map_Oran(_831104, _831100, _831096)), _831106 = _831104, _831102 = _831100, _831098 = _831096], (3130 ^ _784416) ^ [_831317, _831319, _831321, _831323, _831325, _831327, _831329, _831331] : [-(c_Nitpick_Osetsum_H(_831331, _831327, _831323, _831319) = c_Nitpick_Osetsum_H(_831329, _831325, _831321, _831317)), _831331 = _831329, _831327 = _831325, _831323 = _831321, _831319 = _831317], (3148 ^ _784416) ^ [_831618, _831620, _831622, _831624, _831626, _831628, _831630, _831632, _831634, _831636, _831638, _831640] : [-(c_Product__Type_Omap__pair(_831640, _831636, _831632, _831628, _831624, _831620) = c_Product__Type_Omap__pair(_831638, _831634, _831630, _831626, _831622, _831618)), _831640 = _831638, _831636 = _831634, _831632 = _831630, _831628 = _831626, _831624 = _831622, _831620 = _831618], (3174 ^ _784416) ^ [_832103, _832105, _832107, _832109] : [-(c_List_Olexn(_832109, _832105) = c_List_Olexn(_832107, _832103)), _832109 = _832107, _832105 = _832103], (3184 ^ _784416) ^ [_832252, _832254, _832256, _832258] : [-(c_List_Olenlex(_832258, _832254) = c_List_Olenlex(_832256, _832252)), _832258 = _832256, _832254 = _832252], (3194 ^ _784416) ^ [_832401, _832403, _832405, _832407, _832409, _832411, _832413, _832415] : [-(c_Wellfounded_Olex__prod(_832415, _832411, _832407, _832403) = c_Wellfounded_Olex__prod(_832413, _832409, _832405, _832401)), _832415 = _832413, _832411 = _832409, _832407 = _832405, _832403 = _832401], (3212 ^ _784416) ^ [_832702, _832704, _832706, _832708] : [-(c_Hilbert__Choice_OEps(_832708, _832704) = c_Hilbert__Choice_OEps(_832706, _832702)), _832708 = _832706, _832704 = _832702], (3222 ^ _784416) ^ [_832851, _832853, _832855, _832857] : [-(c_Nitpick_Ocard_H(_832857, _832853) = c_Nitpick_Ocard_H(_832855, _832851)), _832857 = _832855, _832853 = _832851], (3232 ^ _784416) ^ [_833000, _833002] : [_833002 = _833000, -(c_Power_Opower__class_Opower(_833002) = c_Power_Opower__class_Opower(_833000))], (3238 ^ _784416) ^ [_833085, _833087, _833089, _833091] : [-(c_Transitive__Closure_Ortrancl(_833091, _833087) = c_Transitive__Closure_Ortrancl(_833089, _833085)), _833091 = _833089, _833087 = _833085], (3248 ^ _784416) ^ [_833234, _833236] : [_833236 = _833234, -(c_Enum_Oenum__class_Oenum__ex(_833236) = c_Enum_Oenum__class_Oenum__ex(_833234))], (3254 ^ _784416) ^ [_833319, _833321] : [_833321 = _833319, -(c_Enum_Oenum__class_Oenum__all(_833321) = c_Enum_Oenum__class_Oenum__all(_833319))], (3260 ^ _784416) ^ [_833404, _833406, _833408, _833410] : [-(c_Product__Type_OSigma(_833410, _833406) = c_Product__Type_OSigma(_833408, _833404)), _833410 = _833408, _833406 = _833404], (3270 ^ _784416) ^ [_833553, _833555] : [_833555 = _833553, -(c_HOL_OEx(_833555) = c_HOL_OEx(_833553))], (3276 ^ _784416) ^ [_833638, _833640, _833642, _833644] : [-(c_Wellfounded_Oacc(_833644, _833640) = c_Wellfounded_Oacc(_833642, _833638)), _833644 = _833642, _833640 = _833638], (3286 ^ _784416) ^ [_833787, _833789, _833791, _833793, _833795, _833797, _833799, _833801] : [-(c_Map_Orestrict__map(_833801, _833797, _833793, _833789) = c_Map_Orestrict__map(_833799, _833795, _833791, _833787)), _833801 = _833799, _833797 = _833795, _833793 = _833791, _833789 = _833787], (3304 ^ _784416) ^ [_834088, _834090, _834092, _834094, _834096, _834098] : [-(c_Map_Odom(_834098, _834094, _834090) = c_Map_Odom(_834096, _834092, _834088)), _834098 = _834096, _834094 = _834092, _834090 = _834088], (3318 ^ _784416) ^ [_834309, _834311] : [_834311 = _834309, -(c_Random_Orange(_834311) = c_Random_Orange(_834309))], (3324 ^ _784416) ^ [_834394, _834396, _834398, _834400] : [-(c_Code__Numeral_Onat__of__aux(_834400, _834396) = c_Code__Numeral_Onat__of__aux(_834398, _834394)), _834400 = _834398, _834396 = _834394], (3334 ^ _784416) ^ [_834543, _834545, _834547, _834549] : [-(c_Random_Oselect(_834549, _834545) = c_Random_Oselect(_834547, _834543)), _834549 = _834547, _834545 = _834543], (3344 ^ _784416) ^ [_834692, _834694, _834696, _834698, _834700, _834702] : [-(c_Relation_OImage(_834702, _834698, _834694) = c_Relation_OImage(_834700, _834696, _834692)), _834702 = _834700, _834698 = _834696, _834694 = _834692], (3358 ^ _784416) ^ [_834913, _834915, _834917, _834919] : [-(c_List_Olistrel(_834919, _834915) = c_List_Olistrel(_834917, _834913)), _834919 = _834917, _834915 = _834913], (3368 ^ _784416) ^ [_835062, _835064, _835066, _835068, _835070, _835072] : [-(c_List_Oset__Cons(_835072, _835068, _835064) = c_List_Oset__Cons(_835070, _835066, _835062)), _835072 = _835070, _835068 = _835066, _835064 = _835062], (3382 ^ _784416) ^ [_835283, _835285, _835287, _835289] : [-(c_List_Olistset(_835289, _835285) = c_List_Olistset(_835287, _835283)), _835289 = _835287, _835285 = _835283], (3392 ^ _784416) ^ [_835432, _835434, _835436, _835438] : [-(c_Enum_Osublists(_835438, _835434) = c_Enum_Osublists(_835436, _835432)), _835438 = _835436, _835434 = _835432], (3402 ^ _784416) ^ [_835581, _835583, _835585, _835587, _835589, _835591, _835593, _835595] : [-(c_Enum_Oproduct(_835595, _835591, _835587, _835583) = c_Enum_Oproduct(_835593, _835589, _835585, _835581)), _835595 = _835593, _835591 = _835589, _835587 = _835585, _835583 = _835581], (3420 ^ _784416) ^ [_835882, _835884, _835886, _835888] : [-(c_List_Olistrel1(_835888, _835884) = c_List_Olistrel1(_835886, _835882)), _835888 = _835886, _835884 = _835882], (3430 ^ _784416) ^ [_836031, _836033, _836035, _836037, _836039, _836041, _836043, _836045] : [-(c_Nat_Onat_Onat__case(_836045, _836041, _836037, _836033) = c_Nat_Onat_Onat__case(_836043, _836039, _836035, _836031)), _836045 = _836043, _836041 = _836039, _836037 = _836035, _836033 = _836031], (3448 ^ _784416) ^ [_836332, _836334, _836336, _836338] : [-(c_Nat_Ocompow(_836338, _836334) = c_Nat_Ocompow(_836336, _836332)), _836338 = _836336, _836334 = _836332], (3458 ^ _784416) ^ [_836481, _836483] : [_836483 = _836481, -(c_List_Orotate1(_836483) = c_List_Orotate1(_836481))], (3464 ^ _784416) ^ [_836566, _836568] : [_836568 = _836566, -(c_Fun_Oid(_836568) = c_Fun_Oid(_836566))], (3470 ^ _784416) ^ [_836651, _836653, _836655, _836657] : [-(c_Finite__Set_Ofold1(_836657, _836653) = c_Finite__Set_Ofold1(_836655, _836651)), _836657 = _836655, _836653 = _836651], (3480 ^ _784416) ^ [_836800, _836802, _836804, _836806] : [-(c_Complete__Lattice_OInf__class_OInf(_836806, _836802) = c_Complete__Lattice_OInf__class_OInf(_836804, _836800)), _836806 = _836804, _836802 = _836800], (3490 ^ _784416) ^ [_836949, _836951, _836953, _836955] : [-(c_Big__Operators_Olattice__class_OSup__fin(_836955, _836951) = c_Big__Operators_Olattice__class_OSup__fin(_836953, _836949)), _836955 = _836953, _836951 = _836949], (3500 ^ _784416) ^ [_837098, _837100, _837102, _837104] : [-(c_Big__Operators_Olattice__class_OInf__fin(_837104, _837100) = c_Big__Operators_Olattice__class_OInf__fin(_837102, _837098)), _837104 = _837102, _837100 = _837098], (3510 ^ _784416) ^ [_837247, _837249, _837251, _837253] : [-(c_Big__Operators_Olinorder__class_OMin(_837253, _837249) = c_Big__Operators_Olinorder__class_OMin(_837251, _837247)), _837253 = _837251, _837249 = _837247], (3520 ^ _784416) ^ [_837396, _837398, _837400, _837402] : [-(c_Big__Operators_Olinorder__class_OMax(_837402, _837398) = c_Big__Operators_Olinorder__class_OMax(_837400, _837396)), _837402 = _837400, _837398 = _837396], (3530 ^ _784416) ^ [_837545, _837547, _837549, _837551, _837553, _837555] : [-(c_Big__Operators_Olattice_OInf__fin(_837555, _837551, _837547) = c_Big__Operators_Olattice_OInf__fin(_837553, _837549, _837545)), _837555 = _837553, _837551 = _837549, _837547 = _837545], (3544 ^ _784416) ^ [_837766, _837768, _837770, _837772, _837774, _837776] : [-(c_Big__Operators_Olattice_OSup__fin(_837776, _837772, _837768) = c_Big__Operators_Olattice_OSup__fin(_837774, _837770, _837766)), _837776 = _837774, _837772 = _837770, _837768 = _837766], (3558 ^ _784416) ^ [_837987, _837989, _837991, _837993] : [-(c_Fun_Ofun__upd(_837993, _837989) = c_Fun_Ofun__upd(_837991, _837987)), _837993 = _837991, _837989 = _837987], (3568 ^ _784416) ^ [_838136, _838138] : [_838138 = _838136, -(c_Lazy__Sequence_Ohb__not__seq(_838138) = c_Lazy__Sequence_Ohb__not__seq(_838136))], (3574 ^ _784416) ^ [_838221, _838223, _838225, _838227] : [-(c_List_Olexord(_838227, _838223) = c_List_Olexord(_838225, _838221)), _838227 = _838225, _838223 = _838221], (3584 ^ _784416) ^ [_838370, _838372, _838374, _838376, _838378, _838380] : [-(c_List_Olist_Olist__size(_838380, _838376, _838372) = c_List_Olist_Olist__size(_838378, _838374, _838370)), _838380 = _838378, _838376 = _838374, _838372 = _838370], (3598 ^ _784416) ^ [_838591, _838593] : [_838593 = _838591, -(c_Option_Othe(_838593) = c_Option_Othe(_838591))], (3604 ^ _784416) ^ [_838676, _838678, _838680, _838682] : [-(c_Random_Opick(_838682, _838678) = c_Random_Opick(_838680, _838676)), _838682 = _838680, _838678 = _838676], (3614 ^ _784416) ^ [_838825, _838827, _838829, _838831] : [-(c_Random_Oselect__weight(_838831, _838827) = c_Random_Oselect__weight(_838829, _838825)), _838831 = _838829, _838827 = _838825], (3624 ^ _784416) ^ [_838974, _838976, _838978, _838980, _838982, _838984] : [-(c_Enum_On__lists(_838984, _838980, _838976) = c_Enum_On__lists(_838982, _838978, _838974)), _838984 = _838982, _838980 = _838978, _838976 = _838974], (3638 ^ _784416) ^ [_839195, _839197] : [_839197 = _839195, -(c_List_Otranspose__rel(_839197) = c_List_Otranspose__rel(_839195))], (3644 ^ _784416) ^ [_839280, _839282, _839284, _839286, _839288, _839290, _839292, _839294] : [-(c_List_Olist_Olist__case(_839294, _839290, _839286, _839282) = c_List_Olist_Olist__case(_839292, _839288, _839284, _839280)), _839294 = _839292, _839290 = _839288, _839286 = _839284, _839282 = _839280], (3662 ^ _784416) ^ [_839581, _839583, _839585, _839587, _839589, _839591, _839593, _839595] : [-(c_List_Omap__filter(_839595, _839591, _839587, _839583) = c_List_Omap__filter(_839593, _839589, _839585, _839581)), _839595 = _839593, _839591 = _839589, _839587 = _839585, _839583 = _839581], (3680 ^ _784416) ^ [_839882, _839884, _839886, _839888, _839890, _839892] : [-(c_List_Osublist(_839892, _839888, _839884) = c_List_Osublist(_839890, _839886, _839882)), _839892 = _839890, _839888 = _839886, _839884 = _839882], (3694 ^ _784416) ^ [_840103, _840105] : [_840105 = _840103, -(c_SetInterval_Oord__class_OlessThan(_840105) = c_SetInterval_Oord__class_OlessThan(_840103))], (3700 ^ _784416) ^ [_840188, _840190, _840192, _840194, _840196, _840198] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_840198, _840194, _840190) = c_SetInterval_Oord__class_OgreaterThanAtMost(_840196, _840192, _840188)), _840198 = _840196, _840194 = _840192, _840190 = _840188], (3714 ^ _784416) ^ [_840409, _840411, _840413, _840415, _840417, _840419] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_840419, _840415, _840411) = c_SetInterval_Oord__class_OgreaterThanLessThan(_840417, _840413, _840409)), _840419 = _840417, _840415 = _840413, _840411 = _840409], (3728 ^ _784416) ^ [_840630, _840632] : [_840632 = _840630, -(c_SetInterval_Oord__class_OatMost(_840632) = c_SetInterval_Oord__class_OatMost(_840630))], (3734 ^ _784416) ^ [_840715, _840717] : [_840717 = _840715, -(c_Finite__Set_Ocard(_840717) = c_Finite__Set_Ocard(_840715))], (3740 ^ _784416) ^ [_840800, _840802, _840804, _840806, _840808, _840810] : [-(c_Finite__Set_Ofold(_840810, _840806, _840802) = c_Finite__Set_Ofold(_840808, _840804, _840800)), _840810 = _840808, _840806 = _840804, _840802 = _840800], (3754 ^ _784416) ^ [_841021, _841023] : [_841023 = _841021, -(c_List_Oreturn__list(_841023) = c_List_Oreturn__list(_841021))], (3760 ^ _784416) ^ [_841106, _841108] : [_841108 = _841106, -(c_List_Oembed__list(_841108) = c_List_Oembed__list(_841106))], (3766 ^ _784416) ^ [_841191, _841193, _841195, _841197] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_841197, _841193) = c_SetInterval_Oord__class_OatLeastLessThan(_841195, _841191)), _841197 = _841195, _841193 = _841191], (3776 ^ _784416) ^ [_841340, _841342, _841344, _841346, _841348, _841350] : [-(c_List_Opartition(_841350, _841346, _841342) = c_List_Opartition(_841348, _841344, _841340)), _841350 = _841348, _841346 = _841344, _841342 = _841340], (3790 ^ _784416) ^ [_841561, _841563, _841565, _841567, _841569, _841571, _841573, _841575] : [-(c_List_Olinorder__class_Osort__key(_841575, _841571, _841567, _841563) = c_List_Olinorder__class_Osort__key(_841573, _841569, _841565, _841561)), _841575 = _841573, _841571 = _841569, _841567 = _841565, _841563 = _841561], (3808 ^ _784416) ^ [_841862, _841864, _841866, _841868] : [-(c_List_Olinorder__class_Osorted__list__of__set(_841868, _841864) = c_List_Olinorder__class_Osorted__list__of__set(_841866, _841862)), _841868 = _841866, _841864 = _841862], (3818 ^ _784416) ^ [_842011, _842013, _842015, _842017, _842019, _842021] : [-(c_Set_Oimage(_842021, _842017, _842013) = c_Set_Oimage(_842019, _842015, _842011)), _842021 = _842019, _842017 = _842015, _842013 = _842011], (3832 ^ _784416) ^ [_842232, _842234, _842236, _842238, _842240, _842242, _842244, _842246, _842248, _842250] : [-(c_List_Olinorder__class_Oinsort__insert__key(_842250, _842246, _842242, _842238, _842234) = c_List_Olinorder__class_Oinsort__insert__key(_842248, _842244, _842240, _842236, _842232)), _842250 = _842248, _842246 = _842244, _842242 = _842240, _842238 = _842236, _842234 = _842232], (3854 ^ _784416) ^ [_842621, _842623] : [_842623 = _842621, -(c_List_Omonoid__add__class_Olistsum(_842623) = c_List_Omonoid__add__class_Olistsum(_842621))], (3860 ^ _784416) ^ [_842706, _842708, _842710, _842712] : [-(c_List_Orotate(_842712, _842708) = c_List_Orotate(_842710, _842706)), _842712 = _842710, _842708 = _842706], (3870 ^ _784416) ^ [_842855, _842857, _842859, _842861, _842863, _842865] : [-(c_Divides_Odiv__class_Omod(_842865, _842861, _842857) = c_Divides_Odiv__class_Omod(_842863, _842859, _842855)), _842865 = _842863, _842861 = _842859, _842857 = _842855], (3884 ^ _784416) ^ [_843076, _843078, _843080, _843082, _843084, _843086, _843088, _843090, _843092, _843094] : [-(c_List_Ofoldr(_843094, _843090, _843086, _843082, _843078) = c_List_Ofoldr(_843092, _843088, _843084, _843080, _843076)), _843094 = _843092, _843090 = _843088, _843086 = _843084, _843082 = _843080, _843078 = _843076], (3906 ^ _784416) ^ [_843465, _843467] : [_843467 = _843465, -(c_Orderings_Oord__class_Omax(_843467) = c_Orderings_Oord__class_Omax(_843465))], (3912 ^ _784416) ^ [_843550, _843552, _843554, _843556] : [-(c_List_Otranspose(_843556, _843552) = c_List_Otranspose(_843554, _843550)), _843556 = _843554, _843552 = _843550], (3922 ^ _784416) ^ [_843699, _843701, _843703, _843705, _843707, _843709, _843711, _843713, _843715, _843717] : [-(c_Map_Omap__upds(_843717, _843713, _843709, _843705, _843701) = c_Map_Omap__upds(_843715, _843711, _843707, _843703, _843699)), _843717 = _843715, _843713 = _843711, _843709 = _843707, _843705 = _843703, _843701 = _843699], (3944 ^ _784416) ^ [_844088, _844090, _844092, _844094, _844096, _844098, _844100, _844102] : [-(c_Map_Omap__add(_844102, _844098, _844094, _844090) = c_Map_Omap__add(_844100, _844096, _844092, _844088)), _844102 = _844100, _844098 = _844096, _844094 = _844092, _844090 = _844088], (3962 ^ _784416) ^ [_844389, _844391, _844393, _844395] : [-(c_List_Obutlast(_844395, _844391) = c_List_Obutlast(_844393, _844389)), _844395 = _844393, _844391 = _844389], (3972 ^ _784416) ^ [_844538, _844540, _844542, _844544] : [-(c_List_Olistsp(_844544, _844540) = c_List_Olistsp(_844542, _844538)), _844544 = _844542, _844540 = _844538], (3982 ^ _784416) ^ [_844687, _844689, _844691, _844693] : [-(c_List_Olists(_844693, _844689) = c_List_Olists(_844691, _844687)), _844693 = _844691, _844689 = _844687], (3992 ^ _784416) ^ [_844836, _844838, _844840, _844842] : [-(c_List_Olist__update(_844842, _844838) = c_List_Olist__update(_844840, _844836)), _844842 = _844840, _844838 = _844836], (4002 ^ _784416) ^ [_844985, _844987, _844989, _844991] : [-(c_List_Oremdups(_844991, _844987) = c_List_Oremdups(_844989, _844985)), _844991 = _844989, _844987 = _844985], (4012 ^ _784416) ^ [_845134, _845136, _845138, _845140, _845142, _845144] : [-(c_List_Oremove1(_845144, _845140, _845136) = c_List_Oremove1(_845142, _845138, _845134)), _845144 = _845142, _845140 = _845138, _845136 = _845134], (4026 ^ _784416) ^ [_845355, _845357] : [_845357 = _845355, -(c_Orderings_Otop__class_Otop(_845357) = c_Orderings_Otop__class_Otop(_845355))], (4032 ^ _784416) ^ [_845440, _845442, _845444, _845446] : [-(c_List_OremoveAll(_845446, _845442) = c_List_OremoveAll(_845444, _845440)), _845446 = _845444, _845442 = _845440], (4042 ^ _784416) ^ [_845589, _845591, _845593, _845595, _845597, _845599] : [-(c_List_Oinsert(_845599, _845595, _845591) = c_List_Oinsert(_845597, _845593, _845589)), _845599 = _845597, _845595 = _845593, _845591 = _845589], (4056 ^ _784416) ^ [_845810, _845812, _845814, _845816, _845818, _845820, _845822, _845824] : [-(c_List_Omaps(_845824, _845820, _845816, _845812) = c_List_Omaps(_845822, _845818, _845814, _845810)), _845824 = _845822, _845820 = _845818, _845816 = _845814, _845812 = _845810], (4074 ^ _784416) ^ [_846111, _846113, _846115, _846117] : [-(c_Relation_Oinv__image(_846117, _846113) = c_Relation_Oinv__image(_846115, _846111)), _846117 = _846115, _846113 = _846111], (4084 ^ _784416) ^ [_846260, _846262, _846264, _846266] : [-(c_List_Olex(_846266, _846262) = c_List_Olex(_846264, _846260)), _846266 = _846264, _846262 = _846260], (4094 ^ _784416) ^ [_846409, _846411, _846413, _846415] : [-(c_List_Omeasures(_846415, _846411) = c_List_Omeasures(_846413, _846409)), _846415 = _846413, _846411 = _846409], (4104 ^ _784416) ^ [_846558, _846560, _846562, _846564, _846566, _846568, _846570, _846572] : [-(c_List_Ofoldl(_846572, _846568, _846564, _846560) = c_List_Ofoldl(_846570, _846566, _846562, _846558)), _846572 = _846570, _846568 = _846566, _846564 = _846562, _846560 = _846558], (4122 ^ _784416) ^ [_846859, _846861, _846863, _846865] : [-(c_Map_Omap__of(_846865, _846861) = c_Map_Omap__of(_846863, _846859)), _846865 = _846863, _846861 = _846859], (4132 ^ _784416) ^ [_847008, _847010, _847012, _847014, _847016, _847018, _847020, _847022] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_847022, _847018, _847014, _847010) = c_New__Random__Sequence_Opos__not__random__dseq(_847020, _847016, _847012, _847008)), _847022 = _847020, _847018 = _847016, _847014 = _847012, _847010 = _847008], (4150 ^ _784416) ^ [_847309, _847311] : [_847311 = _847309, -(c_New__DSequence_Opos__not__seq(_847311) = c_New__DSequence_Opos__not__seq(_847309))], (4156 ^ _784416) ^ [_847394, _847396, _847398, _847400, _847402, _847404] : [-(c_List_OdropWhile(_847404, _847400, _847396) = c_List_OdropWhile(_847402, _847398, _847394)), _847404 = _847402, _847400 = _847398, _847396 = _847394], (4170 ^ _784416) ^ [_847615, _847617] : [_847617 = _847615, -(c_List_Odistinct(_847617) = c_List_Odistinct(_847615))], (4176 ^ _784416) ^ [_847700, _847702, _847704, _847706, _847708, _847710] : [-(c_List_OtakeWhile(_847710, _847706, _847702) = c_List_OtakeWhile(_847708, _847704, _847700)), _847710 = _847708, _847706 = _847704, _847702 = _847700], (4190 ^ _784416) ^ [_847921, _847923, _847925, _847927, _847929, _847931] : [-(c_List_Olinorder__class_Oinsort__key(_847931, _847927, _847923) = c_List_Olinorder__class_Oinsort__key(_847929, _847925, _847921)), _847931 = _847929, _847927 = _847925, _847923 = _847921], (4204 ^ _784416) ^ [_848142, _848144, _848146, _848148] : [-(c_HOL_OLet(_848148, _848144) = c_HOL_OLet(_848146, _848142)), _848148 = _848146, _848144 = _848142], (4214 ^ _784416) ^ [_848291, _848293, _848295, _848297] : [-(c_Nitpick_Oint__lcm(_848297, _848293) = c_Nitpick_Oint__lcm(_848295, _848291)), _848297 = _848295, _848293 = _848291], (4224 ^ _784416) ^ [_848440, _848442] : [_848442 = _848440, -(c_Divides_Odiv__class_Odiv(_848442) = c_Divides_Odiv__class_Odiv(_848440))], (4230 ^ _784416) ^ [_848525, _848527, _848529, _848531, _848533, _848535] : [-(c_Nitpick_Otimes__frac(_848535, _848531, _848527) = c_Nitpick_Otimes__frac(_848533, _848529, _848525)), _848535 = _848533, _848531 = _848529, _848527 = _848525], (4244 ^ _784416) ^ [_848746, _848748] : [_848748 = _848746, -(c_Groups_Otimes__class_Otimes(_848748) = c_Groups_Otimes__class_Otimes(_848746))], (4250 ^ _784416) ^ [_848831, _848833, _848835, _848837, _848839, _848841] : [-(c_Nitpick_Oof__frac(_848841, _848837, _848833) = c_Nitpick_Oof__frac(_848839, _848835, _848831)), _848841 = _848839, _848837 = _848835, _848833 = _848831], (4264 ^ _784416) ^ [_849052, _849054] : [_849054 = _849052, -(c_Rings_Oinverse__class_Odivide(_849054) = c_Rings_Oinverse__class_Odivide(_849052))], (4270 ^ _784416) ^ [_849137, _849139] : [_849139 = _849137, -(c_Int_Oring__1__class_Oof__int(_849139) = c_Int_Oring__1__class_Oof__int(_849137))], (4276 ^ _784416) ^ [_849222, _849224, _849226, _849228] : [-(c_Nitpick_Oinverse__frac(_849228, _849224) = c_Nitpick_Oinverse__frac(_849226, _849222)), _849228 = _849226, _849224 = _849222], (4286 ^ _784416) ^ [_849371, _849373] : [_849373 = _849371, -(c_Nitpick_Ofrac(_849373) = c_Nitpick_Ofrac(_849371))], (4292 ^ _784416) ^ [_849456, _849458, _849460, _849462] : [-(c_Nitpick_OAbs__Frac(_849462, _849458) = c_Nitpick_OAbs__Frac(_849460, _849456)), _849462 = _849460, _849458 = _849456], (4302 ^ _784416) ^ [_849605, _849607, _849609, _849611, _849613, _849615] : [-(c_Nitpick_Oplus__frac(_849615, _849611, _849607) = c_Nitpick_Oplus__frac(_849613, _849609, _849605)), _849615 = _849613, _849611 = _849609, _849607 = _849605], (4316 ^ _784416) ^ [_849826, _849828, _849830, _849832] : [-(c_Nitpick_Ouminus__frac(_849832, _849828) = c_Nitpick_Ouminus__frac(_849830, _849826)), _849832 = _849830, _849828 = _849826], (4326 ^ _784416) ^ [_849975, _849977] : [_849977 = _849975, -(c_Nitpick_Odenom(_849977) = c_Nitpick_Odenom(_849975))], (4332 ^ _784416) ^ [_850060, _850062] : [_850062 = _850060, -(c_Nitpick_Onum(_850062) = c_Nitpick_Onum(_850060))], (4338 ^ _784416) ^ [_850145, _850147] : [_850147 = _850145, -(c_Nitpick_ORep__Frac(_850147) = c_Nitpick_ORep__Frac(_850145))], (4344 ^ _784416) ^ [_850230, _850232, _850234, _850236, _850238, _850240] : [-(c_Product__Type_Ointernal__split(_850240, _850236, _850232) = c_Product__Type_Ointernal__split(_850238, _850234, _850230)), _850240 = _850238, _850236 = _850234, _850232 = _850230], (4358 ^ _784416) ^ [_850451, _850453, _850455, _850457] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_850457, _850453) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_850455, _850451)), _850457 = _850455, _850453 = _850451], (4368 ^ _784416) ^ [_850600, _850602] : [_850602 = _850600, -(c_HOL_Obool_Obool__size(_850602) = c_HOL_Obool_Obool__size(_850600))], (4374 ^ _784416) ^ [_850685, _850687] : [_850687 = _850685, -(c_Groups_Oabs__class_Oabs(_850687) = c_Groups_Oabs__class_Oabs(_850685))], (4380 ^ _784416) ^ [_850770, _850772] : [_850772 = _850770, -(c_Enum_Oenum__class_Oenum(_850772) = c_Enum_Oenum__class_Oenum(_850770))], (4386 ^ _784416) ^ [_850855, _850857, _850859, _850861] : [-(c_Product__Type_Osnd(_850861, _850857) = c_Product__Type_Osnd(_850859, _850855)), _850861 = _850859, _850857 = _850855], (4396 ^ _784416) ^ [_851004, _851006] : [_851006 = _851004, -(c_Nat_Osemiring__1__class_Oof__nat(_851006) = c_Nat_Osemiring__1__class_Oof__nat(_851004))], (4402 ^ _784416) ^ [_851089, _851091] : [_851091 = _851089, -(c_Int_Onumber__class_Onumber__of(_851091) = c_Int_Onumber__class_Onumber__of(_851089))], (4408 ^ _784416) ^ [_851174, _851176] : [_851176 = _851174, -(c_Int_OBit0(_851176) = c_Int_OBit0(_851174))], (4414 ^ _784416) ^ [_851259, _851261] : [_851261 = _851259, -(c_Int_OBit1(_851261) = c_Int_OBit1(_851259))], (4420 ^ _784416) ^ [_851344, _851346, _851348, _851350, _851352, _851354, _851356, _851358, _851360, _851362, _851364, _851366, _851368, _851370] : [-(c_New__Random__Sequence_Opos__decr__bind(_851370, _851366, _851362, _851358, _851354, _851350, _851346) = c_New__Random__Sequence_Opos__decr__bind(_851368, _851364, _851360, _851356, _851352, _851348, _851344)), _851370 = _851368, _851366 = _851364, _851362 = _851360, _851358 = _851356, _851354 = _851352, _851350 = _851348, _851346 = _851344], (4450 ^ _784416) ^ [_851933, _851935, _851937, _851939, _851941, _851943, _851945, _851947] : [-(c_New__DSequence_Opos__decr__bind(_851947, _851943, _851939, _851935) = c_New__DSequence_Opos__decr__bind(_851945, _851941, _851937, _851933)), _851947 = _851945, _851943 = _851941, _851939 = _851937, _851935 = _851933], (4468 ^ _784416) ^ [_852234, _852236] : [_852236 = _852234, -(c_HOL_Oequal__class_Oequal(_852236) = c_HOL_Oequal__class_Oequal(_852234))], (4474 ^ _784416) ^ [_852319, _852321, _852323, _852325, _852327, _852329, _852331, _852333] : [-(c_New__Random__Sequence_Opos__empty(_852333, _852329, _852325, _852321) = c_New__Random__Sequence_Opos__empty(_852331, _852327, _852323, _852319)), _852333 = _852331, _852329 = _852327, _852325 = _852323, _852321 = _852319], (4492 ^ _784416) ^ [_852620, _852622] : [_852622 = _852620, -(c_New__DSequence_Opos__empty(_852622) = c_New__DSequence_Opos__empty(_852620))], (4498 ^ _784416) ^ [_852705, _852707, _852709, _852711, _852713, _852715, _852717, _852719] : [-(c_New__DSequence_Opos__bind(_852719, _852715, _852711, _852707) = c_New__DSequence_Opos__bind(_852717, _852713, _852709, _852705)), _852719 = _852717, _852715 = _852713, _852711 = _852709, _852707 = _852705], (4516 ^ _784416) ^ [_853006, _853008] : [_853008 = _853006, -(c_Lazy__Sequence_Oyieldn(_853008) = c_Lazy__Sequence_Oyieldn(_853006))], (4522 ^ _784416) ^ [_853091, _853093, _853095, _853097, _853099, _853101] : [-(c_Lazy__Sequence_Oanamorph(_853101, _853097, _853093) = c_Lazy__Sequence_Oanamorph(_853099, _853095, _853091)), _853101 = _853099, _853097 = _853095, _853093 = _853091], (4536 ^ _784416) ^ [_853312, _853314] : [_853314 = _853312, -(c_Option_Ooption_OSome(_853314) = c_Option_Ooption_OSome(_853312))], (4542 ^ _784416) ^ [_853397, _853399, _853401, _853403, _853405, _853407, _853409, _853411] : [-(c_New__Random__Sequence_Opos__map(_853411, _853407, _853403, _853399) = c_New__Random__Sequence_Opos__map(_853409, _853405, _853401, _853397)), _853411 = _853409, _853407 = _853405, _853403 = _853401, _853399 = _853397], (4560 ^ _784416) ^ [_853698, _853700, _853702, _853704, _853706, _853708, _853710, _853712] : [-(c_New__Random__Sequence_Opos__bind(_853712, _853708, _853704, _853700) = c_New__Random__Sequence_Opos__bind(_853710, _853706, _853702, _853698)), _853712 = _853710, _853708 = _853706, _853704 = _853702, _853700 = _853698], (4578 ^ _784416) ^ [_853999, _854001, _854003, _854005, _854007, _854009, _854011, _854013, _854015, _854017, _854019, _854021, _854023, _854025] : [-(c_New__Random__Sequence_Oneg__decr__bind(_854025, _854021, _854017, _854013, _854009, _854005, _854001) = c_New__Random__Sequence_Oneg__decr__bind(_854023, _854019, _854015, _854011, _854007, _854003, _853999)), _854025 = _854023, _854021 = _854019, _854017 = _854015, _854013 = _854011, _854009 = _854007, _854005 = _854003, _854001 = _853999], (4608 ^ _784416) ^ [_854588, _854590, _854592, _854594, _854596, _854598, _854600, _854602] : [-(c_New__DSequence_Oneg__decr__bind(_854602, _854598, _854594, _854590) = c_New__DSequence_Oneg__decr__bind(_854600, _854596, _854592, _854588)), _854602 = _854600, _854598 = _854596, _854594 = _854592, _854590 = _854588], (4626 ^ _784416) ^ [_854889, _854891] : [_854891 = _854889, -(c_New__Random__Sequence_Opos__single(_854891) = c_New__Random__Sequence_Opos__single(_854889))], (4632 ^ _784416) ^ [_854974, _854976, _854978, _854980] : [-(c_New__DSequence_Opos__single(_854980, _854976) = c_New__DSequence_Opos__single(_854978, _854974)), _854980 = _854978, _854976 = _854974], (4642 ^ _784416) ^ [_855123, _855125, _855127, _855129, _855131, _855133, _855135, _855137] : [-(c_New__DSequence_Oneg__bind(_855137, _855133, _855129, _855125) = c_New__DSequence_Oneg__bind(_855135, _855131, _855127, _855123)), _855137 = _855135, _855133 = _855131, _855129 = _855127, _855125 = _855123], (4660 ^ _784416) ^ [_855424, _855426, _855428, _855430, _855432, _855434, _855436, _855438] : [-(c_New__Random__Sequence_Oneg__map(_855438, _855434, _855430, _855426) = c_New__Random__Sequence_Oneg__map(_855436, _855432, _855428, _855424)), _855438 = _855436, _855434 = _855432, _855430 = _855428, _855426 = _855424], (4678 ^ _784416) ^ [_855725, _855727, _855729, _855731, _855733, _855735, _855737, _855739] : [-(c_New__Random__Sequence_Oneg__bind(_855739, _855735, _855731, _855727) = c_New__Random__Sequence_Oneg__bind(_855737, _855733, _855729, _855725)), _855739 = _855737, _855735 = _855733, _855731 = _855729, _855727 = _855725], (4696 ^ _784416) ^ [_856026, _856028] : [_856028 = _856026, -(c_If(_856028) = c_If(_856026))], (4702 ^ _784416) ^ [_856111, _856113, _856115, _856117, _856119, _856121] : [-(c_Lazy__Sequence_Obind(_856121, _856117, _856113) = c_Lazy__Sequence_Obind(_856119, _856115, _856111)), _856121 = _856119, _856117 = _856115, _856113 = _856111], (4716 ^ _784416) ^ [_856332, _856334, _856336, _856338, _856340, _856342, _856344, _856346] : [-(c_Lazy__Sequence_Oproduct(_856346, _856342, _856338, _856334) = c_Lazy__Sequence_Oproduct(_856344, _856340, _856336, _856332)), _856346 = _856344, _856342 = _856340, _856338 = _856336, _856334 = _856332], (4734 ^ _784416) ^ [_856633, _856635] : [_856635 = _856633, -(c_New__Random__Sequence_Oneg__single(_856635) = c_New__Random__Sequence_Oneg__single(_856633))], (4740 ^ _784416) ^ [_856718, _856720, _856722, _856724] : [-(c_New__DSequence_Oneg__single(_856724, _856720) = c_New__DSequence_Oneg__single(_856722, _856718)), _856724 = _856722, _856720 = _856718], (4750 ^ _784416) ^ [_856867, _856869, _856871, _856873] : [-(c_Lazy__Sequence_Ohb__single(_856873, _856869) = c_Lazy__Sequence_Ohb__single(_856871, _856867)), _856873 = _856871, _856869 = _856867], (4760 ^ _784416) ^ [_857016, _857018, _857020, _857022, _857024, _857026, _857028, _857030, _857032, _857034, _857036, _857038] : [-(c_New__Random__Sequence_Opos__union(_857038, _857034, _857030, _857026, _857022, _857018) = c_New__Random__Sequence_Opos__union(_857036, _857032, _857028, _857024, _857020, _857016)), _857038 = _857036, _857034 = _857032, _857030 = _857028, _857026 = _857024, _857022 = _857020, _857018 = _857016], (4786 ^ _784416) ^ [_857501, _857503, _857505, _857507, _857509, _857511] : [-(c_New__DSequence_Opos__union(_857511, _857507, _857503) = c_New__DSequence_Opos__union(_857509, _857505, _857501)), _857511 = _857509, _857507 = _857505, _857503 = _857501], (4800 ^ _784416) ^ [_857722, _857724] : [_857724 = _857722, -(c_Lazy__Sequence_Oempty(_857724) = c_Lazy__Sequence_Oempty(_857722))], (4806 ^ _784416) ^ [_857807, _857809] : [_857809 = _857807, -(c_Lazy__Sequence_Osingle(_857809) = c_Lazy__Sequence_Osingle(_857807))], (4812 ^ _784416) ^ [_857892, _857894, _857896, _857898] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_857898, _857894) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_857896, _857892)), _857898 = _857896, _857894 = _857892], (4822 ^ _784416) ^ [_858041, _858043, _858045, _858047] : [-(c_Lazy__Sequence_Osmall__lazy_H(_858047, _858043) = c_Lazy__Sequence_Osmall__lazy_H(_858045, _858041)), _858047 = _858045, _858043 = _858041], (4832 ^ _784416) ^ [_858190, _858192] : [_858192 = _858190, -(c_Groups_Ouminus__class_Ouminus(_858192) = c_Groups_Ouminus__class_Ouminus(_858190))], (4838 ^ _784416) ^ [_858275, _858277, _858279, _858281] : [-(c_Wellfounded_Oaccp(_858281, _858277) = c_Wellfounded_Oaccp(_858279, _858275)), _858281 = _858279, _858277 = _858275], (4848 ^ _784416) ^ [_858424, _858426, _858428, _858430, _858432, _858434, _858436, _858438] : [-(c_Option_Ooption_Ooption__case(_858438, _858434, _858430, _858426) = c_Option_Ooption_Ooption__case(_858436, _858432, _858428, _858424)), _858438 = _858436, _858434 = _858432, _858430 = _858428, _858426 = _858424], (4866 ^ _784416) ^ [_858725, _858727] : [_858727 = _858725, -(c_Lazy__Sequence_Ohit__bound(_858727) = c_Lazy__Sequence_Ohit__bound(_858725))], (4872 ^ _784416) ^ [_858810, _858812, _858814, _858816, _858818, _858820, _858822, _858824] : [-(c_Lazy__Sequence_Ohb__bind(_858824, _858820, _858816, _858812) = c_Lazy__Sequence_Ohb__bind(_858822, _858818, _858814, _858810)), _858824 = _858822, _858820 = _858818, _858816 = _858814, _858812 = _858810], (4890 ^ _784416) ^ [_859111, _859113, _859115, _859117, _859119, _859121, _859123, _859125, _859127, _859129, _859131, _859133] : [-(c_New__Random__Sequence_Oneg__union(_859133, _859129, _859125, _859121, _859117, _859113) = c_New__Random__Sequence_Oneg__union(_859131, _859127, _859123, _859119, _859115, _859111)), _859133 = _859131, _859129 = _859127, _859125 = _859123, _859121 = _859119, _859117 = _859115, _859113 = _859111], (4916 ^ _784416) ^ [_859596, _859598, _859600, _859602, _859604, _859606] : [-(c_New__DSequence_Oneg__union(_859606, _859602, _859598) = c_New__DSequence_Oneg__union(_859604, _859600, _859596)), _859606 = _859604, _859602 = _859600, _859598 = _859596], (4930 ^ _784416) ^ [_859817, _859819, _859821, _859823, _859825, _859827, _859829, _859831, _859833, _859835] : [-(c_New__DSequence_Oneg__map(_859835, _859831, _859827, _859823, _859819) = c_New__DSequence_Oneg__map(_859833, _859829, _859825, _859821, _859817)), _859835 = _859833, _859831 = _859829, _859827 = _859825, _859823 = _859821, _859819 = _859817], (4952 ^ _784416) ^ [_860206, _860208] : [_860208 = _860206, -(c_Set_OCollect(_860208) = c_Set_OCollect(_860206))], (4958 ^ _784416) ^ [_860291, _860293, _860295, _860297, _860299, _860301] : [-(c_Product__Type_Oprod_Oprod__case(_860301, _860297, _860293) = c_Product__Type_Oprod_Oprod__case(_860299, _860295, _860291)), _860301 = _860299, _860297 = _860295, _860293 = _860291], (4972 ^ _784416) ^ [_860512, _860514] : [_860514 = _860512, -(c_Lattices_Osemilattice__sup__class_Osup(_860514) = c_Lattices_Osemilattice__sup__class_Osup(_860512))], (4978 ^ _784416) ^ [_860597, _860599] : [_860599 = _860597, -(c_Lattices_Osemilattice__inf__class_Oinf(_860599) = c_Lattices_Osemilattice__inf__class_Oinf(_860597))], (4984 ^ _784416) ^ [_860682, _860684, _860686, _860688, _860690, _860692] : [-(c_Predicate_Oconversep(_860692, _860688, _860684) = c_Predicate_Oconversep(_860690, _860686, _860682)), _860692 = _860690, _860688 = _860686, _860684 = _860682], (4998 ^ _784416) ^ [_860903, _860905, _860907, _860909] : [-(c_Relation_Oconverse(_860909, _860905) = c_Relation_Oconverse(_860907, _860903)), _860909 = _860907, _860905 = _860903], (5008 ^ _784416) ^ [_861052, _861054, _861056, _861058, _861060, _861062] : [-(c_List_Osplice(_861062, _861058, _861054) = c_List_Osplice(_861060, _861056, _861052)), _861062 = _861060, _861058 = _861056, _861054 = _861052], (5022 ^ _784416) ^ [_861273, _861275] : [_861275 = _861273, -(c_List_Otl(_861275) = c_List_Otl(_861273))], (5028 ^ _784416) ^ [_861358, _861360, _861362, _861364, _861366, _861368, _861370, _861372, _861374, _861376] : [-(c_Predicate_Opred__comp(_861376, _861372, _861368, _861364, _861360) = c_Predicate_Opred__comp(_861374, _861370, _861366, _861362, _861358)), _861376 = _861374, _861372 = _861370, _861368 = _861366, _861364 = _861362, _861360 = _861358], (5050 ^ _784416) ^ [_861747, _861749] : [_861749 = _861747, -(c_List_Orev(_861749) = c_List_Orev(_861747))], (5056 ^ _784416) ^ [_861832, _861834] : [_861834 = _861832, -(c_List_Oappend(_861834) = c_List_Oappend(_861832))], (5062 ^ _784416) ^ [_861917, _861919, _861921, _861923] : [-(c_List_Olast(_861923, _861919) = c_List_Olast(_861921, _861917)), _861923 = _861921, _861919 = _861917], (5072 ^ _784416) ^ [_862066, _862068] : [_862068 = _862066, -(c_List_Otake(_862068) = c_List_Otake(_862066))], (5078 ^ _784416) ^ [_862151, _862153] : [_862153 = _862151, -(c_List_Ohd(_862153) = c_List_Ohd(_862151))], (5084 ^ _784416) ^ [_862236, _862238] : [_862238 = _862236, -(c_List_Odrop(_862238) = c_List_Odrop(_862236))], (5090 ^ _784416) ^ [_862321, _862323] : [_862323 = _862321, -(c_List_Onth(_862323) = c_List_Onth(_862321))], (5096 ^ _784416) ^ [_862406, _862408, _862410, _862412] : [-(c_List_Oconcat(_862412, _862408) = c_List_Oconcat(_862410, _862406)), _862412 = _862410, _862408 = _862406], (5106 ^ _784416) ^ [_862555, _862557, _862559, _862561] : [-(c_List_Ofilter(_862561, _862557) = c_List_Ofilter(_862559, _862555)), _862561 = _862559, _862557 = _862555], (5116 ^ _784416) ^ [_862704, _862706, _862708, _862710] : [-(c_List_Ozip(_862710, _862706) = c_List_Ozip(_862708, _862704)), _862710 = _862708, _862706 = _862704], (5126 ^ _784416) ^ [_862853, _862855] : [_862855 = _862853, -(c_Orderings_Oord__class_Omin(_862855) = c_Orderings_Oord__class_Omin(_862853))], (5132 ^ _784416) ^ [_862938, _862940, _862942, _862944] : [-(c_List_Omap(_862944, _862940) = c_List_Omap(_862942, _862938)), _862944 = _862942, _862940 = _862938], (5142 ^ _784416) ^ [_863087, _863089, _863091, _863093] : [-(c_List_Oupt(_863093, _863089) = c_List_Oupt(_863091, _863087)), _863093 = _863091, _863089 = _863087], (5152 ^ _784416) ^ [_863236, _863238, _863240, _863242, _863244, _863246] : [-(c_List_Oreplicate(_863246, _863242, _863238) = c_List_Oreplicate(_863244, _863240, _863236)), _863246 = _863244, _863242 = _863240, _863238 = _863236], (5166 ^ _784416) ^ [_863457, _863459] : [_863459 = _863457, -(c_List_Olist_OCons(_863459) = c_List_Olist_OCons(_863457))], (5172 ^ _784416) ^ [_863542, _863544] : [_863544 = _863542, -(c_List_Omember(_863544) = c_List_Omember(_863542))], (5178 ^ _784416) ^ [_863627, _863629] : [_863629 = _863627, -(c_List_Olist_ONil(_863629) = c_List_Olist_ONil(_863627))], (5184 ^ _784416) ^ [_863712, _863714, _863716, _863718, _863720, _863722, _863724, _863726, _863728, _863730] : [-(c_Nitpick_Opair__box_Opair__box__size(_863730, _863726, _863722, _863718, _863714) = c_Nitpick_Opair__box_Opair__box__size(_863728, _863724, _863720, _863716, _863712)), _863730 = _863728, _863726 = _863724, _863722 = _863720, _863718 = _863716, _863714 = _863712], (5206 ^ _784416) ^ [_864101, _864103] : [_864103 = _864101, -(c_Groups_Oplus__class_Oplus(_864103) = c_Groups_Oplus__class_Oplus(_864101))], (5212 ^ _784416) ^ [_864186, _864188] : [_864188 = _864186, -(c_List_Oset(_864188) = c_List_Oset(_864186))], (5218 ^ _784416) ^ [_864271, _864273, _864275, _864277, _864279, _864281, _864283, _864285, _864287, _864289] : [-(c_Nitpick_Opair__box_Opair__box__case(_864289, _864285, _864281, _864277, _864273) = c_Nitpick_Opair__box_Opair__box__case(_864287, _864283, _864279, _864275, _864271)), _864289 = _864287, _864285 = _864283, _864281 = _864279, _864277 = _864275, _864273 = _864271], (5240 ^ _784416) ^ [_864660, _864662, _864664, _864666, _864668, _864670, _864672, _864674, _864676, _864678] : [-(c_Nitpick_Opair__box_Opair__box__rec(_864678, _864674, _864670, _864666, _864662) = c_Nitpick_Opair__box_Opair__box__rec(_864676, _864672, _864668, _864664, _864660)), _864678 = _864676, _864674 = _864672, _864670 = _864668, _864666 = _864664, _864662 = _864660], (5262 ^ _784416) ^ [_865049, _865051, _865053, _865055, _865057, _865059, _865061, _865063] : [-(c_Nitpick_Opair__box_OPairBox(_865063, _865059, _865055, _865051) = c_Nitpick_Opair__box_OPairBox(_865061, _865057, _865053, _865049)), _865063 = _865061, _865059 = _865057, _865055 = _865053, _865051 = _865049], (5280 ^ _784416) ^ [_865350, _865352, _865354, _865356] : [-(c_HOL_OThe(_865356, _865352) = c_HOL_OThe(_865354, _865350)), _865356 = _865354, _865352 = _865350], (5290 ^ _784416) ^ [_865499, _865501, _865503, _865505, _865507, _865509] : [-(c_FunDef_OTHE__default(_865509, _865505, _865501) = c_FunDef_OTHE__default(_865507, _865503, _865499)), _865509 = _865507, _865505 = _865503, _865501 = _865499], (5304 ^ _784416) ^ [_865720, _865722, _865724, _865726] : [-(c_Complete__Lattice_OSup__class_OSup(_865726, _865722) = c_Complete__Lattice_OSup__class_OSup(_865724, _865720)), _865726 = _865724, _865722 = _865720], (5314 ^ _784416) ^ [_865869, _865871, _865873, _865875] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_865875, _865871) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_865873, _865869)), _865875 = _865873, _865871 = _865869], (5324 ^ _784416) ^ [_866018, _866020, _866022, _866024] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_866024, _866020) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_866022, _866018)), _866024 = _866022, _866020 = _866018], (5334 ^ _784416) ^ [_866167, _866169, _866171, _866173] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_866173, _866169) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_866171, _866167)), _866173 = _866171, _866169 = _866167], (5344 ^ _784416) ^ [_866316, _866318] : [_866318 = _866316, -(c_Finite__Set_Ofinite(_866318) = c_Finite__Set_Ofinite(_866316))], (5350 ^ _784416) ^ [_866401, _866403] : [_866403 = _866401, -(c_Orderings_Oord__class_Oless(_866403) = c_Orderings_Oord__class_Oless(_866401))], (5356 ^ _784416) ^ [_866486, _866488, _866490, _866492] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_866492, _866488) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_866490, _866486)), _866492 = _866490, _866488 = _866486], (5366 ^ _784416) ^ [_866635, _866637, _866639, _866641, _866643, _866645, _866647, _866649] : [-(c_Lazy__Sequence_Ohb__map(_866649, _866645, _866641, _866637) = c_Lazy__Sequence_Ohb__map(_866647, _866643, _866639, _866635)), _866649 = _866647, _866645 = _866643, _866641 = _866639, _866637 = _866635], (5384 ^ _784416) ^ [_866936, _866938, _866940, _866942, _866944, _866946] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_866946, _866942, _866938) = c_Lazy__Sequence_Olazy__sequence_OInsert(_866944, _866940, _866936)), _866946 = _866944, _866942 = _866940, _866938 = _866936], (5398 ^ _784416) ^ [_867157, _867159, _867161, _867163, _867165, _867167] : [-(c_Lazy__Sequence_Oappend(_867167, _867163, _867159) = c_Lazy__Sequence_Oappend(_867165, _867161, _867157)), _867167 = _867165, _867163 = _867161, _867159 = _867157], (5412 ^ _784416) ^ [_867378, _867380, _867382, _867384] : [-(c_Lazy__Sequence_Ohb__flat(_867384, _867380) = c_Lazy__Sequence_Ohb__flat(_867382, _867378)), _867384 = _867382, _867380 = _867378], (5422 ^ _784416) ^ [_867527, _867529, _867531, _867533, _867535, _867537, _867539, _867541, _867543, _867545] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_867545, _867541, _867537, _867533, _867529) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_867543, _867539, _867535, _867531, _867527)), _867545 = _867543, _867541 = _867539, _867537 = _867535, _867533 = _867531, _867529 = _867527], (5444 ^ _784416) ^ [_867916, _867918] : [_867918 = _867916, -(c_Lazy__Sequence_Oyield(_867918) = c_Lazy__Sequence_Oyield(_867916))], (5450 ^ _784416) ^ [_868001, _868003] : [_868003 = _868001, -(c_Option_Ooption_ONone(_868003) = c_Option_Ooption_ONone(_868001))], (5456 ^ _784416) ^ [_868086, _868088] : [_868088 = _868086, -(c_Nat_Osize__class_Osize(_868088) = c_Nat_Osize__class_Osize(_868086))], (5462 ^ _784416) ^ [_868171, _868173] : [_868173 = _868171, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_868173) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_868171))], (5468 ^ _784416) ^ [_868256, _868258, _868260, _868262] : [-(c_List_Oupto(_868262, _868258) = c_List_Oupto(_868260, _868256)), _868262 = _868260, _868258 = _868256], (5478 ^ _784416) ^ [_868405, _868407] : [_868407 = _868405, -(c_member(_868407) = c_member(_868405))], (5484 ^ _784416) ^ [_868490, _868492, _868494, _868496, _868498, _868500] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_868500, _868496, _868492) = c_SetInterval_Oord__class_OatLeastAtMost(_868498, _868494, _868490)), _868500 = _868498, _868496 = _868494, _868492 = _868490], (5498 ^ _784416) ^ [_868711, _868713] : [_868713 = _868711, -(c_Code__Numeral_OSuc__code__numeral(_868713) = c_Code__Numeral_OSuc__code__numeral(_868711))], (5504 ^ _784416) ^ [_868796, _868798, _868800, _868802, _868804, _868806, _868808, _868810] : [-(c_Product__Type_Oscomp(_868810, _868806, _868802, _868798) = c_Product__Type_Oscomp(_868808, _868804, _868800, _868796)), _868810 = _868808, _868806 = _868804, _868802 = _868800, _868798 = _868796], (5522 ^ _784416) ^ [_869097, _869099, _869101, _869103, _869105, _869107, _869109, _869111] : [-(c_Random__Sequence_ORandom(_869111, _869107, _869103, _869099) = c_Random__Sequence_ORandom(_869109, _869105, _869101, _869097)), _869111 = _869109, _869107 = _869105, _869103 = _869101, _869099 = _869097], (5540 ^ _784416) ^ [_869398, _869400] : [_869400 = _869398, -(c_Groups_Ominus__class_Ominus(_869400) = c_Groups_Ominus__class_Ominus(_869398))], (5546 ^ _784416) ^ [_869483, _869485] : [_869485 = _869483, -(c_Groups_Oone__class_Oone(_869485) = c_Groups_Oone__class_Oone(_869483))], (5552 ^ _784416) ^ [_869568, _869570] : [_869570 = _869568, -(c_DSequence_Ounion(_869570) = c_DSequence_Ounion(_869568))], (5558 ^ _784416) ^ [_869653, _869655, _869657, _869659] : [-(c_Product__Type_Ofst(_869659, _869655) = c_Product__Type_Ofst(_869657, _869653)), _869659 = _869657, _869655 = _869653], (5568 ^ _784416) ^ [_869802, _869804, _869806, _869808, _869810, _869812, _869814, _869816] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_869816, _869812, _869808, _869804) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_869814, _869810, _869806, _869802)), _869816 = _869814, _869812 = _869810, _869808 = _869806, _869804 = _869802], (5586 ^ _784416) ^ [_870103, _870105] : [_870105 = _870103, -(c_Groups_Ozero__class_Ozero(_870105) = c_Groups_Ozero__class_Ozero(_870103))], (5592 ^ _784416) ^ [_870188, _870190, _870192, _870194, _870196, _870198] : [-(c_Random__Sequence_Oempty(_870198, _870194, _870190) = c_Random__Sequence_Oempty(_870196, _870192, _870188)), _870198 = _870196, _870194 = _870192, _870190 = _870188], (5606 ^ _784416) ^ [_870409, _870411] : [_870411 = _870409, -(c_DSequence_Oempty(_870411) = c_DSequence_Oempty(_870409))], (5612 ^ _784416) ^ [_870494, _870496, _870498, _870500] : [-(c_Product__Type_OPair(_870500, _870496) = c_Product__Type_OPair(_870498, _870494)), _870500 = _870498, _870496 = _870494], (5622 ^ _784416) ^ [_870643, _870645] : [_870645 = _870643, -(c_DSequence_Osingle(_870645) = c_DSequence_Osingle(_870643))], (5628 ^ _784416) ^ [_870728, _870730, _870732, _870734, _870736, _870738, _870740, _870742] : [-(c_Random__Sequence_Omap(_870742, _870738, _870734, _870730) = c_Random__Sequence_Omap(_870740, _870736, _870732, _870728)), _870742 = _870740, _870738 = _870736, _870734 = _870732, _870730 = _870728], (5646 ^ _784416) ^ [_871029, _871031, _871033, _871035, _871037, _871039, _871041, _871043] : [-(c_Random__Sequence_Obind(_871043, _871039, _871035, _871031) = c_Random__Sequence_Obind(_871041, _871037, _871033, _871029)), _871043 = _871041, _871039 = _871037, _871035 = _871033, _871031 = _871029], (5664 ^ _784416) ^ [_871330, _871332] : [_871332 = _871330, -(c_Random__Sequence_Osingle(_871332) = c_Random__Sequence_Osingle(_871330))], (5670 ^ _784416) ^ [_871415, _871417, _871419, _871421, _871423, _871425, _871427, _871429] : [-(c_Fun_Ocomp(_871429, _871425, _871421, _871417) = c_Fun_Ocomp(_871427, _871423, _871419, _871415)), _871429 = _871427, _871425 = _871423, _871421 = _871419, _871417 = _871415], (5688 ^ _784416) ^ [_871716, _871718, _871720, _871722] : [-(c_Option_Omap(_871722, _871718) = c_Option_Omap(_871720, _871716)), _871722 = _871720, _871718 = _871716], (5698 ^ _784416) ^ [_871865, _871867, _871869, _871871, _871873, _871875, _871877, _871879, _871881, _871883] : [-(c_Sum__Type_Osum_Osum__case(_871883, _871879, _871875, _871871, _871867) = c_Sum__Type_Osum_Osum__case(_871881, _871877, _871873, _871869, _871865)), _871883 = _871881, _871879 = _871877, _871875 = _871873, _871871 = _871869, _871867 = _871865], (5720 ^ _784416) ^ [_872254, _872256] : [_872256 = _872254, -(tc_List_Olist(_872256) = tc_List_Olist(_872254))], (5726 ^ _784416) ^ [_872339, _872341, _872343, _872345] : [-(tc_sum(_872345, _872341) = tc_sum(_872343, _872339)), _872345 = _872343, _872341 = _872339], (5736 ^ _784416) ^ [_872488, _872490] : [_872490 = _872488, -(tc_Option_Ooption(_872490) = tc_Option_Ooption(_872488))], (5742 ^ _784416) ^ [_872573, _872575, _872577, _872579] : [-(tc_Nitpick_Opair__box(_872579, _872575) = tc_Nitpick_Opair__box(_872577, _872573)), _872579 = _872577, _872575 = _872573], (5752 ^ _784416) ^ [_872722, _872724, _872726, _872728] : [-(tc_prod(_872728, _872724) = tc_prod(_872726, _872722)), _872728 = _872726, _872724 = _872722], (5762 ^ _784416) ^ [_872871, _872873] : [_872873 = _872871, -(tc_Lazy__Sequence_Olazy__sequence(_872873) = tc_Lazy__Sequence_Olazy__sequence(_872871))], (5768 ^ _784416) ^ [_872956, _872958] : [_872958 = _872956, -(c_COMBI(_872958) = c_COMBI(_872956))], (5774 ^ _784416) ^ [_873041, _873043, _873045, _873047] : [-(c_COMBK(_873047, _873043) = c_COMBK(_873045, _873041)), _873047 = _873045, _873043 = _873041], (5784 ^ _784416) ^ [_873190, _873192, _873194, _873196, _873198, _873200] : [-(c_COMBB(_873200, _873196, _873192) = c_COMBB(_873198, _873194, _873190)), _873200 = _873198, _873196 = _873194, _873192 = _873190], (5798 ^ _784416) ^ [_873411, _873413, _873415, _873417, _873419, _873421] : [-(c_COMBC(_873421, _873417, _873413) = c_COMBC(_873419, _873415, _873411)), _873421 = _873419, _873417 = _873415, _873413 = _873411], (5812 ^ _784416) ^ [_873632, _873634, _873636, _873638, _873640, _873642] : [-(c_COMBS(_873642, _873638, _873634) = c_COMBS(_873640, _873636, _873632)), _873642 = _873640, _873638 = _873636, _873634 = _873632], (5826 ^ _784416) ^ [_873853, _873855] : [_873855 = _873853, -(c_Orderings_Oord__class_Oless__eq(_873855) = c_Orderings_Oord__class_Oless__eq(_873853))], (5832 ^ _784416) ^ [_873938, _873940] : [_873940 = _873938, -(c_Orderings_Obot__class_Obot(_873940) = c_Orderings_Obot__class_Obot(_873938))], (5838 ^ _784416) ^ [_874023, _874025, _874027, _874029] : [-(tc_fun(_874029, _874025) = tc_fun(_874027, _874023)), _874029 = _874027, _874025 = _874023], (5848 ^ _784416) ^ [_874172, _874174, _874176, _874178] : [-(hAPP(_874178, _874174) = hAPP(_874176, _874172)), _874178 = _874176, _874174 = _874172], (5858 ^ _784416) ^ [_874321, _874323] : [_874323 = _874321, -(c_Set_Oinsert(_874323) = c_Set_Oinsert(_874321))], (5864 ^ _784416) ^ [_874402, _874404] : [_874404 = _874402, -(tc_Hoare__Mirabelle_Otriple(_874404) = tc_Hoare__Mirabelle_Otriple(_874402))], (5870 ^ _784416) ^ [_877471, _877473] : [hAPP(_877471, 5871 ^ [_877471, _877473]) = hAPP(_877473, 5871 ^ [_877471, _877473]), -(_877471 = _877473)], (5877 ^ _784416) ^ [_877597, _877599] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_877597, _877599, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877597), tc_HOL_Obool))))], (5879 ^ _784416) ^ [_877630, _877632] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_877630, _877632, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_877630), tc_HOL_Obool))))], (5881 ^ _784416) ^ [_877663, _877665, _877667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_877663), tc_HOL_Obool)), _877665), _877667)), -(c_Hoare__Mirabelle_Ohoare__derivs(_877663, _877667, _877665))], (5887 ^ _784416) ^ [_877768, _877770, _877772, _877774] : [c_Hoare__Mirabelle_Ohoare__derivs(_877768, _877770, _877772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_877768), tc_HOL_Obool)), _877774), _877772)), -(c_Hoare__Mirabelle_Ohoare__derivs(_877768, _877770, _877774))], (5897 ^ _784416) ^ [_877933, _877935, _877937, _877939] : [c_Hoare__Mirabelle_Ohoare__derivs(_877933, _877935, _877937), c_Hoare__Mirabelle_Ohoare__derivs(_877933, _877939, _877935), -(c_Hoare__Mirabelle_Ohoare__derivs(_877933, _877939, _877937))], (5907 ^ _784416) ^ [_878076, _878078, _878080, _878082] : [c_Hoare__Mirabelle_Ohoare__derivs(_878076, _878078, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_878076)), _878080), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_878076), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_878076, _878078, _878082), -(c_Hoare__Mirabelle_Ohoare__derivs(_878076, _878078, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_878076)), _878080), _878082)))], (5917 ^ _784416) ^ [_878273, _878275] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878273, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_878273, tc_HOL_Obool))), _878275)))], (5919 ^ _784416) ^ [_878313, _878315, _878317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878313, tc_HOL_Obool)), _878315), hAPP(hAPP(c_Set_Oinsert(_878313), _878317), c_Orderings_Obot__class_Obot(tc_fun(_878313, tc_HOL_Obool))))), -(_878315 = c_Orderings_Obot__class_Obot(tc_fun(_878313, tc_HOL_Obool))), -(_878315 = hAPP(hAPP(c_Set_Oinsert(_878313), _878317), c_Orderings_Obot__class_Obot(tc_fun(_878313, tc_HOL_Obool))))], (5929 ^ _784416) ^ [_878487, _878489, _878491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878487, tc_HOL_Obool)), _878489), _878491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878487, tc_HOL_Obool)), _878491), _878489)), -(_878489 = _878491)], (5939 ^ _784416) ^ [_878660, _878662] : [class_Orderings_Opreorder(_878660), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878660), _878662), _878662)))], (5945 ^ _784416) ^ [_878749, _878751, _878753] : [class_Orderings_Obot(_878749), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_878751, _878749)), _878753) = c_Orderings_Obot__class_Obot(_878749))], (5951 ^ _784416) ^ [_878846, _878848, _878850] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878846, tc_HOL_Obool)), _878848), hAPP(hAPP(c_Set_Oinsert(_878846), _878850), _878848))))], (5953 ^ _784416) ^ [_878891, _878893, _878895, _878897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878891, tc_HOL_Obool)), _878893), _878895)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878891, tc_HOL_Obool)), _878893), hAPP(hAPP(c_Set_Oinsert(_878891), _878897), _878895))))], (5959 ^ _784416) ^ [_879028, _879030, _879032, _879034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879028, tc_HOL_Obool)), _879030), _879032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879028, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_879028), _879034), _879030)), hAPP(hAPP(c_Set_Oinsert(_879028), _879034), _879032))))], (5965 ^ _784416) ^ [_879196, _879198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879196, tc_HOL_Obool)), _879198), c_Orderings_Obot__class_Obot(tc_fun(_879196, tc_HOL_Obool)))), -(_879198 = c_Orderings_Obot__class_Obot(tc_fun(_879196, tc_HOL_Obool)))], (5971 ^ _784416) ^ [_879309, _879311] : [_879311 = c_Orderings_Obot__class_Obot(tc_fun(_879309, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879309, tc_HOL_Obool)), _879311), c_Orderings_Obot__class_Obot(tc_fun(_879309, tc_HOL_Obool)))))], (5977 ^ _784416) ^ [_879443, _879445, _879447] : [c_Orderings_Obot__class_Obot(tc_fun(_879443, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_879443), _879445), _879447)], (5979 ^ _784416) ^ [_879498, _879500, _879502] : [hAPP(hAPP(c_Set_Oinsert(_879498), _879500), _879502) = c_Orderings_Obot__class_Obot(tc_fun(_879498, tc_HOL_Obool))], (5981 ^ _784416) ^ [_879562, _879564, _879566, _879568, _879570] : [hAPP(hAPP(c_Set_Oinsert(_879562), _879564), hAPP(hAPP(c_Set_Oinsert(_879562), _879566), c_Orderings_Obot__class_Obot(tc_fun(_879562, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_879562), _879568), hAPP(hAPP(c_Set_Oinsert(_879562), _879570), c_Orderings_Obot__class_Obot(tc_fun(_879562, tc_HOL_Obool)))), 5986 ^ _784416 : [(5987 ^ _784416) ^ [] : [-(_879564 = _879568)], (5989 ^ _784416) ^ [] : [-(_879566 = _879570)]], 5990 ^ _784416 : [(5991 ^ _784416) ^ [] : [-(_879564 = _879570)], (5993 ^ _784416) ^ [] : [-(_879566 = _879568)]]], (5995 ^ _784416) ^ [_879824, _879826, _879828, _879830, _879832] : [-(hAPP(hAPP(c_Set_Oinsert(_879824), _879826), hAPP(hAPP(c_Set_Oinsert(_879824), _879828), c_Orderings_Obot__class_Obot(tc_fun(_879824, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_879824), _879830), hAPP(hAPP(c_Set_Oinsert(_879824), _879832), c_Orderings_Obot__class_Obot(tc_fun(_879824, tc_HOL_Obool))))), 5996 ^ _784416 : [(5997 ^ _784416) ^ [] : [_879826 = _879830, _879828 = _879832], (6003 ^ _784416) ^ [] : [_879826 = _879832, _879828 = _879830]]], (6011 ^ _784416) ^ [_880140, _880142, _880144] : [class_Orderings_Olinorder(_880140), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880140), _880142), _880144))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880140), _880144), _880142)))], (6021 ^ _784416) ^ [_880260, _880262, _880264, _880266] : [class_Orderings_Oorder(_880260), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880260), _880262), _880264)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880260), _880266), _880262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880260), _880266), _880264)))], (6035 ^ _784416) ^ [_880493, _880495, _880497] : [class_Orderings_Oorder(_880493), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880493), _880495), _880497)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880493), _880497), _880495)), -(_880497 = _880495)], (6049 ^ _784416) ^ [_880706, _880708, _880710, _880712] : [class_Orderings_Opreorder(_880706), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880706), _880708), _880710)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880706), _880710), _880712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880706), _880708), _880712)))], (6063 ^ _784416) ^ [_880939, _880941, _880943] : [class_Orderings_Oorder(_880939), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880939), _880941), _880943)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880939), _880943), _880941)), -(_880941 = _880943)], (6077 ^ _784416) ^ [_881152, _881154, _881156, _881158] : [class_Orderings_Oorder(_881152), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881152), _881154), _881156)), _881154 = _881158, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881152), _881158), _881156)))], (6091 ^ _784416) ^ [_881371, _881373, _881375, _881377] : [class_Orderings_Oord(_881371), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881371), _881373), _881375)), _881375 = _881377, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881371), _881373), _881377)))], (6105 ^ _784416) ^ [_881590, _881592, _881594, _881596] : [class_Orderings_Oorder(_881590), _881592 = _881594, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881590), _881596), _881594)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881590), _881596), _881592)))], (6119 ^ _784416) ^ [_881809, _881811, _881813, _881815] : [class_Orderings_Oord(_881809), _881811 = _881813, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881809), _881813), _881815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881809), _881811), _881815)))], (6133 ^ _784416) ^ [_882028, _882030, _882032] : [class_Orderings_Oorder(_882028), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882028), _882030), _882032)), 6140 ^ _784416 : [(6141 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882028), _882032), _882030)), -(_882032 = _882030)], (6147 ^ _784416) ^ [] : [_882032 = _882030, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882028), _882032), _882030)))]]], (6153 ^ _784416) ^ [_882328, _882330, _882332] : [class_Orderings_Opreorder(_882328), _882330 = _882332, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882328), _882330), _882332)))], (6163 ^ _784416) ^ [_882473, _882475, _882477] : [class_Orderings_Oorder(_882473), 6166 ^ _784416 : [(6167 ^ _784416) ^ [] : [_882475 = _882477, 6170 ^ _784416 : [(6171 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882473), _882475), _882477)))], (6173 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882473), _882477), _882475)))]]], (6175 ^ _784416) ^ [] : [-(_882475 = _882477), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882473), _882475), _882477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882473), _882477), _882475))]]], (6185 ^ _784416) ^ [_882800, _882802, _882804] : [class_Orderings_Olinorder(_882800), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882800), _882802), _882804))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882800), _882804), _882802)))], (6205 ^ _784416) ^ [_883053, _883055, _883057, _883059] : [6206 ^ _784416 : [(6207 ^ _784416) ^ [] : [_883055 = _883059], (6209 ^ _784416) ^ [] : [hBOOL(hAPP(_883057, _883059))]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_883053), _883055), _883057), _883059)))], (6195 ^ _784416) ^ [_882939, _882941, _882943, _882945] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_882939), _882941), _882943), _882945)), -(_882941 = _882945), -(hBOOL(hAPP(_882943, _882945)))], (6213 ^ _784416) ^ [_883198, _883200, _883202, _883204] : [-(hAPP(hAPP(c_Set_Oinsert(_883198), _883200), hAPP(hAPP(c_Set_Oinsert(_883198), _883202), _883204)) = hAPP(hAPP(c_Set_Oinsert(_883198), _883202), hAPP(hAPP(c_Set_Oinsert(_883198), _883200), _883204)))], (6215 ^ _784416) ^ [_883259, _883261, _883263] : [-(hAPP(hAPP(c_Set_Oinsert(_883259), _883261), hAPP(hAPP(c_Set_Oinsert(_883259), _883261), _883263)) = hAPP(hAPP(c_Set_Oinsert(_883259), _883261), _883263))], (6217 ^ _784416) ^ [_883310, _883312, _883314] : [_883310 = _883312, 6220 ^ _784416 : [(6221 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883314, tc_HOL_Obool)), _883310), _883312)))], (6223 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883314, tc_HOL_Obool)), _883312), _883310)))]]], (6225 ^ _784416) ^ [_883459, _883461, _883463, _883465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883459, tc_HOL_Obool)), _883461), _883463)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883459, tc_HOL_Obool)), _883463), _883465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883459, tc_HOL_Obool)), _883461), _883465)))], (6235 ^ _784416) ^ [_883656, _883658, _883660] : [_883656 = _883658, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883660, tc_HOL_Obool)), _883658), _883656)))], (6241 ^ _784416) ^ [_883755, _883757, _883759] : [_883755 = _883757, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883759, tc_HOL_Obool)), _883755), _883757)))], (6247 ^ _784416) ^ [_883872, _883874, _883876] : [_883872 = _883874, 6250 ^ _784416 : [(6251 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883876, tc_HOL_Obool)), _883872), _883874)))], (6253 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883876, tc_HOL_Obool)), _883874), _883872)))]]], (6255 ^ _784416) ^ [_884013, _884015, _884017] : [-(_884013 = _884015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884017, tc_HOL_Obool)), _884013), _884015)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884017, tc_HOL_Obool)), _884015), _884013))], (6265 ^ _784416) ^ [_884188, _884190] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884188, tc_HOL_Obool)), _884190), _884190)))], (6267 ^ _784416) ^ [_884223, _884225] : [class_Orderings_Obot(_884223), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884223), c_Orderings_Obot__class_Obot(_884223)), _884225)))], (6273 ^ _784416) ^ [_884316, _884318, _884320, _884322, _884324] : [class_Orderings_Oord(_884316), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884318, _884316)), _884320), _884322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884316), hAPP(_884320, _884324)), hAPP(_884322, _884324))))], (6283 ^ _784416) ^ [_884501, _884503, _884505, _884507, _884509] : [class_Orderings_Oord(_884501), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884503, _884501)), _884505), _884507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884501), hAPP(_884505, _884509)), hAPP(_884507, _884509))))], (6293 ^ _784416) ^ [_884686, _884688, _884690, _884692] : [class_Orderings_Oord(_884686), 6296 ^ _784416 : [(6297 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884688, _884686)), _884690), _884692)), 6300 ^ _784416 : [(6301 ^ _784416) ^ [_884843] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884686), hAPP(_884690, _884843)), hAPP(_884692, _884843))))]]], (6303 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884686), hAPP(_884690, 6304 ^ [_884686, _884688, _884690, _884692])), hAPP(_884692, 6304 ^ [_884686, _884688, _884690, _884692]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884688, _884686)), _884690), _884692)))]]], (6310 ^ _784416) ^ [_885032, _885034, _885036] : [class_Orderings_Obot(_885032), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_885034, _885032)), _885036) = c_Orderings_Obot__class_Obot(_885032))], (6316 ^ _784416) ^ [_885129, _885131, _885133] : [hAPP(hAPP(c_Set_Oinsert(_885129), _885131), c_Orderings_Obot__class_Obot(tc_fun(_885129, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_885129), _885133), c_Orderings_Obot__class_Obot(tc_fun(_885129, tc_HOL_Obool))), -(_885131 = _885133)], (6322 ^ _784416) ^ [_885260, _885262] : [-(c_Set_Othe__elem(_885260, hAPP(hAPP(c_Set_Oinsert(_885260), _885262), c_Orderings_Obot__class_Obot(tc_fun(_885260, tc_HOL_Obool)))) = _885262)], (6324 ^ _784416) ^ [_885301, _885303, _885305, _885307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885301, tc_HOL_Obool)), _885303), _885305)), hBOOL(hAPP(_885303, _885307)), -(hBOOL(hAPP(_885305, _885307)))], (6334 ^ _784416) ^ [_885466, _885468, _885470, _885472] : [hBOOL(hAPP(_885466, _885468)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885470, tc_HOL_Obool)), _885466), _885472)), -(hBOOL(hAPP(_885472, _885468)))], (6344 ^ _784416) ^ [_885631, _885633, _885635, _885637] : [class_Orderings_Oorder(_885631), class_Enum_Oenum(_885633), 6351 ^ _784416 : [(6352 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885633, _885631)), _885635), _885637)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_885633), hAPP(hAPP(c_COMBS(_885633, _885631, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_885631, tc_fun(_885631, tc_HOL_Obool), _885633), c_Orderings_Oord__class_Oless__eq(_885631)), _885635)), _885637))))], (6358 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_885633), hAPP(hAPP(c_COMBS(_885633, _885631, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_885631, tc_fun(_885631, tc_HOL_Obool), _885633), c_Orderings_Oord__class_Oless__eq(_885631)), _885635)), _885637))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885633, _885631)), _885635), _885637)))]]], (6364 ^ _784416) ^ [_886021, _886023, _886025] : [class_Orderings_Owellorder(_886021), hBOOL(hAPP(_886023, _886025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886021), c_Orderings_Oord__class_OLeast(_886021, _886023)), _886025)))], (6374 ^ _784416) ^ [_886176, _886178, _886180, _886182] : [class_Orderings_Oord(_886176), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886176), hAPP(_886178, 6379 ^ [_886176, _886178, _886180, _886182])), hAPP(_886180, 6379 ^ [_886176, _886178, _886180, _886182]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_886182, _886176)), _886178), _886180)))], (6385 ^ _784416) ^ [_886413, _886415, _886417, _886419, _886421] : [class_Orderings_Oorder(_886413), class_Orderings_Olinorder(_886415), c_Orderings_Oorder__class_Ostrict__mono(_886415, _886413, _886417), 6396 ^ _784416 : [(6397 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886413), hAPP(_886417, _886419)), hAPP(_886417, _886421))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886415), _886419), _886421)))], (6403 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886415), _886419), _886421)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886413), hAPP(_886417, _886419)), hAPP(_886417, _886421))))]]], (6409 ^ _784416) ^ [_886814, _886816] : [-(c_Set_Othe__elem(_886814, _886816) = c_HOL_OThe(_886814, hAPP(hAPP(c_COMBB(tc_fun(_886814, tc_HOL_Obool), tc_HOL_Obool, _886814), hAPP(c_fequal, _886816)), hAPP(hAPP(c_COMBC(_886814, tc_fun(_886814, tc_HOL_Obool), tc_fun(_886814, tc_HOL_Obool)), c_Set_Oinsert(_886814)), c_Orderings_Obot__class_Obot(tc_fun(_886814, tc_HOL_Obool))))))], (6411 ^ _784416) ^ [_886896, _886898, _886900] : [hBOOL(hAPP(_886896, _886898)), -(hAPP(c_Set_OCollect(_886900), hAPP(hAPP(c_COMBS(_886900, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _886900), c_fconj), hAPP(hAPP(c_COMBC(_886900, _886900, tc_HOL_Obool), c_fequal), _886898))), _886896)) = hAPP(hAPP(c_Set_Oinsert(_886900), _886898), c_Orderings_Obot__class_Obot(tc_fun(_886900, tc_HOL_Obool))))], (6417 ^ _784416) ^ [_887069, _887071, _887073] : [-(hBOOL(hAPP(_887069, _887071))), -(hAPP(c_Set_OCollect(_887073), hAPP(hAPP(c_COMBS(_887073, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _887073), c_fconj), hAPP(hAPP(c_COMBC(_887073, _887073, tc_HOL_Obool), c_fequal), _887071))), _887069)) = c_Orderings_Obot__class_Obot(tc_fun(_887073, tc_HOL_Obool)))], (6423 ^ _784416) ^ [_887163, _887165, _887167] : [hBOOL(hAPP(_887163, _887165)), -(hAPP(c_Set_OCollect(_887167), hAPP(hAPP(c_COMBS(_887167, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _887167), c_fconj), hAPP(c_fequal, _887165))), _887163)) = hAPP(hAPP(c_Set_Oinsert(_887167), _887165), c_Orderings_Obot__class_Obot(tc_fun(_887167, tc_HOL_Obool))))], (6429 ^ _784416) ^ [_887322, _887324, _887326] : [-(hBOOL(hAPP(_887322, _887324))), -(hAPP(c_Set_OCollect(_887326), hAPP(hAPP(c_COMBS(_887326, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _887326), c_fconj), hAPP(c_fequal, _887324))), _887322)) = c_Orderings_Obot__class_Obot(tc_fun(_887326, tc_HOL_Obool)))], (6435 ^ _784416) ^ [_887397, _887399] : [-(hAPP(c_Set_OCollect(_887397), hAPP(hAPP(c_COMBC(_887397, _887397, tc_HOL_Obool), c_fequal), _887399)) = hAPP(hAPP(c_Set_Oinsert(_887397), _887399), c_Orderings_Obot__class_Obot(tc_fun(_887397, tc_HOL_Obool))))], (6437 ^ _784416) ^ [_887450, _887452] : [-(hAPP(c_Set_OCollect(_887450), hAPP(c_fequal, _887452)) = hAPP(hAPP(c_Set_Oinsert(_887450), _887452), c_Orderings_Obot__class_Obot(tc_fun(_887450, tc_HOL_Obool))))], (6439 ^ _784416) ^ [_887496, _887498] : [-(hAPP(c_Set_OCollect(_887496), _887498) = _887498)], (6441 ^ _784416) ^ [_887526, _887528] : [class_Enum_Oenum(_887526), 6444 ^ _784416 : [(6445 ^ _784416) ^ [] : [hBOOL(hAPP(_887528, 6446 ^ [_887526, _887528])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_887526), _887528)))], (6452 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_887526), _887528)), 6455 ^ _784416 : [(6456 ^ _784416) ^ [_887744] : [-(hBOOL(hAPP(_887528, _887744)))]]]]], (6458 ^ _784416) ^ [_887779, _887781] : [class_Enum_Oenum(_887779), 6461 ^ _784416 : [(6462 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_887779), _887781)), 6465 ^ _784416 : [(6466 ^ _784416) ^ [_887905] : [-(hBOOL(hAPP(_887781, _887905)))]]], (6468 ^ _784416) ^ [] : [hBOOL(hAPP(_887781, 6469 ^ [_887779, _887781])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_887779), _887781)))]]], (6475 ^ _784416) ^ [_888032, _888034] : [class_Orderings_Owellorder(_888032), 6480 ^ _784416 : [(6481 ^ _784416) ^ [_888126] : [hBOOL(hAPP(_888034, _888126))]], -(hBOOL(hAPP(_888034, c_Orderings_Oord__class_OLeast(_888032, _888034))))], (6485 ^ _784416) ^ [_888186, _888188, _888190, _888192, _888194] : [class_Orderings_Oorder(_888186), class_Orderings_Olinorder(_888188), c_Orderings_Oorder__class_Ostrict__mono(_888188, _888186, _888190), 6496 ^ _784416 : [(6497 ^ _784416) ^ [] : [hAPP(_888190, _888192) = hAPP(_888190, _888194), -(_888192 = _888194)], (6503 ^ _784416) ^ [] : [_888192 = _888194, -(hAPP(_888190, _888192) = hAPP(_888190, _888194))]]], (6509 ^ _784416) ^ [_888560, _888562] : [c_Orderings_Obot__class_Obot(tc_fun(_888560, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_888560), _888562), 6512 ^ _784416 : [(6513 ^ _784416) ^ [_888645] : [hBOOL(hAPP(_888562, _888645))]]], (6515 ^ _784416) ^ [_888668, _888670] : [-(hBOOL(hAPP(_888670, 6516 ^ [_888668, _888670]))), -(c_Orderings_Obot__class_Obot(tc_fun(_888668, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_888668), _888670))], (6522 ^ _784416) ^ [_888740, _888742] : [hAPP(c_Set_OCollect(_888740), _888742) = c_Orderings_Obot__class_Obot(tc_fun(_888740, tc_HOL_Obool)), 6525 ^ _784416 : [(6526 ^ _784416) ^ [_888825] : [hBOOL(hAPP(_888742, _888825))]]], (6528 ^ _784416) ^ [_888848, _888850] : [-(hBOOL(hAPP(_888850, 6529 ^ [_888848, _888850]))), -(hAPP(c_Set_OCollect(_888848), _888850) = c_Orderings_Obot__class_Obot(tc_fun(_888848, tc_HOL_Obool)))], (6535 ^ _784416) ^ [_888905, _888907, _888909] : [class_Orderings_Owellorder(_888905), hBOOL(hAPP(_888907, _888909)), -(hBOOL(hAPP(_888907, c_Orderings_Oord__class_OLeast(_888905, _888907))))], (6545 ^ _784416) ^ [_889050] : [-(c_Orderings_Obot__class_Obot(tc_fun(_889050, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_889050), hAPP(c_COMBK(tc_HOL_Obool, _889050), c_fFalse)))], (6547 ^ _784416) ^ [_889089, _889091, _889093] : [-(hAPP(hAPP(c_Set_Oinsert(_889089), _889091), hAPP(c_Set_OCollect(_889089), _889093)) = hAPP(c_Set_OCollect(_889089), hAPP(hAPP(c_COMBS(_889089, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _889089), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _889089), c_fNot), hAPP(hAPP(c_COMBC(_889089, _889089, tc_HOL_Obool), c_fequal), _889091)))), _889093)))], (6549 ^ _784416) ^ [_889174, _889176] : [-(c_Enum_Oenum__the(_889174, _889176) = c_HOL_OThe(_889174, _889176))], (6551 ^ _784416) ^ [_889205, _889207] : [-(c_HOL_OThe(_889205, hAPP(hAPP(c_COMBC(_889205, _889205, tc_HOL_Obool), c_fequal), _889207)) = _889207)], (6553 ^ _784416) ^ [_889243, _889245] : [-(c_HOL_OThe(_889243, hAPP(c_fequal, _889245)) = _889245)], (6555 ^ _784416) ^ [_889274, _889276, _889278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889274, tc_HOL_Obool)), _889276), _889278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_889274, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_889274, _889276)), c_Predicate_OPowp(_889274, _889278))))], (6561 ^ _784416) ^ [_889411, _889413, _889415] : [class_Orderings_Oorder(_889411), hBOOL(hAPP(_889413, _889415)), 6571 ^ _784416 : [(6572 ^ _784416) ^ [] : [-(hBOOL(hAPP(_889413, 6570 ^ [_889411, _889413, _889415])))], (6574 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_889411), _889415), 6570 ^ [_889411, _889413, _889415]))]], -(c_Orderings_Oord__class_OLeast(_889411, _889413) = _889415)], (6578 ^ _784416) ^ [_889700, _889702, _889704] : [6580 ^ _784416 : [(6581 ^ _784416) ^ [] : [-(hBOOL(hAPP(_889700, 6579 ^ [_889700, _889702, _889704])))], (6583 ^ _784416) ^ [] : [hBOOL(hAPP(_889702, 6579 ^ [_889700, _889702, _889704]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889704, tc_HOL_Obool)), hAPP(c_Set_OCollect(_889704), _889700)), hAPP(c_Set_OCollect(_889704), _889702))))], (6587 ^ _784416) ^ [_889898, _889900, _889902] : [-(hAPP(hAPP(c_Set_Oinsert(_889898), _889900), _889902) = hAPP(c_Set_OCollect(_889898), hAPP(hAPP(c_COMBS(_889898, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _889898), c_fdisj), hAPP(hAPP(c_COMBC(_889898, _889898, tc_HOL_Obool), c_fequal), _889900))), hAPP(hAPP(c_COMBC(_889898, tc_fun(_889898, tc_HOL_Obool), tc_HOL_Obool), c_member(_889898)), _889902))))], (6589 ^ _784416) ^ [_889983, _889985, _889987] : [-(hAPP(hAPP(c_Set_Oinsert(_889983), _889985), _889987) = hAPP(c_Set_OCollect(_889983), hAPP(hAPP(c_COMBS(_889983, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _889983), c_fdisj), hAPP(hAPP(c_COMBC(_889983, _889983, tc_HOL_Obool), c_fequal), _889985))), hAPP(hAPP(c_COMBC(_889983, tc_fun(_889983, tc_HOL_Obool), tc_HOL_Obool), c_member(_889983)), _889987))))], (6591 ^ _784416) ^ [_890095, _890097, _890099, _890101, _890103, _890105] : [c_Predicate_Oinv__imagep(_890095, _890097, _890099, _890101, _890103, _890105), -(hBOOL(hAPP(hAPP(_890099, hAPP(_890101, _890103)), hAPP(_890101, _890105))))], (6597 ^ _784416) ^ [_890206, _890208, _890210, _890212, _890214, _890216] : [hBOOL(hAPP(hAPP(_890210, hAPP(_890212, _890214)), hAPP(_890212, _890216))), -(c_Predicate_Oinv__imagep(_890206, _890208, _890210, _890212, _890214, _890216))], (6603 ^ _784416) ^ [_890323, _890325, _890327] : [-(hAPP(hAPP(c_Set_Oinsert(_890323), _890325), _890327) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890323, tc_HOL_Obool)), hAPP(c_Set_OCollect(_890323), hAPP(hAPP(c_COMBC(_890323, _890323, tc_HOL_Obool), c_fequal), _890325))), _890327))], (6605 ^ _784416) ^ [_890399, _890401, _890403, _890405] : [_890399 = c_Orderings_Obot__class_Obot(tc_fun(_890401, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_890401, _890403, hAPP(c_COMBK(_890403, _890401), _890405)), _890399) = c_Orderings_Obot__class_Obot(tc_fun(_890403, tc_HOL_Obool)))], (6611 ^ _784416) ^ [_890520, _890522, _890524, _890526] : [-(_890520 = c_Orderings_Obot__class_Obot(tc_fun(_890522, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_890522, _890524, hAPP(c_COMBK(_890524, _890522), _890526)), _890520) = hAPP(hAPP(c_Set_Oinsert(_890524), _890526), c_Orderings_Obot__class_Obot(tc_fun(_890524, tc_HOL_Obool))))], (6617 ^ _784416) ^ [_890593, _890595, _890597] : [class_Orderings_Oorder(_890593), class_Orderings_Oorder(_890595), c_Orderings_Oorder__class_Ostrict__mono(_890595, _890593, _890597), -(c_Orderings_Oorder__class_Omono(_890595, _890593, _890597))], (6631 ^ _784416) ^ [_890782, _890784, _890786, _890788] : [_890782 = _890784, 6636 ^ _784416 : [(6637 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_890786), _890788), _890782)))], (6639 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_890786), _890788), _890784)))]], 6640 ^ _784416 : [(6641 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890786), _890788), _890782))], (6643 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890786), _890788), _890784))]]], (6645 ^ _784416) ^ [_891045, _891047, _891049, _891051] : [6646 ^ _784416 : [(6647 ^ _784416) ^ [] : [hBOOL(hAPP(_891045, _891047))], (6649 ^ _784416) ^ [] : [hBOOL(hAPP(_891049, _891047))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891051, tc_HOL_Obool)), _891049), _891045), _891047)))], (6653 ^ _784416) ^ [_891200, _891202, _891204, _891206] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_891200, tc_HOL_Obool)), _891202), _891204), _891206)), -(hBOOL(hAPP(_891202, _891206))), -(hBOOL(hAPP(_891204, _891206)))], (6663 ^ _784416) ^ [_891342, _891344] : [hBOOL(hAPP(hAPP(c_member(_891342), _891344), c_Orderings_Obot__class_Obot(tc_fun(_891342, tc_HOL_Obool))))], (6665 ^ _784416) ^ [_891379, _891381, _891383, _891385] : [6666 ^ _784416 : [(6667 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_891379), _891381), _891383))], (6669 ^ _784416) ^ [] : [_891381 = _891385]], -(hBOOL(hAPP(hAPP(c_member(_891379), _891381), hAPP(hAPP(c_Set_Oinsert(_891379), _891385), _891383))))], (6673 ^ _784416) ^ [_891544, _891546, _891548, _891550] : [hBOOL(hAPP(hAPP(c_member(_891544), _891546), hAPP(hAPP(c_Set_Oinsert(_891544), _891548), _891550))), -(_891546 = _891548), -(hBOOL(hAPP(hAPP(c_member(_891544), _891546), _891550)))], (6683 ^ _784416) ^ [_891684, _891686, _891688, _891690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891684, tc_HOL_Obool)), _891686), _891688)), hBOOL(hAPP(hAPP(c_member(_891684), _891690), _891686)), -(hBOOL(hAPP(hAPP(c_member(_891684), _891690), _891688)))], (6693 ^ _784416) ^ [_891869, _891871, _891873, _891875, _891877, _891879] : [_891869 = hAPP(_891871, _891873), hBOOL(hAPP(hAPP(c_member(_891875), _891873), _891877)), -(hBOOL(hAPP(hAPP(c_member(_891879), _891869), hAPP(c_Set_Oimage(_891875, _891879, _891871), _891877))))], (6703 ^ _784416) ^ [_892062, _892064, _892066, _892068] : [6704 ^ _784416 : [(6705 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_892062), _892064), _892066))], (6707 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_892062), _892064), _892068))]], -(hBOOL(hAPP(hAPP(c_member(_892062), _892064), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892062, tc_HOL_Obool)), _892068), _892066))))], (6711 ^ _784416) ^ [_892247, _892249, _892251, _892253] : [hBOOL(hAPP(hAPP(c_member(_892247), _892249), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892247, tc_HOL_Obool)), _892251), _892253))), -(hBOOL(hAPP(hAPP(c_member(_892247), _892249), _892251))), -(hBOOL(hAPP(hAPP(c_member(_892247), _892249), _892253)))], (6721 ^ _784416) ^ [_892407, _892409, _892411] : [hBOOL(hAPP(_892407, _892409)), -(hBOOL(hAPP(hAPP(c_member(_892411), _892409), hAPP(c_Set_OCollect(_892411), _892407))))], (6727 ^ _784416) ^ [_892514, _892516, _892518, _892520] : [hBOOL(hAPP(_892514, _892516)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892518, tc_HOL_Obool)), _892520), _892514), _892516)))], (6733 ^ _784416) ^ [_892625, _892627, _892629, _892631] : [hBOOL(hAPP(_892625, _892627)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892629, tc_HOL_Obool)), _892625), _892631), _892627)))], (6739 ^ _784416) ^ [_892757, _892759, _892761, _892763] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892757, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_892757, tc_fun(_892757, tc_HOL_Obool), tc_HOL_Obool), c_member(_892757)), _892759)), hAPP(hAPP(c_COMBC(_892757, tc_fun(_892757, tc_HOL_Obool), tc_HOL_Obool), c_member(_892757)), _892761)), _892763)), -(hBOOL(hAPP(hAPP(c_member(_892757), _892763), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892757, tc_HOL_Obool)), _892759), _892761))))], (6745 ^ _784416) ^ [_892956, _892958, _892960, _892962] : [hBOOL(hAPP(hAPP(c_member(_892956), _892962), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892956, tc_HOL_Obool)), _892958), _892960))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_892956, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_892956, tc_fun(_892956, tc_HOL_Obool), tc_HOL_Obool), c_member(_892956)), _892958)), hAPP(hAPP(c_COMBC(_892956, tc_fun(_892956, tc_HOL_Obool), tc_HOL_Obool), c_member(_892956)), _892960)), _892962)))], (6751 ^ _784416) ^ [_893179, _893181, _893183] : [hBOOL(hAPP(hAPP(c_member(_893179), _893181), hAPP(c_fequal, _893183))), -(_893181 = _893183)], (6757 ^ _784416) ^ [_893274, _893276, _893278] : [_893276 = _893278, -(hBOOL(hAPP(hAPP(c_member(_893274), _893276), hAPP(c_fequal, _893278))))], (6763 ^ _784416) ^ [_893375, _893377, _893379, _893381, _893383, _893385] : [hBOOL(hAPP(hAPP(c_member(_893375), _893377), _893379)), _893381 = hAPP(_893383, _893377), -(hBOOL(hAPP(hAPP(c_member(_893385), _893381), hAPP(c_Set_Oimage(_893375, _893385, _893383), _893379))))], (6773 ^ _784416) ^ [_893568, _893570, _893572, _893574] : [_893568 = _893570, hBOOL(hAPP(hAPP(c_member(_893572), _893570), _893574)), -(hBOOL(hAPP(hAPP(c_member(_893572), _893568), _893574)))], (6783 ^ _784416) ^ [_893733, _893735, _893737, _893739] : [_893733 = _893735, 6786 ^ _784416 : [(6787 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_893737), _893733), _893739)), -(hBOOL(hAPP(hAPP(c_member(_893737), _893735), _893739)))], (6793 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_893737), _893735), _893739)), -(hBOOL(hAPP(hAPP(c_member(_893737), _893733), _893739)))]]], (6799 ^ _784416) ^ [_893994, _893996, _893998, _894000] : [_893994 = _893996, 6802 ^ _784416 : [(6803 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_893998), _894000), _893994)), -(hBOOL(hAPP(hAPP(c_member(_893998), _894000), _893996)))], (6809 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_893998), _894000), _893996)), -(hBOOL(hAPP(hAPP(c_member(_893998), _894000), _893994)))]]], (6815 ^ _784416) ^ [_894255, _894257, _894259, _894261, _894263] : [hBOOL(hAPP(hAPP(c_member(_894255), _894257), _894259)), -(hBOOL(hAPP(hAPP(c_member(_894261), hAPP(_894263, _894257)), hAPP(c_Set_Oimage(_894255, _894261, _894263), _894259))))], (6821 ^ _784416) ^ [_894386, _894388, _894390, _894392] : [hBOOL(hAPP(hAPP(c_member(_894386), _894388), _894390)), -(hBOOL(hAPP(hAPP(c_member(_894386), _894388), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894386, tc_HOL_Obool)), _894392), _894390))))], (6827 ^ _784416) ^ [_894517, _894519, _894521, _894523] : [hBOOL(hAPP(hAPP(c_member(_894517), _894519), _894521)), -(hBOOL(hAPP(hAPP(c_member(_894517), _894519), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894517, tc_HOL_Obool)), _894521), _894523))))], (6852 ^ _784416) ^ [_895091, _895093, _895095, _895097] : [6856 ^ _784416 : [(6857 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_895091), 6855 ^ [_895091, _895093, _895095, _895097]), _895093)))], (6859 ^ _784416) ^ [] : [hBOOL(hAPP(_895097, 6855 ^ [_895091, _895093, _895095, _895097]))]], 6861 ^ _784416 : [(6862 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_895091), 6860 ^ [_895091, _895093, _895095, _895097]), _895095)))], (6864 ^ _784416) ^ [] : [hBOOL(hAPP(_895097, 6860 ^ [_895091, _895093, _895095, _895097]))]], 6865 ^ _784416 : [(6866 ^ _784416) ^ [_895424] : [hBOOL(hAPP(hAPP(c_member(_895091), _895424), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895091, tc_HOL_Obool)), _895093), _895095))), -(hBOOL(hAPP(_895097, _895424)))]]], (6833 ^ _784416) ^ [_894669, _894671, _894673, _894675] : [6835 ^ _784416 : [(6836 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_894669), 6834 ^ [_894669, _894671, _894673, _894675]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894669, tc_HOL_Obool)), _894671), _894673))))], (6838 ^ _784416) ^ [] : [hBOOL(hAPP(_894675, 6834 ^ [_894669, _894671, _894673, _894675]))]], 6839 ^ _784416 : [(6840 ^ _784416) ^ [_894889] : [hBOOL(hAPP(hAPP(c_member(_894669), _894889), _894671)), -(hBOOL(hAPP(_894675, _894889)))], (6846 ^ _784416) ^ [_894986] : [hBOOL(hAPP(hAPP(c_member(_894669), _894986), _894673)), -(hBOOL(hAPP(_894675, _894986)))]]], (6872 ^ _784416) ^ [_895576, _895578, _895580, _895582] : [6873 ^ _784416 : [(6874 ^ _784416) ^ [_895686] : [hBOOL(hAPP(hAPP(c_member(_895576), _895686), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895576, tc_HOL_Obool)), _895578), _895580))), hBOOL(hAPP(_895582, _895686))]], 6882 ^ _784416 : [(6883 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_895576), 6881 ^ [_895576, _895578, _895580, _895582]), _895578)))], (6885 ^ _784416) ^ [] : [-(hBOOL(hAPP(_895582, 6881 ^ [_895576, _895578, _895580, _895582])))]], 6887 ^ _784416 : [(6888 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_895576), 6886 ^ [_895576, _895578, _895580, _895582]), _895580)))], (6890 ^ _784416) ^ [] : [-(hBOOL(hAPP(_895582, 6886 ^ [_895576, _895578, _895580, _895582])))]]], (6892 ^ _784416) ^ [_895975, _895977, _895979, _895981] : [6906 ^ _784416 : [(6907 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_895975), 6905 ^ [_895975, _895977, _895979, _895981]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895975, tc_HOL_Obool)), _895977), _895979))))], (6909 ^ _784416) ^ [] : [-(hBOOL(hAPP(_895981, 6905 ^ [_895975, _895977, _895979, _895981])))]], 6893 ^ _784416 : [(6894 ^ _784416) ^ [_896088] : [hBOOL(hAPP(hAPP(c_member(_895975), _896088), _895977)), hBOOL(hAPP(_895981, _896088))], (6900 ^ _784416) ^ [_896184] : [hBOOL(hAPP(hAPP(c_member(_895975), _896184), _895979)), hBOOL(hAPP(_895981, _896184))]]], (6911 ^ _784416) ^ [_896378, _896380, _896382, _896384] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896378, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896378, tc_HOL_Obool)), _896380), _896382)), _896384) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896378, tc_HOL_Obool)), _896380), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896378, tc_HOL_Obool)), _896382), _896384)))], (6923 ^ _784416) ^ [_896626, _896628, _896630, _896632] : [6924 ^ _784416 : [(6925 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_896626), _896628), _896630))], (6927 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_896626), _896628), _896632))]], -(hBOOL(hAPP(hAPP(c_member(_896626), _896628), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896626, tc_HOL_Obool)), _896630), _896632))))], (6913 ^ _784416) ^ [_896472, _896474, _896476, _896478] : [hBOOL(hAPP(hAPP(c_member(_896472), _896474), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896472, tc_HOL_Obool)), _896476), _896478))), -(hBOOL(hAPP(hAPP(c_member(_896472), _896474), _896476))), -(hBOOL(hAPP(hAPP(c_member(_896472), _896474), _896478)))], (6931 ^ _784416) ^ [_896811, _896813, _896815, _896817, _896819] : [-(hAPP(c_Set_Oimage(_896811, _896813, _896815), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896811, tc_HOL_Obool)), _896817), _896819)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896813, tc_HOL_Obool)), hAPP(c_Set_Oimage(_896811, _896813, _896815), _896817)), hAPP(c_Set_Oimage(_896811, _896813, _896815), _896819)))], (6933 ^ _784416) ^ [_896885, _896887, _896889, _896891] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896885, tc_HOL_Obool)), _896887), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896885, tc_HOL_Obool)), _896889), _896891)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896885, tc_HOL_Obool)), _896889), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_896885, tc_HOL_Obool)), _896887), _896891)))], (6935 ^ _784416) ^ [_896982, _896984, _896986, _896988, _896990] : [hBOOL(hAPP(hAPP(c_member(_896982), _896984), hAPP(c_Set_Oimage(_896986, _896982, _896988), _896990))), 6939 ^ _784416 : [(6940 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_896986), 6938 ^ [_896982, _896984, _896986, _896988, _896990]), _896990)))], (6942 ^ _784416) ^ [] : [-(_896984 = hAPP(_896988, 6938 ^ [_896982, _896984, _896986, _896988, _896990]))]]], (6944 ^ _784416) ^ [_897166, _897168, _897170, _897172, _897174] : [-(hBOOL(hAPP(hAPP(c_member(_897166), _897168), hAPP(c_Set_Oimage(_897170, _897166, _897172), _897174)))), 6945 ^ _784416 : [(6946 ^ _784416) ^ [_897236] : [hBOOL(hAPP(hAPP(c_member(_897170), _897236), _897174)), _897168 = hAPP(_897172, _897236)]]], (6954 ^ _784416) ^ [_897384, _897386, _897388] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897384, tc_HOL_Obool)), _897386), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897384, tc_HOL_Obool)), _897386), _897388)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897384, tc_HOL_Obool)), _897386), _897388))], (6956 ^ _784416) ^ [_897444, _897446, _897448] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897444, tc_HOL_Obool)), _897446), _897448) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897444, tc_HOL_Obool)), _897448), _897446))], (6958 ^ _784416) ^ [_897511, _897513, _897515] : [hBOOL(hAPP(hAPP(c_member(_897511), _897513), _897515)), -(hBOOL(hAPP(_897515, _897513)))], (6964 ^ _784416) ^ [_897604, _897606, _897608] : [hBOOL(hAPP(_897608, _897606)), -(hBOOL(hAPP(hAPP(c_member(_897604), _897606), _897608)))], (6970 ^ _784416) ^ [_897703, _897705] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897703, tc_HOL_Obool)), _897705), _897705) = _897705)], (6972 ^ _784416) ^ [_897739, _897741, _897743, _897745, _897747] : [hBOOL(hAPP(hAPP(c_member(_897739), _897741), _897743)), -(hAPP(hAPP(c_Set_Oinsert(_897745), hAPP(_897747, _897741)), hAPP(c_Set_Oimage(_897739, _897745, _897747), _897743)) = hAPP(c_Set_Oimage(_897739, _897745, _897747), _897743))], (6978 ^ _784416) ^ [_897886, _897888, _897890, _897892, _897894, _897896] : [-(hAPP(c_Set_Oimage(_897886, _897888, _897890), hAPP(c_Set_Oimage(_897892, _897886, _897894), _897896)) = hAPP(c_Set_Oimage(_897892, _897888, hAPP(hAPP(c_COMBB(_897886, _897888, _897892), _897890), _897894)), _897896))], (6980 ^ _784416) ^ [_897950, _897952, _897954, _897956, _897958] : [c_Orderings_Oorder__class_Omono(tc_fun(_897950, tc_HOL_Obool), tc_fun(_897952, tc_HOL_Obool), _897954), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897952, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897952, tc_HOL_Obool)), hAPP(_897954, _897956)), hAPP(_897954, _897958))), hAPP(_897954, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_897950, tc_HOL_Obool)), _897956), _897958)))))], (6986 ^ _784416) ^ [_898147, _898149, _898151] : [hAPP(hAPP(c_COMBC(_898147, tc_fun(_898147, tc_HOL_Obool), tc_HOL_Obool), c_member(_898147)), _898149) = hAPP(hAPP(c_COMBC(_898147, tc_fun(_898147, tc_HOL_Obool), tc_HOL_Obool), c_member(_898147)), _898151), -(_898149 = _898151)], (6992 ^ _784416) ^ [_898282, _898284, _898286] : [_898284 = _898286, -(hAPP(hAPP(c_COMBC(_898282, tc_fun(_898282, tc_HOL_Obool), tc_HOL_Obool), c_member(_898282)), _898284) = hAPP(hAPP(c_COMBC(_898282, tc_fun(_898282, tc_HOL_Obool), tc_HOL_Obool), c_member(_898282)), _898286))], (6998 ^ _784416) ^ [_898423, _898425, _898427] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898423, tc_HOL_Obool)), _898425), _898427) = hAPP(c_Set_OCollect(_898423), hAPP(hAPP(c_COMBS(_898423, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _898423), c_fdisj), hAPP(hAPP(c_COMBC(_898423, tc_fun(_898423, tc_HOL_Obool), tc_HOL_Obool), c_member(_898423)), _898425))), hAPP(hAPP(c_COMBC(_898423, tc_fun(_898423, tc_HOL_Obool), tc_HOL_Obool), c_member(_898423)), _898427))))], (7000 ^ _784416) ^ [_898516, _898518, _898520, _898522] : [class_Orderings_Oorder(_898516), class_Orderings_Oorder(_898518), c_Orderings_Oorder__class_Omono(_898518, _898516, _898520), -(c_Orderings_Oord__class_OLeast(_898516, hAPP(hAPP(c_COMBC(_898516, tc_fun(_898516, tc_HOL_Obool), tc_HOL_Obool), c_member(_898516)), hAPP(c_Set_Oimage(_898518, _898516, _898520), _898522))) = hAPP(_898520, c_Orderings_Oord__class_OLeast(_898518, hAPP(hAPP(c_COMBC(_898518, tc_fun(_898518, tc_HOL_Obool), tc_HOL_Obool), c_member(_898518)), _898522)))), 7013 ^ _784416 : [(7014 ^ _784416) ^ [_898800] : [hBOOL(hAPP(hAPP(c_member(_898518), _898800), _898522)), 7018 ^ _784416 : [(7019 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898518), 7017 ^ [_898516, _898518, _898520, _898522, _898800]), _898522)))], (7021 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898518), _898800), 7017 ^ [_898516, _898518, _898520, _898522, _898800]))]]]]], (7025 ^ _784416) ^ [_899114, _899116, _899118, _899120] : [hAPP(c_Set_Oimage(_899114, _899116, _899118), _899120) = c_Orderings_Obot__class_Obot(tc_fun(_899116, tc_HOL_Obool)), -(_899120 = c_Orderings_Obot__class_Obot(tc_fun(_899114, tc_HOL_Obool)))], (7031 ^ _784416) ^ [_899225, _899227, _899229, _899231] : [_899231 = c_Orderings_Obot__class_Obot(tc_fun(_899225, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_899225, _899227, _899229), _899231) = c_Orderings_Obot__class_Obot(tc_fun(_899227, tc_HOL_Obool)))], (7037 ^ _784416) ^ [_899342, _899344, _899346] : [-(hAPP(c_Set_Oimage(_899342, _899344, _899346), c_Orderings_Obot__class_Obot(tc_fun(_899342, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_899344, tc_HOL_Obool)))], (7039 ^ _784416) ^ [_899407, _899409, _899411, _899413] : [c_Orderings_Obot__class_Obot(tc_fun(_899407, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_899409, _899407, _899411), _899413), -(_899413 = c_Orderings_Obot__class_Obot(tc_fun(_899409, tc_HOL_Obool)))], (7045 ^ _784416) ^ [_899518, _899520, _899522, _899524] : [_899524 = c_Orderings_Obot__class_Obot(tc_fun(_899520, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_899518, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_899520, _899518, _899522), _899524))], (7051 ^ _784416) ^ [_899635, _899637, _899639, _899641, _899643] : [-(hAPP(c_Set_Oimage(_899635, _899637, _899639), hAPP(hAPP(c_Set_Oinsert(_899635), _899641), _899643)) = hAPP(hAPP(c_Set_Oinsert(_899637), hAPP(_899639, _899641)), hAPP(c_Set_Oimage(_899635, _899637, _899639), _899643)))], (7053 ^ _784416) ^ [_899699, _899701, _899703, _899705, _899707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899699, tc_HOL_Obool)), _899701), _899703)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899705, tc_HOL_Obool)), hAPP(c_Set_Oimage(_899699, _899705, _899707), _899701)), hAPP(c_Set_Oimage(_899699, _899705, _899707), _899703))))], (7059 ^ _784416) ^ [_899874, _899876, _899878, _899880, _899882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899874, tc_HOL_Obool)), _899876), hAPP(c_Set_Oimage(_899878, _899874, _899880), _899882))), 7063 ^ _784416 : [(7064 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899878, tc_HOL_Obool)), 7062 ^ [_899874, _899876, _899878, _899880, _899882]), _899882)))], (7066 ^ _784416) ^ [] : [-(_899876 = hAPP(c_Set_Oimage(_899878, _899874, _899880), 7062 ^ [_899874, _899876, _899878, _899880, _899882]))]]], (7068 ^ _784416) ^ [_900078, _900080, _900082, _900084, _900086] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900078, tc_HOL_Obool)), _900080), hAPP(c_Set_Oimage(_900082, _900078, _900084), _900086)))), 7069 ^ _784416 : [(7070 ^ _784416) ^ [_900158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900082, tc_HOL_Obool)), _900158), _900086)), _900080 = hAPP(c_Set_Oimage(_900082, _900078, _900084), _900158)]]], (7078 ^ _784416) ^ [_900323, _900325, _900327, _900329, _900331] : [hBOOL(hAPP(hAPP(c_member(_900323), _900325), _900327)), -(hAPP(c_Set_Oimage(_900323, _900329, hAPP(c_COMBK(_900329, _900323), _900331)), _900327) = hAPP(hAPP(c_Set_Oinsert(_900329), _900331), c_Orderings_Obot__class_Obot(tc_fun(_900329, tc_HOL_Obool))))], (7084 ^ _784416) ^ [_900490, _900492, _900494] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900490, tc_HOL_Obool)), _900492), _900494) = c_Orderings_Obot__class_Obot(tc_fun(_900490, tc_HOL_Obool)), 7087 ^ _784416 : [(7088 ^ _784416) ^ [] : [-(_900492 = c_Orderings_Obot__class_Obot(tc_fun(_900490, tc_HOL_Obool)))], (7090 ^ _784416) ^ [] : [-(_900494 = c_Orderings_Obot__class_Obot(tc_fun(_900490, tc_HOL_Obool)))]]], (7092 ^ _784416) ^ [_900643, _900645, _900647] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900643, tc_HOL_Obool)), _900645), _900647) = c_Orderings_Obot__class_Obot(tc_fun(_900643, tc_HOL_Obool))), _900645 = c_Orderings_Obot__class_Obot(tc_fun(_900643, tc_HOL_Obool)), _900647 = c_Orderings_Obot__class_Obot(tc_fun(_900643, tc_HOL_Obool))], (7102 ^ _784416) ^ [_900830, _900832] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900830, tc_HOL_Obool)), _900832), c_Orderings_Obot__class_Obot(tc_fun(_900830, tc_HOL_Obool))) = _900832)], (7104 ^ _784416) ^ [_900871, _900873] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900871, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_900871, tc_HOL_Obool))), _900873) = _900873)], (7106 ^ _784416) ^ [_900912, _900914, _900916, _900918] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900912, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_900912), _900914), _900916)), _900918) = hAPP(hAPP(c_Set_Oinsert(_900912), _900914), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900912, tc_HOL_Obool)), _900916), _900918)))], (7108 ^ _784416) ^ [_900979, _900981, _900983, _900985] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900979, tc_HOL_Obool)), _900981), hAPP(hAPP(c_Set_Oinsert(_900979), _900983), _900985)) = hAPP(hAPP(c_Set_Oinsert(_900979), _900983), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_900979, tc_HOL_Obool)), _900981), _900985)))], (7110 ^ _784416) ^ [_901046, _901048, _901050, _901052, _901054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901046, tc_HOL_Obool)), _901048), _901050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901046, tc_HOL_Obool)), _901052), _901054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901046, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901046, tc_HOL_Obool)), _901048), _901052)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901046, tc_HOL_Obool)), _901050), _901054))))], (7120 ^ _784416) ^ [_901291, _901293, _901295, _901297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901291, tc_HOL_Obool)), _901293), _901295)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901291, tc_HOL_Obool)), _901297), _901295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901291, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901291, tc_HOL_Obool)), _901293), _901297)), _901295)))], (7130 ^ _784416) ^ [_901510, _901512, _901514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901510, tc_HOL_Obool)), _901512), _901514)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901510, tc_HOL_Obool)), _901514), _901512) = _901514)], (7136 ^ _784416) ^ [_901631, _901633, _901635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901631, tc_HOL_Obool)), _901633), _901635)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901631, tc_HOL_Obool)), _901633), _901635) = _901635)], (7142 ^ _784416) ^ [_901770, _901772, _901774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901770, tc_HOL_Obool)), _901772), _901774)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901770, tc_HOL_Obool)), _901772), _901774) = _901774)], (7148 ^ _784416) ^ [_901887, _901889, _901891] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_901887, tc_HOL_Obool)), _901889), _901891) = _901891, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901887, tc_HOL_Obool)), _901889), _901891)))], (7154 ^ _784416) ^ [_902010, _902012, _902014] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902010, tc_HOL_Obool)), _902012), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_902010, tc_HOL_Obool)), _902014), _902012))))], (7156 ^ _784416) ^ [_902058, _902060, _902062] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902058, tc_HOL_Obool)), _902060), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_902058, tc_HOL_Obool)), _902060), _902062))))], (7158 ^ _784416) ^ [_902133, _902135, _902137, _902139, _902141, _902143] : [c_Predicate_Oinv__imagep(_902133, _902135, _902137, _902139, _902141, _902143), -(hBOOL(hAPP(hAPP(_902137, hAPP(_902139, _902141)), hAPP(_902139, _902143))))], (7164 ^ _784416) ^ [_902244, _902246, _902248, _902250, _902252, _902254] : [hBOOL(hAPP(hAPP(_902248, hAPP(_902250, _902252)), hAPP(_902250, _902254))), -(c_Predicate_Oinv__imagep(_902244, _902246, _902248, _902250, _902252, _902254))], (7170 ^ _784416) ^ [_902361, _902363, _902365] : [_902361 = c_Orderings_Obot__class_Obot(tc_fun(_902363, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_902363), _902365), _902361))], (7176 ^ _784416) ^ [_902477, _902479] : [hBOOL(hAPP(hAPP(c_member(_902477), _902479), c_Orderings_Obot__class_Obot(tc_fun(_902477, tc_HOL_Obool))))], (7178 ^ _784416) ^ [_902529, _902531] : [7179 ^ _784416 : [(7180 ^ _784416) ^ [_902582] : [hBOOL(hAPP(hAPP(c_member(_902529), _902582), _902531))]], _902531 = c_Orderings_Obot__class_Obot(tc_fun(_902529, tc_HOL_Obool))], (7184 ^ _784416) ^ [_902638, _902640] : [-(_902640 = c_Orderings_Obot__class_Obot(tc_fun(_902638, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_902638), 7187 ^ [_902638, _902640]), _902640)))], (7191 ^ _784416) ^ [_902704, _902706] : [-(hBOOL(hAPP(hAPP(c_member(_902704), 7192 ^ [_902704, _902706]), _902706))), -(_902706 = c_Orderings_Obot__class_Obot(tc_fun(_902704, tc_HOL_Obool)))], (7198 ^ _784416) ^ [_902755, _902757] : [_902757 = c_Orderings_Obot__class_Obot(tc_fun(_902755, tc_HOL_Obool)), 7201 ^ _784416 : [(7202 ^ _784416) ^ [_902835] : [hBOOL(hAPP(hAPP(c_member(_902755), _902835), _902757))]]], (7204 ^ _784416) ^ [_902871, _902873, _902875] : [hBOOL(hAPP(hAPP(c_member(_902871), _902873), _902875)), -(hAPP(hAPP(c_Set_Oinsert(_902871), _902873), _902875) = _902875)], (7210 ^ _784416) ^ [_902980, _902982, _902984, _902986] : [hBOOL(hAPP(hAPP(c_member(_902980), _902982), _902984)), -(hBOOL(hAPP(hAPP(c_member(_902980), _902982), hAPP(hAPP(c_Set_Oinsert(_902980), _902986), _902984))))], (7216 ^ _784416) ^ [_903104, _903106, _903108, _903110] : [-(hBOOL(hAPP(hAPP(c_member(_903104), _903106), _903108))), -(hBOOL(hAPP(hAPP(c_member(_903104), _903106), _903110))), 7223 ^ _784416 : [(7224 ^ _784416) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_903104), _903106), _903108) = hAPP(hAPP(c_Set_Oinsert(_903104), _903106), _903110), -(_903108 = _903110)], (7230 ^ _784416) ^ [] : [_903108 = _903110, -(hAPP(hAPP(c_Set_Oinsert(_903104), _903106), _903108) = hAPP(hAPP(c_Set_Oinsert(_903104), _903106), _903110))]]], (7246 ^ _784416) ^ [_903604, _903606, _903608, _903610] : [7247 ^ _784416 : [(7248 ^ _784416) ^ [] : [_903606 = _903608], (7250 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_903604), _903606), _903610))]], -(hBOOL(hAPP(hAPP(c_member(_903604), _903606), hAPP(hAPP(c_Set_Oinsert(_903604), _903608), _903610))))], (7236 ^ _784416) ^ [_903470, _903472, _903474, _903476] : [hBOOL(hAPP(hAPP(c_member(_903470), _903472), hAPP(hAPP(c_Set_Oinsert(_903470), _903474), _903476))), -(_903472 = _903474), -(hBOOL(hAPP(hAPP(c_member(_903470), _903472), _903476)))], (7254 ^ _784416) ^ [_903769, _903771, _903773] : [-(hBOOL(hAPP(hAPP(c_member(_903769), _903771), hAPP(hAPP(c_Set_Oinsert(_903769), _903771), _903773))))], (7256 ^ _784416) ^ [_903811, _903813, _903815, _903817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903811, tc_HOL_Obool)), _903813), _903815)), hBOOL(hAPP(hAPP(c_member(_903811), _903817), _903813)), -(hBOOL(hAPP(hAPP(c_member(_903811), _903817), _903815)))], (7266 ^ _784416) ^ [_903996, _903998, _904000, _904002] : [hBOOL(hAPP(hAPP(c_member(_903996), _903998), _904000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903996, tc_HOL_Obool)), _904000), _904002)), -(hBOOL(hAPP(hAPP(c_member(_903996), _903998), _904002)))], (7276 ^ _784416) ^ [_904181, _904183, _904185, _904187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904181, tc_HOL_Obool)), _904183), _904185)), hBOOL(hAPP(hAPP(c_member(_904181), _904187), _904183)), -(hBOOL(hAPP(hAPP(c_member(_904181), _904187), _904185)))], (7286 ^ _784416) ^ [_904366, _904368, _904370] : [-(hAPP(c_Set_OCollect(_904366), hAPP(hAPP(c_COMBS(_904366, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _904366), c_fdisj), _904368)), _904370)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904366, tc_HOL_Obool)), hAPP(c_Set_OCollect(_904366), _904368)), hAPP(c_Set_OCollect(_904366), _904370)))], (7288 ^ _784416) ^ [_904439, _904441, _904443, _904445, _904447] : [class_Orderings_Oorder(_904439), class_Orderings_Oorder(_904441), c_Orderings_Oorder__class_Omono(_904441, _904439, _904443), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904441), _904445), _904447)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904439), hAPP(_904443, _904445)), hAPP(_904443, _904447))))], (7306 ^ _784416) ^ [_904751, _904753] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_904751, tc_HOL_Obool)), _904753)), -(hBOOL(hAPP(hAPP(c_member(_904751), _904753), c_Orderings_Obot__class_Obot(tc_fun(_904751, tc_HOL_Obool)))))], (7312 ^ _784416) ^ [_904862, _904864] : [hBOOL(hAPP(hAPP(c_member(_904862), _904864), c_Orderings_Obot__class_Obot(tc_fun(_904862, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_904862, tc_HOL_Obool)), _904864)))], (7318 ^ _784416) ^ [_904979, _904981, _904983] : [hBOOL(hAPP(hAPP(c_member(_904979), _904981), hAPP(c_Set_OCollect(_904979), _904983))), -(hBOOL(hAPP(_904983, _904981)))], (7324 ^ _784416) ^ [_905086, _905088, _905090] : [hBOOL(hAPP(hAPP(c_member(_905086), _905088), hAPP(c_Set_OCollect(_905086), _905090))), -(hBOOL(hAPP(_905090, _905088)))], (7330 ^ _784416) ^ [_905211, _905213, _905215] : [hBOOL(hAPP(hAPP(c_member(_905211), _905213), hAPP(c_Set_OCollect(_905211), _905215))), -(hBOOL(hAPP(_905215, _905213)))], (7336 ^ _784416) ^ [_905314, _905316, _905318] : [hBOOL(hAPP(_905318, _905316)), -(hBOOL(hAPP(hAPP(c_member(_905314), _905316), hAPP(c_Set_OCollect(_905314), _905318))))], (7342 ^ _784416) ^ [_905423, _905425] : [-(hAPP(c_Set_OCollect(_905423), hAPP(hAPP(c_COMBC(_905423, tc_fun(_905423, tc_HOL_Obool), tc_HOL_Obool), c_member(_905423)), _905425)) = _905425)], (7344 ^ _784416) ^ [_905486, _905488, _905490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905486, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_905486, tc_fun(_905486, tc_HOL_Obool), tc_HOL_Obool), c_member(_905486)), _905488)), hAPP(hAPP(c_COMBC(_905486, tc_fun(_905486, tc_HOL_Obool), tc_HOL_Obool), c_member(_905486)), _905490))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905486, tc_HOL_Obool)), _905488), _905490)))], (7350 ^ _784416) ^ [_905661, _905663, _905665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905661, tc_HOL_Obool)), _905663), _905665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905661, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_905661, tc_fun(_905661, tc_HOL_Obool), tc_HOL_Obool), c_member(_905661)), _905663)), hAPP(hAPP(c_COMBC(_905661, tc_fun(_905661, tc_HOL_Obool), tc_HOL_Obool), c_member(_905661)), _905665))))], (7356 ^ _784416) ^ [_905842, _905844, _905846] : [-(hAPP(hAPP(c_Set_Oinsert(_905842), _905844), _905846) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_905842, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_905842), _905844), c_Orderings_Obot__class_Obot(tc_fun(_905842, tc_HOL_Obool)))), _905846))], (7358 ^ _784416) ^ [_905901, _905903, _905905] : [hBOOL(hAPP(hAPP(c_member(_905901), _905903), hAPP(hAPP(c_Set_Oinsert(_905901), _905905), c_Orderings_Obot__class_Obot(tc_fun(_905901, tc_HOL_Obool))))), -(_905903 = _905905)], (7364 ^ _784416) ^ [_906038, _906040, _906042] : [hBOOL(hAPP(hAPP(c_member(_906038), _906040), hAPP(hAPP(c_Set_Oinsert(_906038), _906042), c_Orderings_Obot__class_Obot(tc_fun(_906038, tc_HOL_Obool))))), -(_906040 = _906042)], (7370 ^ _784416) ^ [_906153, _906155, _906157] : [_906155 = _906157, -(hBOOL(hAPP(hAPP(c_member(_906153), _906155), hAPP(hAPP(c_Set_Oinsert(_906153), _906157), c_Orderings_Obot__class_Obot(tc_fun(_906153, tc_HOL_Obool))))))], (7376 ^ _784416) ^ [_906273, _906275, _906277, _906279] : [-(hBOOL(hAPP(hAPP(c_member(_906273), _906275), _906277))), 7379 ^ _784416 : [(7380 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906273, tc_HOL_Obool)), _906277), hAPP(hAPP(c_Set_Oinsert(_906273), _906275), _906279))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906273, tc_HOL_Obool)), _906277), _906279)))], (7386 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906273, tc_HOL_Obool)), _906277), _906279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906273, tc_HOL_Obool)), _906277), hAPP(hAPP(c_Set_Oinsert(_906273), _906275), _906279))))]]], (7392 ^ _784416) ^ [_906602, _906604, _906606, _906608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906602, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_906602), _906604), _906606)), _906608)), 7395 ^ _784416 : [(7396 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_906602), _906604), _906608)))], (7398 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906602, tc_HOL_Obool)), _906606), _906608)))]]], (7400 ^ _784416) ^ [_906775, _906777, _906779, _906781] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906775, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_906775), _906777), _906779)), _906781))), hBOOL(hAPP(hAPP(c_member(_906775), _906777), _906781)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906775, tc_HOL_Obool)), _906779), _906781))], (7410 ^ _784416) ^ [_906984, _906986, _906988, _906990, _906992] : [class_Lattices_Osemilattice__sup(_906984), class_Lattices_Osemilattice__sup(_906986), c_Orderings_Oorder__class_Omono(_906986, _906984, _906988), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906984), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_906984), hAPP(_906988, _906990)), hAPP(_906988, _906992))), hAPP(_906988, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_906986), _906990), _906992)))))], (7424 ^ _784416) ^ [_907247, _907249, _907251, _907253, _907255] : [class_Lattices_Olattice(_907247), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907249, _907247)), _907251), _907253), _907255) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_907247), hAPP(_907251, _907255)), hAPP(_907253, _907255)))], (7430 ^ _784416) ^ [_907384, _907386, _907388, _907390, _907392] : [class_Lattices_Olattice(_907384), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_907386, _907384)), _907388), _907390), _907392) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_907384), hAPP(_907388, _907392)), hAPP(_907390, _907392)))], (7436 ^ _784416) ^ [_907521, _907523, _907525] : [class_Lattices_Obounded__lattice__bot(_907521), 7439 ^ _784416 : [(7440 ^ _784416) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_907521), _907523), _907525) = c_Orderings_Obot__class_Obot(_907521), 7443 ^ _784416 : [(7444 ^ _784416) ^ [] : [-(_907523 = c_Orderings_Obot__class_Obot(_907521))], (7446 ^ _784416) ^ [] : [-(_907525 = c_Orderings_Obot__class_Obot(_907521))]]], (7448 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_907521), _907523), _907525) = c_Orderings_Obot__class_Obot(_907521)), _907523 = c_Orderings_Obot__class_Obot(_907521), _907525 = c_Orderings_Obot__class_Obot(_907521)]]], (7458 ^ _784416) ^ [_907848, _907850] : [class_Lattices_Obounded__lattice__bot(_907848), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_907848), _907850), c_Orderings_Obot__class_Obot(_907848)) = _907850)], (7464 ^ _784416) ^ [_907943, _907945] : [class_Lattices_Obounded__lattice__bot(_907943), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_907943), c_Orderings_Obot__class_Obot(_907943)), _907945) = _907945)], (7470 ^ _784416) ^ [_908038, _908040, _908042, _908044] : [class_Lattices_Osemilattice__sup(_908038), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908038), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_908038), _908040), _908042)), _908044)), 7477 ^ _784416 : [(7478 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908038), _908040), _908044)))], (7480 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908038), _908042), _908044)))]]], (7482 ^ _784416) ^ [_908261, _908263, _908265, _908267, _908269] : [class_Lattices_Osemilattice__sup(_908261), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908261), _908263), _908265)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908261), _908267), _908269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908261), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_908261), _908263), _908267)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_908261), _908265), _908269))))], (7496 ^ _784416) ^ [_908532, _908534, _908536, _908538] : [class_Lattices_Osemilattice__sup(_908532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908532), _908534), _908536)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908532), _908538), _908536)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908532), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_908532), _908534), _908538)), _908536)))], (7510 ^ _784416) ^ [_908781, _908783, _908785, _908787] : [class_Lattices_Osemilattice__sup(_908781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908781), _908783), _908785)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908781), _908787), _908785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908781), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_908781), _908783), _908787)), _908785)))], (7524 ^ _784416) ^ [_909030, _909032, _909034] : [class_Lattices_Osemilattice__sup(_909030), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909030), _909032), _909034)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909030), _909034), _909032) = _909034)], (7534 ^ _784416) ^ [_909191, _909193, _909195] : [class_Lattices_Osemilattice__sup(_909191), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909191), _909193), _909195)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909191), _909193), _909195) = _909195)], (7544 ^ _784416) ^ [_909352, _909354, _909356, _909358] : [class_Lattices_Osemilattice__sup(_909352), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909352), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909352), _909354), _909356)), _909358) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909352), _909354), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909352), _909356), _909358)))], (7550 ^ _784416) ^ [_909495, _909497, _909499, _909501] : [class_Lattices_Olattice(_909495), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909495), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909495), _909497), _909499)), _909501) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909495), _909497), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909495), _909499), _909501)))], (7556 ^ _784416) ^ [_909638, _909640, _909642, _909644] : [class_Lattices_Osemilattice__sup(_909638), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909638), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909638), _909640), _909642)), _909644) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909638), _909640), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909638), _909642), _909644)))], (7562 ^ _784416) ^ [_909781, _909783, _909785, _909787] : [class_Lattices_Osemilattice__sup(_909781), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909781), _909783), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909781), _909785), _909787)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909781), _909785), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909781), _909783), _909787)))], (7568 ^ _784416) ^ [_909924, _909926, _909928, _909930] : [class_Lattices_Olattice(_909924), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909924), _909926), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909924), _909928), _909930)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909924), _909928), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_909924), _909926), _909930)))], (7574 ^ _784416) ^ [_910067, _910069, _910071, _910073] : [class_Lattices_Osemilattice__sup(_910067), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910067), _910069), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910067), _910071), _910073)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910067), _910071), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910067), _910069), _910073)))], (7580 ^ _784416) ^ [_910210, _910212, _910214] : [class_Lattices_Osemilattice__sup(_910210), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910210), _910212), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910210), _910212), _910214)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910210), _910212), _910214))], (7586 ^ _784416) ^ [_910335, _910337, _910339] : [class_Lattices_Olattice(_910335), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910335), _910337), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910335), _910337), _910339)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910335), _910337), _910339))], (7592 ^ _784416) ^ [_910460, _910462, _910464] : [class_Lattices_Osemilattice__sup(_910460), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910460), _910462), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910460), _910462), _910464)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910460), _910462), _910464))], (7598 ^ _784416) ^ [_910585, _910587, _910589] : [class_Lattices_Osemilattice__sup(_910585), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910585), _910587), _910589) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910585), _910589), _910587))], (7604 ^ _784416) ^ [_910694, _910696, _910698] : [class_Lattices_Olattice(_910694), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910694), _910696), _910698) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910694), _910698), _910696))], (7610 ^ _784416) ^ [_910803, _910805, _910807] : [class_Lattices_Osemilattice__sup(_910803), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910803), _910805), _910807) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910803), _910807), _910805))], (7616 ^ _784416) ^ [_910912, _910914] : [class_Lattices_Osemilattice__sup(_910912), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_910912), _910914), _910914) = _910914)], (7622 ^ _784416) ^ [_911003, _911005] : [class_Lattices_Osemilattice__sup(_911003), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_911003), _911005), _911005) = _911005)], (7628 ^ _784416) ^ [_911094, _911096, _911098] : [class_Lattices_Olattice(_911094), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911094), _911096), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_911094), _911096), _911098))))], (7634 ^ _784416) ^ [_911201, _911203, _911205] : [class_Lattices_Osemilattice__sup(_911201), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911201), _911203), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_911201), _911203), _911205))))], (7640 ^ _784416) ^ [_911308, _911310, _911312] : [class_Lattices_Olattice(_911308), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911308), _911310), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_911308), _911312), _911310))))], (7646 ^ _784416) ^ [_911415, _911417, _911419] : [class_Lattices_Osemilattice__sup(_911415), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911415), _911417), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_911415), _911419), _911417))))], (7652 ^ _784416) ^ [_911522, _911524, _911526] : [class_Lattices_Osemilattice__sup(_911522), 7655 ^ _784416 : [(7656 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911522), _911524), _911526)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_911522), _911524), _911526) = _911526)], (7662 ^ _784416) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_911522), _911524), _911526) = _911526, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911522), _911524), _911526)))]]], (7668 ^ _784416) ^ [_911778, _911780, _911782, _911784] : [class_Lattices_Osemilattice__sup(_911778), 7671 ^ _784416 : [(7672 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911778), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_911778), _911780), _911782)), _911784)), 7675 ^ _784416 : [(7676 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911778), _911780), _911784)))], (7678 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911778), _911782), _911784)))]]], (7680 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911778), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_911778), _911780), _911782)), _911784))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911778), _911780), _911784)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_911778), _911782), _911784))]]], (7690 ^ _784416) ^ [_912158, _912160, _912162, _912164] : [class_Lattices_Osemilattice__sup(_912158), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912158), _912160), _912162)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912158), _912160), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_912158), _912162), _912164))))], (7700 ^ _784416) ^ [_912337, _912339, _912341, _912343] : [class_Lattices_Osemilattice__sup(_912337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912337), _912339), _912341)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912337), _912339), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_912337), _912343), _912341))))], (7710 ^ _784416) ^ [_912516, _912518, _912520, _912522, _912524] : [class_Orderings_Oorder(_912516), c_Orderings_Oorder__class_Omono(_912516, tc_fun(_912518, tc_HOL_Obool), _912520), -(c_Orderings_Oorder__class_Omono(_912516, tc_fun(_912518, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_912516, tc_fun(_912518, tc_HOL_Obool), tc_fun(_912518, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_912518, tc_HOL_Obool), tc_fun(tc_fun(_912518, tc_HOL_Obool), tc_fun(_912518, tc_HOL_Obool)), _912516), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912518, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_912516, tc_fun(_912518, tc_HOL_Obool), tc_fun(_912518, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_912518, tc_HOL_Obool), tc_fun(tc_fun(_912518, tc_HOL_Obool), tc_fun(_912518, tc_HOL_Obool)), _912516), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912518, tc_HOL_Obool))), _912520)), _912522))), _912524)))], (7720 ^ _784416) ^ [_912843, _912845] : [-(hAPP(c_Set_Oimage(_912843, _912843, c_COMBI(_912843)), _912845) = _912845)], (7722 ^ _784416) ^ [_912877, _912879, _912881, _912883, _912885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912877, tc_HOL_Obool)), hAPP(c_Set_Oimage(_912879, _912877, _912881), _912883)), _912885)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_912877, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_912879, tc_HOL_Obool), tc_fun(_912877, tc_HOL_Obool), c_Set_Oimage(_912879, _912877, _912881)), hAPP(c_Set_OPow(_912879), _912883))), hAPP(c_Set_OPow(_912877), _912885))))], (7744 ^ _784416) ^ [_913427, _913429, _913431, _913433] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913427, tc_HOL_Obool)), _913429), hAPP(hAPP(c_Set_Oinsert(_913427), _913431), _913433)))), 7747 ^ _784416 : [(7748 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_913427), _913431), _913429)))], (7750 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913427, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913427, tc_HOL_Obool)), _913429), hAPP(hAPP(c_Set_Oinsert(_913427), _913431), c_Orderings_Obot__class_Obot(tc_fun(_913427, tc_HOL_Obool))))), _913433))]], 7751 ^ _784416 : [(7752 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_913427), _913431), _913429))], (7754 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913427, tc_HOL_Obool)), _913429), _913433))]]], (7728 ^ _784416) ^ [_913095, _913097, _913099, _913101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913095, tc_HOL_Obool)), _913097), hAPP(hAPP(c_Set_Oinsert(_913095), _913099), _913101))), 7731 ^ _784416 : [(7732 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_913095), _913099), _913097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913095, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913095, tc_HOL_Obool)), _913097), hAPP(hAPP(c_Set_Oinsert(_913095), _913099), c_Orderings_Obot__class_Obot(tc_fun(_913095, tc_HOL_Obool))))), _913101)))], (7738 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_913095), _913099), _913097))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913095, tc_HOL_Obool)), _913097), _913101)))]]], (7758 ^ _784416) ^ [_913791, _913793, _913795, _913797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913791, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913791, tc_HOL_Obool)), _913793), hAPP(hAPP(c_Set_Oinsert(_913791), _913795), c_Orderings_Obot__class_Obot(tc_fun(_913791, tc_HOL_Obool))))), _913797)), hBOOL(hAPP(hAPP(c_member(_913791), _913795), _913793)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913791, tc_HOL_Obool)), _913793), hAPP(hAPP(c_Set_Oinsert(_913791), _913795), _913797))))], (7768 ^ _784416) ^ [_914046, _914048, _914050, _914052, _914054] : [hBOOL(hAPP(hAPP(c_member(_914046), _914048), hAPP(c_Set_Oimage(_914050, _914046, _914052), _914054))), 7772 ^ _784416 : [(7773 ^ _784416) ^ [] : [-(_914048 = hAPP(_914052, 7771 ^ [_914046, _914048, _914050, _914052, _914054]))], (7775 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_914050), 7771 ^ [_914046, _914048, _914050, _914052, _914054]), _914054)))]]], (7777 ^ _784416) ^ [_914238, _914240, _914242, _914244, _914246] : [7779 ^ _784416 : [(7780 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_914238), 7778 ^ [_914238, _914240, _914242, _914244, _914246]), _914240)))], (7782 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_914242), hAPP(_914244, 7778 ^ [_914238, _914240, _914242, _914244, _914246])), _914246))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914242, tc_HOL_Obool)), hAPP(c_Set_Oimage(_914238, _914242, _914244), _914240)), _914246)))], (7786 ^ _784416) ^ [_914498, _914500, _914502] : [hBOOL(hAPP(c_Predicate_OPowp(_914498, hAPP(hAPP(c_COMBC(_914498, tc_fun(_914498, tc_HOL_Obool), tc_HOL_Obool), c_member(_914498)), _914500)), _914502)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_914498, tc_HOL_Obool)), _914502), hAPP(c_Set_OPow(_914498), _914500))))], (7792 ^ _784416) ^ [_914643, _914645, _914647] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_914643, tc_HOL_Obool)), _914647), hAPP(c_Set_OPow(_914643), _914645))), -(hBOOL(hAPP(c_Predicate_OPowp(_914643, hAPP(hAPP(c_COMBC(_914643, tc_fun(_914643, tc_HOL_Obool), tc_HOL_Obool), c_member(_914643)), _914645)), _914647)))], (7798 ^ _784416) ^ [_914794, _914796, _914798, _914800, _914802] : [_914794 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_914796, tc_HOL_Obool), _914798), c_Orderings_Oorder__class_Omono(tc_fun(_914796, tc_HOL_Obool), tc_fun(_914796, tc_HOL_Obool), _914798), hBOOL(hAPP(hAPP(c_member(_914796), _914800), _914802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914796, tc_HOL_Obool)), _914802), hAPP(_914798, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_914796, tc_HOL_Obool)), _914802), _914794)))), -(hBOOL(hAPP(hAPP(c_member(_914796), _914800), _914794)))], (7816 ^ _784416) ^ [_915153, _915155, _915157, _915159] : [c_Orderings_Oorder__class_Omono(tc_fun(_915153, tc_HOL_Obool), tc_fun(_915153, tc_HOL_Obool), _915155), hBOOL(hAPP(hAPP(c_member(_915153), _915157), _915159)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_915153, tc_HOL_Obool)), _915159), hAPP(_915155, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915153, tc_HOL_Obool)), _915159), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_915153, tc_HOL_Obool), _915155))))), -(hBOOL(hAPP(hAPP(c_member(_915153), _915157), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_915153, tc_HOL_Obool), _915155))))], (7830 ^ _784416) ^ [_915460, _915462, _915464, _915466, _915468, _915470] : [-(hAPP(c_Set_Oimage(_915460, _915462, hAPP(hAPP(c_COMBS(_915460, _915462, _915462), hAPP(hAPP(c_COMBS(_915460, _915462, tc_fun(_915462, _915462)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_915462, tc_fun(_915462, _915462)), _915460), c_If(_915462)), _915464)), _915466)), _915468)), _915470) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915462, tc_HOL_Obool)), hAPP(c_Set_Oimage(_915460, _915462, _915466), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_915460, tc_HOL_Obool)), _915470), hAPP(c_Set_OCollect(_915460), _915464)))), hAPP(c_Set_Oimage(_915460, _915462, _915468), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_915460, tc_HOL_Obool)), _915470), hAPP(c_Set_OCollect(_915460), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _915460), c_fNot), _915464))))))], (7832 ^ _784416) ^ [_915608, _915610, _915612, _915614] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_915608, tc_HOL_Obool)), _915610), _915612), _915614)), 7835 ^ _784416 : [(7836 ^ _784416) ^ [] : [-(hBOOL(hAPP(_915610, _915614)))], (7838 ^ _784416) ^ [] : [-(hBOOL(hAPP(_915612, _915614)))]]], (7840 ^ _784416) ^ [_915753, _915755, _915757, _915759] : [hBOOL(hAPP(_915753, _915755)), hBOOL(hAPP(_915757, _915755)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_915759, tc_HOL_Obool)), _915753), _915757), _915755)))], (7850 ^ _784416) ^ [_915924, _915926, _915928, _915930] : [hBOOL(hAPP(hAPP(c_member(_915924), _915926), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_915924, tc_HOL_Obool)), _915928), _915930))), 7853 ^ _784416 : [(7854 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_915924), _915926), _915928)))], (7856 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_915924), _915926), _915930)))]]], (7858 ^ _784416) ^ [_916099, _916101, _916103, _916105] : [hBOOL(hAPP(hAPP(c_member(_916099), _916101), _916103)), hBOOL(hAPP(hAPP(c_member(_916099), _916101), _916105)), -(hBOOL(hAPP(hAPP(c_member(_916099), _916101), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_916099, tc_HOL_Obool)), _916103), _916105))))], (7868 ^ _784416) ^ [_916300, _916302, _916304, _916306] : [hBOOL(hAPP(hAPP(c_member(_916300), _916302), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916300, tc_HOL_Obool)), _916304), _916306))), 7871 ^ _784416 : [(7872 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916300), _916302), _916304)))], (7874 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_916300), _916302), _916306))]]], (7876 ^ _784416) ^ [_916479, _916481, _916483, _916485] : [hBOOL(hAPP(hAPP(c_member(_916479), _916481), _916483)), -(hBOOL(hAPP(hAPP(c_member(_916479), _916481), _916485))), -(hBOOL(hAPP(hAPP(c_member(_916479), _916481), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916479, tc_HOL_Obool)), _916483), _916485))))], (7886 ^ _784416) ^ [_916639, _916641, _916643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916639, tc_HOL_Obool)), _916641), _916643)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_916639, tc_HOL_Obool)), _916641), hAPP(c_Set_OPow(_916639), _916643))))], (7892 ^ _784416) ^ [_916768, _916770, _916772, _916774, _916776] : [class_Lattices_Olattice(_916768), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_916770, _916768)), _916772), _916774), _916776) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_916768), hAPP(_916772, _916776)), hAPP(_916774, _916776)))], (7898 ^ _784416) ^ [_916905, _916907, _916909, _916911, _916913] : [class_Groups_Ominus(_916905), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916907, _916905)), _916909), _916911), _916913) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_916905), hAPP(_916909, _916913)), hAPP(_916911, _916913)))], (7904 ^ _784416) ^ [_917042, _917044, _917046, _917048] : [class_Lattices_Osemilattice__inf(_917042), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917042), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917042), _917044), _917046)), _917048) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917042), _917044), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917042), _917046), _917048)))], (7910 ^ _784416) ^ [_917185, _917187, _917189, _917191] : [class_Lattices_Olattice(_917185), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917185), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917185), _917187), _917189)), _917191) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917185), _917187), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917185), _917189), _917191)))], (7916 ^ _784416) ^ [_917328, _917330, _917332, _917334] : [class_Lattices_Osemilattice__inf(_917328), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917328), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917328), _917330), _917332)), _917334) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917328), _917330), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917328), _917332), _917334)))], (7922 ^ _784416) ^ [_917471, _917473, _917475, _917477] : [class_Lattices_Osemilattice__inf(_917471), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917471), _917473), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917471), _917475), _917477)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917471), _917475), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917471), _917473), _917477)))], (7928 ^ _784416) ^ [_917614, _917616, _917618, _917620] : [class_Lattices_Olattice(_917614), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917614), _917616), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917614), _917618), _917620)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917614), _917618), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917614), _917616), _917620)))], (7934 ^ _784416) ^ [_917757, _917759, _917761, _917763] : [class_Lattices_Osemilattice__inf(_917757), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917757), _917759), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917757), _917761), _917763)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917757), _917761), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917757), _917759), _917763)))], (7940 ^ _784416) ^ [_917900, _917902, _917904] : [class_Lattices_Osemilattice__inf(_917900), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917900), _917902), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917900), _917902), _917904)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_917900), _917902), _917904))], (7946 ^ _784416) ^ [_918025, _918027, _918029] : [class_Lattices_Olattice(_918025), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918025), _918027), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918025), _918027), _918029)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918025), _918027), _918029))], (7952 ^ _784416) ^ [_918150, _918152, _918154] : [class_Lattices_Osemilattice__inf(_918150), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918150), _918152), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918150), _918152), _918154)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918150), _918152), _918154))], (7958 ^ _784416) ^ [_918275, _918277, _918279] : [class_Lattices_Osemilattice__inf(_918275), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918275), _918277), _918279) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918275), _918279), _918277))], (7964 ^ _784416) ^ [_918384, _918386, _918388] : [class_Lattices_Olattice(_918384), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918384), _918386), _918388) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918384), _918388), _918386))], (7970 ^ _784416) ^ [_918493, _918495, _918497] : [class_Lattices_Osemilattice__inf(_918493), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918493), _918495), _918497) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918493), _918497), _918495))], (7976 ^ _784416) ^ [_918602, _918604, _918606, _918608, _918610] : [class_Lattices_Olattice(_918602), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_918604, _918602)), _918606), _918608), _918610) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918602), hAPP(_918606, _918610)), hAPP(_918608, _918610)))], (7982 ^ _784416) ^ [_918739, _918741, _918743, _918745, _918747] : [class_Groups_Ominus(_918739), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918741, _918739)), _918743), _918745), _918747) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_918739), hAPP(_918743, _918747)), hAPP(_918745, _918747)))], (7988 ^ _784416) ^ [_918876, _918878] : [class_Lattices_Osemilattice__inf(_918876), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918876), _918878), _918878) = _918878)], (7994 ^ _784416) ^ [_918967, _918969] : [class_Lattices_Osemilattice__inf(_918967), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_918967), _918969), _918969) = _918969)], (8000 ^ _784416) ^ [_919058, _919060, _919062, _919064] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919058, tc_HOL_Obool)), _919060), _919062), _919064)), -(hBOOL(hAPP(_919062, _919064)))], (8006 ^ _784416) ^ [_919169, _919171, _919173, _919175] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919169, tc_HOL_Obool)), _919171), _919173), _919175)), -(hBOOL(hAPP(_919171, _919175)))], (8012 ^ _784416) ^ [_919280, _919282, _919284, _919286] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919280, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919280, tc_HOL_Obool)), _919282), _919284)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919280, tc_HOL_Obool)), _919286), _919284)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919280, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919280, tc_HOL_Obool)), _919282), _919284)), _919286))], (8014 ^ _784416) ^ [_919364, _919366, _919368, _919370] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919364, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919364, tc_HOL_Obool)), _919366), _919368)), _919370) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919364, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919364, tc_HOL_Obool)), _919366), _919370)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919364, tc_HOL_Obool)), _919368), _919370)))], (8016 ^ _784416) ^ [_919448, _919450, _919452, _919454] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919448, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919448, tc_HOL_Obool)), _919450), _919452)), _919454) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919448, tc_HOL_Obool)), _919450), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919448, tc_HOL_Obool)), _919452), _919454)))], (8018 ^ _784416) ^ [_919521, _919523, _919525, _919527] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919521, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919521, tc_HOL_Obool)), _919523), _919525)), _919527) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919521, tc_HOL_Obool)), _919523), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919521, tc_HOL_Obool)), _919525), _919527)))], (8020 ^ _784416) ^ [_919594, _919596, _919598] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919594, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919594, tc_HOL_Obool)), _919596), _919598)), _919598) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919594, tc_HOL_Obool)), _919596), _919598))], (8022 ^ _784416) ^ [_919654, _919656, _919658, _919660] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919654, tc_HOL_Obool)), _919656), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919654, tc_HOL_Obool)), _919658), _919660)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919654, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919654, tc_HOL_Obool)), _919656), _919658)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919654, tc_HOL_Obool)), _919656), _919660)))], (8024 ^ _784416) ^ [_919738, _919740, _919742, _919744] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919738, tc_HOL_Obool)), _919740), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919738, tc_HOL_Obool)), _919742), _919744)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919738, tc_HOL_Obool)), _919742), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919738, tc_HOL_Obool)), _919740), _919744)))], (8026 ^ _784416) ^ [_919811, _919813, _919815] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919811, tc_HOL_Obool)), _919813), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919811, tc_HOL_Obool)), _919813), _919815)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919811, tc_HOL_Obool)), _919813), _919815))], (8028 ^ _784416) ^ [_919871, _919873, _919875] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919871, tc_HOL_Obool)), _919873), _919875) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919871, tc_HOL_Obool)), _919875), _919873))], (8030 ^ _784416) ^ [_919920, _919922] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919920, tc_HOL_Obool)), _919922), _919922) = _919922)], (8032 ^ _784416) ^ [_919956, _919958, _919960] : [-(hAPP(c_Set_OPow(_919956), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_919956, tc_HOL_Obool)), _919958), _919960)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_919956, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_919956), _919958)), hAPP(c_Set_OPow(_919956), _919960)))], (8034 ^ _784416) ^ [_920035, _920037] : [hAPP(c_Set_OPow(_920035), _920037) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_920035, tc_HOL_Obool), tc_HOL_Obool))], (8036 ^ _784416) ^ [_920073, _920075] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_920073, tc_HOL_Obool)), _920075), hAPP(c_Set_OPow(_920073), _920075))))], (8038 ^ _784416) ^ [_920129, _920131, _920133] : [hAPP(c_Set_Oimage(_920131, tc_fun(_920131, tc_HOL_Obool), _920129), _920133) = hAPP(c_Set_OPow(_920131), _920133)], (8040 ^ _784416) ^ [_920171, _920173, _920175] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_920171, tc_HOL_Obool)), _920173), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920171, tc_HOL_Obool)), _920175), _920173)) = c_Orderings_Obot__class_Obot(tc_fun(_920171, tc_HOL_Obool)))], (8042 ^ _784416) ^ [_920225, _920227, _920229] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_920225, tc_HOL_Obool)), _920227), _920229) = c_Orderings_Obot__class_Obot(tc_fun(_920225, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920225, tc_HOL_Obool)), _920227), _920229) = _920227)], (8048 ^ _784416) ^ [_920358, _920360, _920362] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920358, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920358, tc_HOL_Obool)), _920360), _920362)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_920358, tc_HOL_Obool)), _920360), _920362)) = _920360)], (8050 ^ _784416) ^ [_920418, _920420, _920422, _920424] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920418, tc_HOL_Obool)), _920420), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920418, tc_HOL_Obool)), _920422), _920424)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_920418, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920418, tc_HOL_Obool)), _920420), _920422)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920418, tc_HOL_Obool)), _920420), _920424)))], (8052 ^ _784416) ^ [_920502, _920504, _920506, _920508] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920502, tc_HOL_Obool)), _920504), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_920502, tc_HOL_Obool)), _920506), _920508)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920502, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920502, tc_HOL_Obool)), _920504), _920506)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920502, tc_HOL_Obool)), _920504), _920508)))], (8054 ^ _784416) ^ [_920586, _920588, _920590] : [class_Complete__Lattice_Ocomplete__lattice(_920586), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920586), _920588), hAPP(_920590, _920588))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920586), _920588), c_Inductive_Ocomplete__lattice__class_Ogfp(_920586, _920590))))], (8064 ^ _784416) ^ [_920757, _920759] : [class_Complete__Lattice_Ocomplete__lattice(_920757), c_Orderings_Oorder__class_Omono(_920757, _920757, _920759), -(c_Inductive_Ocomplete__lattice__class_Ogfp(_920757, _920759) = hAPP(_920759, c_Inductive_Ocomplete__lattice__class_Ogfp(_920757, _920759)))], (8074 ^ _784416) ^ [_920904, _920906, _920908] : [class_Complete__Lattice_Ocomplete__lattice(_920904), _920906 = c_Inductive_Ocomplete__lattice__class_Ogfp(_920904, _920908), c_Orderings_Oorder__class_Omono(_920904, _920904, _920908), -(_920906 = hAPP(_920908, _920906))], (8088 ^ _784416) ^ [_921103, _921105, _921107, _921109] : [class_Lattices_Osemilattice__inf(_921103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921103), _921105), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921103), _921107), _921109))), 8095 ^ _784416 : [(8096 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921103), _921105), _921107)))], (8098 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921103), _921105), _921109)))]]], (8100 ^ _784416) ^ [_921326, _921328, _921330, _921332, _921334] : [class_Lattices_Osemilattice__inf(_921326), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921326), _921328), _921330)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921326), _921332), _921334)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921326), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921326), _921328), _921332)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921326), _921330), _921334))))], (8114 ^ _784416) ^ [_921597, _921599, _921601, _921603] : [class_Lattices_Osemilattice__inf(_921597), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921597), _921599), _921601)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921597), _921599), _921603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921597), _921599), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921597), _921601), _921603))))], (8128 ^ _784416) ^ [_921846, _921848, _921850, _921852] : [class_Lattices_Osemilattice__inf(_921846), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921846), _921848), _921850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921846), _921848), _921852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921846), _921848), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_921846), _921850), _921852))))], (8142 ^ _784416) ^ [_922095, _922097, _922099] : [class_Lattices_Osemilattice__inf(_922095), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922095), _922097), _922099)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_922095), _922099), _922097) = _922097)], (8152 ^ _784416) ^ [_922256, _922258, _922260] : [class_Lattices_Osemilattice__inf(_922256), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922256), _922258), _922260)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_922256), _922258), _922260) = _922258)], (8162 ^ _784416) ^ [_922417, _922419, _922421, _922423] : [class_Lattices_Osemilattice__inf(_922417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922417), _922419), _922421)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922417), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_922417), _922423), _922419)), _922421)))], (8172 ^ _784416) ^ [_922596, _922598, _922600, _922602] : [class_Lattices_Osemilattice__inf(_922596), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922596), _922598), _922600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922596), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_922596), _922598), _922602)), _922600)))], (8182 ^ _784416) ^ [_922775, _922777, _922779, _922781] : [class_Lattices_Osemilattice__inf(_922775), 8185 ^ _784416 : [(8186 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922775), _922777), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_922775), _922779), _922781))), 8189 ^ _784416 : [(8190 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922775), _922777), _922779)))], (8192 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922775), _922777), _922781)))]]], (8194 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922775), _922777), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_922775), _922779), _922781)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922775), _922777), _922779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922775), _922777), _922781))]]], (8204 ^ _784416) ^ [_923155, _923157, _923159] : [class_Lattices_Osemilattice__inf(_923155), 8207 ^ _784416 : [(8208 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923155), _923157), _923159)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923155), _923157), _923159) = _923157)], (8214 ^ _784416) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923155), _923157), _923159) = _923157, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923155), _923157), _923159)))]]], (8220 ^ _784416) ^ [_923411, _923413, _923415] : [class_Lattices_Osemilattice__inf(_923411), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923411), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923411), _923413), _923415)), _923415)))], (8226 ^ _784416) ^ [_923518, _923520, _923522] : [class_Lattices_Olattice(_923518), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923518), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923518), _923520), _923522)), _923522)))], (8232 ^ _784416) ^ [_923625, _923627, _923629] : [class_Lattices_Osemilattice__inf(_923625), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923625), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923625), _923627), _923629)), _923627)))], (8238 ^ _784416) ^ [_923732, _923734, _923736] : [class_Lattices_Olattice(_923732), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923732), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923732), _923734), _923736)), _923734)))], (8244 ^ _784416) ^ [_923839, _923841] : [class_Lattices_Obounded__lattice__bot(_923839), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923839), _923841), c_Orderings_Obot__class_Obot(_923839)) = c_Orderings_Obot__class_Obot(_923839))], (8250 ^ _784416) ^ [_923938, _923940] : [class_Lattices_Obounded__lattice__bot(_923938), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_923938), c_Orderings_Obot__class_Obot(_923938)), _923940) = c_Orderings_Obot__class_Obot(_923938))], (8256 ^ _784416) ^ [_924037, _924039, _924041] : [class_Lattices_Olattice(_924037), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924037), _924039), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924037), _924039), _924041)) = _924039)], (8262 ^ _784416) ^ [_924146, _924148, _924150] : [class_Lattices_Olattice(_924146), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924146), _924148), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924146), _924148), _924150)) = _924148)], (8268 ^ _784416) ^ [_924255, _924257, _924259, _924261] : [class_Lattices_Odistrib__lattice(_924255), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924255), _924257), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924255), _924259), _924261)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924255), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924255), _924257), _924259)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924255), _924257), _924261)))], (8274 ^ _784416) ^ [_924414, _924416, _924418, _924420] : [class_Lattices_Odistrib__lattice(_924414), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924414), _924416), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924414), _924418), _924420)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924414), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924414), _924416), _924418)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924414), _924416), _924420)))], (8280 ^ _784416) ^ [_924573, _924575, _924577, _924579] : [class_Lattices_Odistrib__lattice(_924573), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924573), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924573), _924575), _924577)), _924579) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924573), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924573), _924575), _924579)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924573), _924577), _924579)))], (8286 ^ _784416) ^ [_924732, _924734, _924736, _924738] : [class_Lattices_Odistrib__lattice(_924732), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924732), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924732), _924734), _924736)), _924738) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_924732), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924732), _924734), _924738)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_924732), _924736), _924738)))], (8292 ^ _784416) ^ [_924891, _924893, _924895, _924897] : [hBOOL(hAPP(hAPP(c_member(_924891), _924893), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924891, tc_HOL_Obool)), _924895), _924897))), hBOOL(hAPP(hAPP(c_member(_924891), _924893), _924897))], (8298 ^ _784416) ^ [_925023, _925025, _925027, _925029] : [hBOOL(hAPP(hAPP(c_member(_925023), _925025), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925023, tc_HOL_Obool)), _925027), _925029))), -(hBOOL(hAPP(hAPP(c_member(_925023), _925025), _925027)))], (8304 ^ _784416) ^ [_925175, _925177, _925179, _925181] : [hBOOL(hAPP(hAPP(c_member(_925175), _925177), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925175, tc_HOL_Obool)), _925179), _925181))), 8307 ^ _784416 : [(8308 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_925175), _925177), _925179)))], (8310 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_925175), _925177), _925181))]]], (8312 ^ _784416) ^ [_925350, _925352, _925354, _925356] : [-(hBOOL(hAPP(hAPP(c_member(_925350), _925352), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925350, tc_HOL_Obool)), _925354), _925356)))), hBOOL(hAPP(hAPP(c_member(_925350), _925352), _925354)), -(hBOOL(hAPP(hAPP(c_member(_925350), _925352), _925356)))], (8322 ^ _784416) ^ [_925556, _925558, _925560, _925562] : [hBOOL(hAPP(hAPP(c_member(_925556), _925558), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_925556, tc_HOL_Obool)), _925560), _925562))), -(hBOOL(hAPP(hAPP(c_member(_925556), _925558), _925562)))], (8328 ^ _784416) ^ [_925687, _925689, _925691, _925693] : [hBOOL(hAPP(hAPP(c_member(_925687), _925689), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_925687, tc_HOL_Obool)), _925691), _925693))), -(hBOOL(hAPP(hAPP(c_member(_925687), _925689), _925691)))], (8334 ^ _784416) ^ [_925839, _925841, _925843, _925845] : [hBOOL(hAPP(hAPP(c_member(_925839), _925841), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_925839, tc_HOL_Obool)), _925843), _925845))), 8337 ^ _784416 : [(8338 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_925839), _925841), _925843)))], (8340 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_925839), _925841), _925845)))]]], (8342 ^ _784416) ^ [_926006, _926008, _926010, _926012] : [-(hBOOL(hAPP(hAPP(c_member(_926006), _926008), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926006, tc_HOL_Obool)), _926010), _926012)))), hBOOL(hAPP(hAPP(c_member(_926006), _926008), _926010)), hBOOL(hAPP(hAPP(c_member(_926006), _926008), _926012))], (8352 ^ _784416) ^ [_926209, _926211] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_926209, tc_HOL_Obool)), _926211), _926211) = c_Orderings_Obot__class_Obot(tc_fun(_926209, tc_HOL_Obool)))], (8354 ^ _784416) ^ [_926250, _926252] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_926250, tc_HOL_Obool)), _926252), c_Orderings_Obot__class_Obot(tc_fun(_926250, tc_HOL_Obool))) = _926252)], (8356 ^ _784416) ^ [_926291, _926293] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_926291, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_926291, tc_HOL_Obool))), _926293) = c_Orderings_Obot__class_Obot(tc_fun(_926291, tc_HOL_Obool)))], (8372 ^ _784416) ^ [_926669, _926671, _926673] : [8374 ^ _784416 : [(8375 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926669), 8373 ^ [_926669, _926671, _926673]), _926671)))], (8378 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926669), 8376 ^ [_926669, _926671, _926673]), _926673)))], (8380 ^ _784416) ^ [] : [-(8373 ^ [_926669, _926671, _926673] = 8376 ^ [_926669, _926671, _926673])]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926669, tc_HOL_Obool)), _926671), _926673) = c_Orderings_Obot__class_Obot(tc_fun(_926669, tc_HOL_Obool)))], (8358 ^ _784416) ^ [_926355, _926357, _926359] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926355, tc_HOL_Obool)), _926357), _926359) = c_Orderings_Obot__class_Obot(tc_fun(_926355, tc_HOL_Obool)), 8361 ^ _784416 : [(8362 ^ _784416) ^ [_926479] : [hBOOL(hAPP(hAPP(c_member(_926355), _926479), _926357)), 8365 ^ _784416 : [(8366 ^ _784416) ^ [_926569] : [hBOOL(hAPP(hAPP(c_member(_926355), _926569), _926359)), _926479 = _926569]]]]], (8384 ^ _784416) ^ [_926830, _926832] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926830, tc_HOL_Obool)), _926832), c_Orderings_Obot__class_Obot(tc_fun(_926830, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_926830, tc_HOL_Obool)))], (8386 ^ _784416) ^ [_926876, _926878] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_926876, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_926876, tc_HOL_Obool))), _926878) = c_Orderings_Obot__class_Obot(tc_fun(_926876, tc_HOL_Obool)))], (8388 ^ _784416) ^ [_926922, _926924, _926926, _926928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926922, tc_HOL_Obool)), _926924), _926926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926922, tc_HOL_Obool)), _926926), _926928)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_926922, tc_HOL_Obool)), _926926), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_926922, tc_HOL_Obool)), _926928), _926924)) = _926924)], (8398 ^ _784416) ^ [_927143, _927145, _927147, _927149, _927151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927143, tc_HOL_Obool)), _927145), _927147)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927143, tc_HOL_Obool)), _927149), _927151)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927143, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_927143, tc_HOL_Obool)), _927145), _927151)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_927143, tc_HOL_Obool)), _927147), _927149))))], (8408 ^ _784416) ^ [_927388, _927390, _927392] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927388, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_927388, tc_HOL_Obool)), _927390), _927392)), _927390)))], (8410 ^ _784416) ^ [_927436, _927438, _927440, _927442] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_927436, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_927436), _927438), _927440)), hAPP(hAPP(c_Set_Oinsert(_927436), _927438), _927442)) = hAPP(hAPP(c_Set_Oinsert(_927436), _927438), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_927436, tc_HOL_Obool)), _927440), _927442)))], (8412 ^ _784416) ^ [_927511, _927513, _927515, _927517] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_927511, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927511, tc_HOL_Obool)), _927513), _927515)), _927517) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927511, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_927511, tc_HOL_Obool)), _927513), _927517)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_927511, tc_HOL_Obool)), _927515), _927517)))], (8414 ^ _784416) ^ [_927595, _927597, _927599] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927595, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_927595, tc_HOL_Obool)), _927597), _927599)), _927599) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927595, tc_HOL_Obool)), _927597), _927599))], (8416 ^ _784416) ^ [_927655, _927657, _927659] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927655, tc_HOL_Obool)), _927657), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_927655, tc_HOL_Obool)), _927659), _927657)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927655, tc_HOL_Obool)), _927657), _927659))], (8418 ^ _784416) ^ [_927715, _927717, _927719, _927721, _927723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927715, tc_HOL_Obool)), _927717), _927719)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927715, tc_HOL_Obool)), _927721), _927723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927715, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_927715, tc_HOL_Obool)), _927717), _927721)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_927715, tc_HOL_Obool)), _927719), _927723))))], (8428 ^ _784416) ^ [_927960, _927962, _927964, _927966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927960, tc_HOL_Obool)), _927962), _927964)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927960, tc_HOL_Obool)), _927962), _927966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927960, tc_HOL_Obool)), _927962), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_927960, tc_HOL_Obool)), _927964), _927966))))], (8438 ^ _784416) ^ [_928179, _928181, _928183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928179, tc_HOL_Obool)), _928181), _928183)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928179, tc_HOL_Obool)), _928183), _928181) = _928181)], (8444 ^ _784416) ^ [_928300, _928302, _928304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928300, tc_HOL_Obool)), _928302), _928304)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928300, tc_HOL_Obool)), _928302), _928304) = _928302)], (8450 ^ _784416) ^ [_928421, _928423, _928425] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928421, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928421, tc_HOL_Obool)), _928423), _928425)), _928425)))], (8452 ^ _784416) ^ [_928469, _928471, _928473] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928469, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928469, tc_HOL_Obool)), _928471), _928473)), _928471)))], (8454 ^ _784416) ^ [_928517, _928519, _928521, _928523] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928517, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928517, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928517, tc_HOL_Obool)), _928519), _928521)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928517, tc_HOL_Obool)), _928521), _928523))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928517, tc_HOL_Obool)), _928523), _928519)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928517, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928517, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928517, tc_HOL_Obool)), _928519), _928521)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928517, tc_HOL_Obool)), _928521), _928523))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928517, tc_HOL_Obool)), _928523), _928519)))], (8456 ^ _784416) ^ [_928656, _928658, _928660, _928662] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928656, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928656, tc_HOL_Obool)), _928658), _928660)), _928662) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928656, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928656, tc_HOL_Obool)), _928658), _928662)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928656, tc_HOL_Obool)), _928660), _928662)))], (8458 ^ _784416) ^ [_928740, _928742, _928744, _928746] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928740, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928740, tc_HOL_Obool)), _928742), _928744)), _928746) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928740, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928740, tc_HOL_Obool)), _928742), _928746)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928740, tc_HOL_Obool)), _928744), _928746)))], (8460 ^ _784416) ^ [_928824, _928826, _928828, _928830] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928824, tc_HOL_Obool)), _928826), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928824, tc_HOL_Obool)), _928828), _928830)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928824, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928824, tc_HOL_Obool)), _928826), _928828)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928824, tc_HOL_Obool)), _928826), _928830)))], (8462 ^ _784416) ^ [_928908, _928910, _928912, _928914] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928908, tc_HOL_Obool)), _928910), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928908, tc_HOL_Obool)), _928912), _928914)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928908, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928908, tc_HOL_Obool)), _928910), _928912)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_928908, tc_HOL_Obool)), _928910), _928914)))], (8464 ^ _784416) ^ [_928992, _928994] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_928992, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_928992, tc_HOL_Obool))), hAPP(c_Set_OPow(_928992), _928994))))], (8466 ^ _784416) ^ [_929037] : [-(hAPP(c_Set_OPow(_929037), c_Orderings_Obot__class_Obot(tc_fun(_929037, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_929037, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_929037, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_929037, tc_HOL_Obool), tc_HOL_Obool))))], (8468 ^ _784416) ^ [_929094, _929096, _929098] : [-(hAPP(c_Set_OPow(_929094), hAPP(hAPP(c_Set_Oinsert(_929094), _929096), _929098)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_929094, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_929094), _929098)), hAPP(c_Set_Oimage(tc_fun(_929094, tc_HOL_Obool), tc_fun(_929094, tc_HOL_Obool), hAPP(c_Set_Oinsert(_929094), _929096)), hAPP(c_Set_OPow(_929094), _929098))))], (8470 ^ _784416) ^ [_929194, _929196, _929198] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_929194, tc_HOL_Obool)), _929196), hAPP(c_Set_OPow(_929194), _929198))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929194, tc_HOL_Obool)), _929196), _929198)))], (8476 ^ _784416) ^ [_929319, _929321, _929323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929319, tc_HOL_Obool)), _929321), _929323)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_929319, tc_HOL_Obool)), _929321), hAPP(c_Set_OPow(_929319), _929323))))], (8482 ^ _784416) ^ [_929450, _929452, _929454] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_929450, tc_HOL_Obool)), _929452), hAPP(c_Set_OPow(_929450), _929454))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929450, tc_HOL_Obool)), _929452), _929454)))], (8488 ^ _784416) ^ [_929579, _929581, _929583, _929585, _929587] : [hAPP(c_Set_Oimage(_929579, _929581, _929583), _929585) = _929587, -(hAPP(c_Set_Oimage(tc_fun(_929579, tc_HOL_Obool), tc_fun(_929581, tc_HOL_Obool), c_Set_Oimage(_929579, _929581, _929583)), hAPP(c_Set_OPow(_929579), _929585)) = hAPP(c_Set_OPow(_929581), _929587))], (8494 ^ _784416) ^ [_929751, _929753, _929755, _929757] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929751, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_929751, tc_fun(_929751, tc_HOL_Obool), tc_HOL_Obool), c_member(_929751)), _929753)), hAPP(hAPP(c_COMBC(_929751, tc_fun(_929751, tc_HOL_Obool), tc_HOL_Obool), c_member(_929751)), _929755)), _929757)), -(hBOOL(hAPP(hAPP(c_member(_929751), _929757), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929751, tc_HOL_Obool)), _929753), _929755))))], (8500 ^ _784416) ^ [_929950, _929952, _929954, _929956] : [hBOOL(hAPP(hAPP(c_member(_929950), _929956), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929950, tc_HOL_Obool)), _929952), _929954))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929950, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_929950, tc_fun(_929950, tc_HOL_Obool), tc_HOL_Obool), c_member(_929950)), _929952)), hAPP(hAPP(c_COMBC(_929950, tc_fun(_929950, tc_HOL_Obool), tc_HOL_Obool), c_member(_929950)), _929954)), _929956)))], (8506 ^ _784416) ^ [_930155, _930157, _930159, _930161] : [hBOOL(hAPP(hAPP(c_member(_930155), _930157), _930159)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930155, tc_HOL_Obool)), _930159), hAPP(_930161, _930159))), -(hBOOL(hAPP(hAPP(c_member(_930155), _930157), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_930155, tc_HOL_Obool), _930161))))], (8516 ^ _784416) ^ [_930358, _930360, _930362] : [-(hAPP(c_Set_OCollect(_930358), hAPP(hAPP(c_COMBS(_930358, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _930358), c_fconj), _930360)), _930362)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930358, tc_HOL_Obool)), hAPP(c_Set_OCollect(_930358), _930360)), hAPP(c_Set_OCollect(_930358), _930362)))], (8518 ^ _784416) ^ [_930431, _930433] : [-(hAPP(c_Set_OPow(_930431), _930433) = hAPP(c_Set_OCollect(tc_fun(_930431, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_930431, tc_HOL_Obool), tc_fun(_930431, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_930431, tc_HOL_Obool))), _930433)))], (8520 ^ _784416) ^ [_930490, _930492] : [class_Complete__Lattice_Ocomplete__lattice(_930490), c_Orderings_Oorder__class_Omono(_930490, _930490, _930492), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930490), c_Inductive_Ocomplete__lattice__class_Ogfp(_930490, _930492)), hAPP(_930492, c_Inductive_Ocomplete__lattice__class_Ogfp(_930490, _930492)))))], (8530 ^ _784416) ^ [_930651, _930653] : [class_Complete__Lattice_Ocomplete__lattice(_930651), c_Orderings_Oorder__class_Omono(_930651, _930651, _930653), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930651), hAPP(_930653, c_Inductive_Ocomplete__lattice__class_Ogfp(_930651, _930653))), c_Inductive_Ocomplete__lattice__class_Ogfp(_930651, _930653))))], (8540 ^ _784416) ^ [_930812, _930814, _930816, _930818] : [class_Lattices_Olattice(_930812), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930812), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930812), _930814), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930812), _930816), _930818))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930812), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930812), _930814), _930816)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930812), _930814), _930818)))))], (8546 ^ _784416) ^ [_930985, _930987, _930989, _930991] : [class_Lattices_Olattice(_930985), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930985), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930985), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930985), _930987), _930989)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930985), _930987), _930991))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930985), _930987), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_930985), _930989), _930991)))))], (8552 ^ _784416) ^ [_931173, _931175, _931177, _931179] : [hBOOL(hAPP(hAPP(c_member(_931173), _931175), _931177)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931173, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_931173), _931175), _931179)), _931177) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931173, tc_HOL_Obool)), _931179), _931177))], (8558 ^ _784416) ^ [_931322, _931324, _931326, _931328] : [-(hBOOL(hAPP(hAPP(c_member(_931322), _931324), _931326))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931322, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_931322), _931324), _931328)), _931326) = hAPP(hAPP(c_Set_Oinsert(_931322), _931324), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931322, tc_HOL_Obool)), _931328), _931326)))], (8564 ^ _784416) ^ [_931409, _931411, _931413, _931415] : [hBOOL(hAPP(hAPP(c_member(_931409), _931411), _931413)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931409, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_931409), _931411), _931415)), _931413) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931409, tc_HOL_Obool)), _931415), _931413))], (8570 ^ _784416) ^ [_931564, _931566, _931568] : [-(hAPP(hAPP(c_Set_Oinsert(_931564), _931566), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931564, tc_HOL_Obool)), _931568), hAPP(hAPP(c_Set_Oinsert(_931564), _931566), c_Orderings_Obot__class_Obot(tc_fun(_931564, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_931564), _931566), _931568))], (8572 ^ _784416) ^ [_931631, _931633, _931635, _931637] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931631, tc_HOL_Obool)), _931633), hAPP(hAPP(c_Set_Oinsert(_931631), _931635), _931637)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931631, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931631, tc_HOL_Obool)), _931633), hAPP(hAPP(c_Set_Oinsert(_931631), _931635), c_Orderings_Obot__class_Obot(tc_fun(_931631, tc_HOL_Obool))))), _931637))], (8574 ^ _784416) ^ [_931714, _931716, _931718, _931720] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931714, tc_HOL_Obool)), _931716), hAPP(hAPP(c_Set_Oinsert(_931714), _931718), _931720)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931714, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931714, tc_HOL_Obool)), _931716), _931720)), hAPP(hAPP(c_Set_Oinsert(_931714), _931718), c_Orderings_Obot__class_Obot(tc_fun(_931714, tc_HOL_Obool)))))], (8576 ^ _784416) ^ [_931812, _931814, _931816, _931818] : [hBOOL(hAPP(hAPP(c_member(_931812), _931814), _931816)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931812, tc_HOL_Obool)), _931816), hAPP(hAPP(c_Set_Oinsert(_931812), _931814), _931818)) = hAPP(hAPP(c_Set_Oinsert(_931812), _931814), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931812, tc_HOL_Obool)), _931816), _931818)))], (8582 ^ _784416) ^ [_931977, _931979, _931981, _931983] : [-(hBOOL(hAPP(hAPP(c_member(_931977), _931979), _931981))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931977, tc_HOL_Obool)), _931981), hAPP(hAPP(c_Set_Oinsert(_931977), _931979), _931983)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_931977, tc_HOL_Obool)), _931981), _931983))], (8588 ^ _784416) ^ [_932071, _932073, _932075, _932077] : [hBOOL(hAPP(hAPP(c_member(_932071), _932073), _932075)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932071, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_932071), _932073), _932077)), _932075) = hAPP(hAPP(c_Set_Oinsert(_932071), _932073), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932071, tc_HOL_Obool)), _932077), _932075)))], (8594 ^ _784416) ^ [_932236, _932238, _932240, _932242] : [-(hBOOL(hAPP(hAPP(c_member(_932236), _932238), _932240))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932236, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_932236), _932238), _932242)), _932240) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932236, tc_HOL_Obool)), _932242), _932240))], (8600 ^ _784416) ^ [_932311, _932313, _932315, _932317] : [-(hBOOL(hAPP(hAPP(c_member(_932311), _932313), _932315))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932311, tc_HOL_Obool)), _932315), hAPP(hAPP(c_Set_Oinsert(_932311), _932313), _932317)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932311, tc_HOL_Obool)), _932315), _932317))], (8606 ^ _784416) ^ [_932384, _932386, _932388, _932390] : [-(hBOOL(hAPP(hAPP(c_member(_932384), _932386), _932388))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932384, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_932384), _932386), _932390)), _932388) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932384, tc_HOL_Obool)), _932390), _932388))], (8612 ^ _784416) ^ [_932461, _932463, _932465, _932467] : [hBOOL(hAPP(hAPP(c_member(_932461), _932463), _932465)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932461, tc_HOL_Obool)), _932465), hAPP(hAPP(c_Set_Oinsert(_932461), _932463), _932467)) = hAPP(hAPP(c_Set_Oinsert(_932461), _932463), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932461, tc_HOL_Obool)), _932465), _932467)))], (8618 ^ _784416) ^ [_932632, _932634, _932636, _932638] : [hBOOL(hAPP(hAPP(c_member(_932632), _932634), _932636)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932632, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_932632), _932634), _932638)), _932636) = hAPP(hAPP(c_Set_Oinsert(_932632), _932634), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932632, tc_HOL_Obool)), _932638), _932636)))], (8624 ^ _784416) ^ [_932803, _932805, _932807, _932809, _932811] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_932803, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_932803, tc_HOL_Obool)), hAPP(c_Set_Oimage(_932805, _932803, _932807), _932809)), hAPP(c_Set_Oimage(_932805, _932803, _932807), _932811))), hAPP(c_Set_Oimage(_932805, _932803, _932807), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_932805, tc_HOL_Obool)), _932809), _932811)))))], (8626 ^ _784416) ^ [_932887, _932889, _932891, _932893, _932895] : [class_Lattices_Osemilattice__inf(_932887), class_Lattices_Osemilattice__inf(_932889), c_Orderings_Oorder__class_Omono(_932889, _932887, _932891), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932887), hAPP(_932891, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932889), _932893), _932895))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932887), hAPP(_932891, _932893)), hAPP(_932891, _932895)))))], (8640 ^ _784416) ^ [_933171, _933173, _933175, _933177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933171, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_933171, tc_HOL_Obool)), _933173), _933175)), _933177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933171, tc_HOL_Obool)), _933173), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_933171, tc_HOL_Obool)), _933175), _933177))))], (8646 ^ _784416) ^ [_933332, _933334, _933336, _933338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933332, tc_HOL_Obool)), _933334), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_933332, tc_HOL_Obool)), _933336), _933338))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933332, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_933332, tc_HOL_Obool)), _933334), _933336)), _933338)))], (8652 ^ _784416) ^ [_933499, _933501, _933503] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933499, tc_HOL_Obool)), _933501), _933503)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_933499, tc_HOL_Obool)), _933501), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_933499, tc_HOL_Obool)), _933503), _933501)) = _933503)], (8658 ^ _784416) ^ [_933642, _933644, _933646, _933648, _933650] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933642, tc_HOL_Obool)), hAPP(c_Set_Oimage(_933644, _933642, _933646), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933644, tc_HOL_Obool)), _933648), _933650))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933642, tc_HOL_Obool)), hAPP(c_Set_Oimage(_933644, _933642, _933646), _933648)), hAPP(c_Set_Oimage(_933644, _933642, _933646), _933650)))))], (8660 ^ _784416) ^ [_933747, _933749, _933751, _933753] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_933747, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933747, tc_HOL_Obool)), _933749), _933751)), _933753) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933747, tc_HOL_Obool)), _933749), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_933747, tc_HOL_Obool)), _933751), _933753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933747, tc_HOL_Obool)), _933753), _933749)))], (8666 ^ _784416) ^ [_933932, _933934, _933936, _933938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933932, tc_HOL_Obool)), _933938), _933934)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_933932, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933932, tc_HOL_Obool)), _933934), _933936)), _933938) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933932, tc_HOL_Obool)), _933934), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_933932, tc_HOL_Obool)), _933936), _933938)))], (8672 ^ _784416) ^ [_934123, _934125, _934127, _934129, _934131, _934133] : [hBOOL(hAPP(hAPP(c_member(_934123), _934125), _934127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_934129, tc_HOL_Obool)), hAPP(c_Set_Oimage(_934123, _934129, _934131), _934127)), hAPP(_934133, hAPP(c_Set_Oimage(_934123, _934129, _934131), _934127)))), -(hBOOL(hAPP(hAPP(c_member(_934129), hAPP(_934131, _934125)), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_934129, tc_HOL_Obool), _934133))))], (8682 ^ _784416) ^ [_934368, _934370, _934372] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_934368, tc_HOL_Obool)), _934370), _934372) = hAPP(c_Set_OCollect(_934368), hAPP(hAPP(c_COMBS(_934368, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _934368), c_fconj), hAPP(hAPP(c_COMBC(_934368, tc_fun(_934368, tc_HOL_Obool), tc_HOL_Obool), c_member(_934368)), _934370))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _934368), c_fNot), hAPP(hAPP(c_COMBC(_934368, tc_fun(_934368, tc_HOL_Obool), tc_HOL_Obool), c_member(_934368)), _934372)))))], (8684 ^ _784416) ^ [_934471, _934473, _934475, _934477, _934479] : [c_Orderings_Oorder__class_Omono(tc_fun(_934471, tc_HOL_Obool), tc_fun(_934473, tc_HOL_Obool), _934475), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_934473, tc_HOL_Obool)), hAPP(_934475, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934471, tc_HOL_Obool)), _934477), _934479))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934473, tc_HOL_Obool)), hAPP(_934475, _934477)), hAPP(_934475, _934479)))))], (8690 ^ _784416) ^ [_934671, _934673, _934675, _934677] : [hBOOL(hAPP(hAPP(c_member(_934671), _934673), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934671, tc_HOL_Obool)), _934675), hAPP(c_Set_OCollect(_934671), _934677)))), 8693 ^ _784416 : [(8694 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_934671), _934673), _934675)))], (8696 ^ _784416) ^ [] : [-(hBOOL(hAPP(_934677, _934673)))]]], (8698 ^ _784416) ^ [_934838, _934840, _934842, _934844] : [-(hBOOL(hAPP(hAPP(c_member(_934838), _934840), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934838, tc_HOL_Obool)), _934842), hAPP(c_Set_OCollect(_934838), _934844))))), hBOOL(hAPP(hAPP(c_member(_934838), _934840), _934842)), hBOOL(hAPP(_934844, _934840))], (8708 ^ _784416) ^ [_935041, _935043, _935045] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_935041, tc_HOL_Obool)), _935043), _935045) = hAPP(c_Set_OCollect(_935041), hAPP(hAPP(c_COMBS(_935041, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _935041), c_fconj), hAPP(hAPP(c_COMBC(_935041, tc_fun(_935041, tc_HOL_Obool), tc_HOL_Obool), c_member(_935041)), _935043))), hAPP(hAPP(c_COMBC(_935041, tc_fun(_935041, tc_HOL_Obool), tc_HOL_Obool), c_member(_935041)), _935045))))], (8710 ^ _784416) ^ [_935134, _935136, _935138, _935140] : [c_Orderings_Oorder__class_Omono(tc_fun(_935134, tc_HOL_Obool), tc_fun(_935134, tc_HOL_Obool), _935136), hBOOL(hAPP(hAPP(c_member(_935134), _935138), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_935134, tc_HOL_Obool), _935136))), -(hBOOL(hAPP(hAPP(c_member(_935134), _935138), hAPP(_935136, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_935134, tc_HOL_Obool)), _935140), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_935134, tc_HOL_Obool), _935136))))))], (8720 ^ _784416) ^ [_935365, _935367, _935369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935365, tc_HOL_Obool)), _935367), _935369)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_935365, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_935365), _935367)), hAPP(c_Set_OPow(_935365), _935369))))], (8726 ^ _784416) ^ [_935510, _935512, _935514] : [class_Complete__Lattice_Ocomplete__lattice(_935510), c_Orderings_Oorder__class_Omono(_935510, _935510, _935512), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935510), _935514), hAPP(_935512, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935510), _935514), c_Inductive_Ocomplete__lattice__class_Ogfp(_935510, _935512))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935510), _935514), c_Inductive_Ocomplete__lattice__class_Ogfp(_935510, _935512))))], (8740 ^ _784416) ^ [_935759, _935761, _935763] : [class_Complete__Lattice_Ocomplete__lattice(_935759), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935759), _935761), hAPP(_935763, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935759), _935761), c_Inductive_Ocomplete__lattice__class_Ogfp(_935759, _935763))))), c_Orderings_Oorder__class_Omono(_935759, _935759, _935763), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935759), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935759), _935761), c_Inductive_Ocomplete__lattice__class_Ogfp(_935759, _935763))), hAPP(_935763, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935759), _935761), c_Inductive_Ocomplete__lattice__class_Ogfp(_935759, _935763))))))], (8754 ^ _784416) ^ [_936052, _936054, _936056, _936058] : [class_Complete__Lattice_Ocomplete__lattice(_936052), _936054 = c_Inductive_Ocomplete__lattice__class_Ogfp(_936052, _936056), c_Orderings_Oorder__class_Omono(_936052, _936052, _936056), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936052), _936058), hAPP(_936056, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_936052), _936058), _936054)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936052), _936058), _936054)))], (8772 ^ _784416) ^ [_936357, _936359, _936361] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_936357, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_936357, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_936357), _936359)), hAPP(c_Set_OPow(_936357), _936361))), hAPP(c_Set_OPow(_936357), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_936357, tc_HOL_Obool)), _936359), _936361)))))], (8774 ^ _784416) ^ [_936437, _936439, _936441] : [hBOOL(hAPP(hAPP(c_member(_936437), _936439), _936441)), -(hAPP(hAPP(c_Set_Oinsert(_936437), _936439), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936437, tc_HOL_Obool)), _936441), hAPP(hAPP(c_Set_Oinsert(_936437), _936439), c_Orderings_Obot__class_Obot(tc_fun(_936437, tc_HOL_Obool))))) = _936441)], (8780 ^ _784416) ^ [_936590, _936592, _936594] : [-(hBOOL(hAPP(hAPP(c_member(_936590), _936592), _936594))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936590, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_936590), _936592), _936594)), hAPP(hAPP(c_Set_Oinsert(_936590), _936592), c_Orderings_Obot__class_Obot(tc_fun(_936590, tc_HOL_Obool)))) = _936594)], (8786 ^ _784416) ^ [_936679, _936681, _936683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936679, tc_HOL_Obool)), _936681), hAPP(hAPP(c_Set_Oinsert(_936679), _936683), c_Orderings_Obot__class_Obot(tc_fun(_936679, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_936679, _936683, _936681) = _936683)], (8792 ^ _784416) ^ [_936806, _936808, _936810] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936806, tc_HOL_Obool)), _936808), hAPP(hAPP(c_Set_Oinsert(_936806), _936810), c_Orderings_Obot__class_Obot(tc_fun(_936806, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_936806, _936810, _936808) = c_HOL_OThe(_936806, hAPP(hAPP(c_COMBC(_936806, tc_fun(_936806, tc_HOL_Obool), tc_HOL_Obool), c_member(_936806)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_936806, tc_HOL_Obool)), _936808), hAPP(hAPP(c_Set_Oinsert(_936806), _936810), c_Orderings_Obot__class_Obot(tc_fun(_936806, tc_HOL_Obool)))))))], (8798 ^ _784416) ^ [_936915, _936917, _936919, _936921] : [c_Orderings_Oorder__class_Omono(tc_fun(_936915, tc_HOL_Obool), tc_fun(_936915, tc_HOL_Obool), _936917), hBOOL(hAPP(hAPP(c_member(_936915), _936919), _936921)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936915, tc_HOL_Obool)), _936921), hAPP(_936917, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_936915, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_936915, tc_HOL_Obool), tc_fun(_936915, tc_HOL_Obool), tc_fun(_936915, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_936915, tc_HOL_Obool), tc_fun(tc_fun(_936915, tc_HOL_Obool), tc_fun(_936915, tc_HOL_Obool)), tc_fun(_936915, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_936915, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_936915, tc_HOL_Obool), tc_fun(_936915, tc_HOL_Obool), tc_fun(_936915, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_936915, tc_HOL_Obool), tc_fun(tc_fun(_936915, tc_HOL_Obool), tc_fun(_936915, tc_HOL_Obool)), tc_fun(_936915, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_936915, tc_HOL_Obool))), _936917)), _936921))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_936915, tc_HOL_Obool), _936917)))))), -(hBOOL(hAPP(hAPP(c_member(_936915), _936919), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_936915, tc_HOL_Obool), _936917))))], (8812 ^ _784416) ^ [_937408, _937410, _937412, _937414, _937416] : [_937408 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_937410, tc_HOL_Obool), _937412), c_Orderings_Oorder__class_Omono(tc_fun(_937410, tc_HOL_Obool), tc_fun(_937410, tc_HOL_Obool), _937412), hBOOL(hAPP(hAPP(c_member(_937410), _937414), _937416)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937410, tc_HOL_Obool)), _937416), hAPP(_937412, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_937410, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_937410, tc_HOL_Obool), tc_fun(_937410, tc_HOL_Obool), tc_fun(_937410, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_937410, tc_HOL_Obool), tc_fun(tc_fun(_937410, tc_HOL_Obool), tc_fun(_937410, tc_HOL_Obool)), tc_fun(_937410, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937410, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_937410, tc_HOL_Obool), tc_fun(_937410, tc_HOL_Obool), tc_fun(_937410, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_937410, tc_HOL_Obool), tc_fun(tc_fun(_937410, tc_HOL_Obool), tc_fun(_937410, tc_HOL_Obool)), tc_fun(_937410, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937410, tc_HOL_Obool))), _937412)), _937416))), _937408))))), -(hBOOL(hAPP(hAPP(c_member(_937410), _937414), _937408)))], (8830 ^ _784416) ^ [_937953, _937955, _937957, _937959, _937961] : [_937953 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_937955, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_937955, tc_HOL_Obool), tc_fun(_937955, tc_HOL_Obool), tc_fun(_937955, tc_HOL_Obool)), c_Set_OCollect(_937955)), _937957)), c_Orderings_Oorder__class_Omono(tc_fun(_937955, tc_HOL_Obool), tc_fun(_937955, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_937955, tc_HOL_Obool), tc_fun(_937955, tc_HOL_Obool), tc_fun(_937955, tc_HOL_Obool)), c_Set_OCollect(_937955)), _937957)), hBOOL(hAPP(hAPP(c_member(_937955), _937959), _937961)), 8844 ^ _784416 : [(8845 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_937955), 8843 ^ [_937953, _937955, _937957, _937959, _937961]), _937961)))], (8847 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_937957, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_937955, tc_HOL_Obool)), _937961), _937953)), 8843 ^ [_937953, _937955, _937957, _937959, _937961]))]], -(hBOOL(hAPP(hAPP(c_member(_937955), _937959), _937953)))], (8851 ^ _784416) ^ [_938493, _938495, _938497, _938499, _938501] : [class_Groups_Oordered__ab__group__add(_938493), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_938493), _938495), _938497) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_938493), _938499), _938501), 8858 ^ _784416 : [(8859 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938493), _938495), _938497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938493), _938499), _938501)))], (8865 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938493), _938499), _938501)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938493), _938495), _938497)))]]], (8871 ^ _784416) ^ [_938869, _938871, _938873, _938875, _938877, _938879] : [hBOOL(hAPP(hAPP(c_member(_938869), _938871), _938873)), -(hAPP(c_Set_Oimage(_938869, _938875, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_938869, _938875), _938877), _938871), _938879)), _938873) = hAPP(hAPP(c_Set_Oinsert(_938875), _938879), hAPP(c_Set_Oimage(_938869, _938875, _938877), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938869, tc_HOL_Obool)), _938873), hAPP(hAPP(c_Set_Oinsert(_938869), _938871), c_Orderings_Obot__class_Obot(tc_fun(_938869, tc_HOL_Obool)))))))], (8877 ^ _784416) ^ [_939078, _939080, _939082, _939084, _939086, _939088] : [-(hBOOL(hAPP(hAPP(c_member(_939078), _939080), _939082))), -(hAPP(c_Set_Oimage(_939078, _939084, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_939078, _939084), _939086), _939080), _939088)), _939082) = hAPP(c_Set_Oimage(_939078, _939084, _939086), _939082))], (8883 ^ _784416) ^ [_939157, _939159, _939161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939157, tc_HOL_Obool)), _939159), hAPP(_939161, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_939157, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_939157, tc_HOL_Obool), tc_fun(tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool)), tc_fun(_939157, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_939157, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_939157, tc_HOL_Obool), tc_fun(tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool)), tc_fun(_939157, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_939157, tc_HOL_Obool))), _939161)), _939159))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_939157, tc_HOL_Obool), _939161)))))), c_Orderings_Oorder__class_Omono(tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool), _939161), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939157, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_939157, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_939157, tc_HOL_Obool), tc_fun(tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool)), tc_fun(_939157, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_939157, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_939157, tc_HOL_Obool), tc_fun(tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool)), tc_fun(_939157, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_939157, tc_HOL_Obool))), _939161)), _939159))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_939157, tc_HOL_Obool), _939161)))), hAPP(_939161, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_939157, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_939157, tc_HOL_Obool), tc_fun(tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool)), tc_fun(_939157, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_939157, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_939157, tc_HOL_Obool), tc_fun(tc_fun(_939157, tc_HOL_Obool), tc_fun(_939157, tc_HOL_Obool)), tc_fun(_939157, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_939157, tc_HOL_Obool))), _939161)), _939159))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_939157, tc_HOL_Obool), _939161)))))))], (8919 ^ _784416) ^ [_940564, _940566, _940568, _940570] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940564, tc_HOL_Obool)), _940566), hAPP(hAPP(c_Set_Oinsert(_940564), _940568), _940570)))), 8922 ^ _784416 : [(8923 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_940564), _940568), _940570)))], (8925 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940564, tc_HOL_Obool)), _940566), _940570))]], 8926 ^ _784416 : [(8927 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_940564), _940568), _940570))], (8929 ^ _784416) ^ [] : [8930 ^ _784416 : [(8931 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_940564), _940568), _940566)))], (8933 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940564, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_940564, tc_HOL_Obool)), _940566), hAPP(hAPP(c_Set_Oinsert(_940564), _940568), c_Orderings_Obot__class_Obot(tc_fun(_940564, tc_HOL_Obool))))), _940570))]], 8934 ^ _784416 : [(8935 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_940564), _940568), _940566))], (8937 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940564, tc_HOL_Obool)), _940566), _940570))]]]]], (8893 ^ _784416) ^ [_940037, _940039, _940041, _940043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940037, tc_HOL_Obool)), _940039), hAPP(hAPP(c_Set_Oinsert(_940037), _940041), _940043))), 8896 ^ _784416 : [(8897 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_940037), _940041), _940043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940037, tc_HOL_Obool)), _940039), _940043)))], (8903 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_940037), _940041), _940043))), 8906 ^ _784416 : [(8907 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_940037), _940041), _940039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940037, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_940037, tc_HOL_Obool)), _940039), hAPP(hAPP(c_Set_Oinsert(_940037), _940041), c_Orderings_Obot__class_Obot(tc_fun(_940037, tc_HOL_Obool))))), _940043)))], (8913 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_940037), _940041), _940039))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940037, tc_HOL_Obool)), _940039), _940043)))]]]]], (8941 ^ _784416) ^ [_941103, _941105, _941107, _941109, _941111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941103, tc_HOL_Obool)), _941105), _941107)), 8947 ^ _784416 : [(8948 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_941103), 8946 ^ [_941103, _941105, _941107, _941109, _941111]), _941105)))], (8950 ^ _784416) ^ [] : [-(hBOOL(hAPP(_941109, 8946 ^ [_941103, _941105, _941107, _941109, _941111])))], (8952 ^ _784416) ^ [] : [hBOOL(hAPP(_941111, 8946 ^ [_941103, _941105, _941107, _941109, _941111]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941103, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941103, tc_HOL_Obool)), _941105), hAPP(c_Set_OCollect(_941103), _941109))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941103, tc_HOL_Obool)), _941107), hAPP(c_Set_OCollect(_941103), _941111)))))], (8956 ^ _784416) ^ [_941503, _941505, _941507, _941509, _941511, _941513, _941515] : [hBOOL(hAPP(hAPP(c_member(_941503), _941505), _941507)), c_Nitpick_Ofold__graph_H(_941503, _941509, _941511, _941513, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_941503, tc_HOL_Obool)), _941507), hAPP(hAPP(c_Set_Oinsert(_941503), _941505), c_Orderings_Obot__class_Obot(tc_fun(_941503, tc_HOL_Obool)))), _941515), -(c_Nitpick_Ofold__graph_H(_941503, _941509, _941511, _941513, _941507, hAPP(hAPP(_941511, _941505), _941515)))], (8966 ^ _784416) ^ [_941742, _941744, _941746] : [class_Complete__Lattice_Ocomplete__lattice(_941742), c_Orderings_Oorder__class_Omono(_941742, _941742, _941744), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941742), hAPP(_941744, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_941742), c_Inductive_Ocomplete__lattice__class_Olfp(_941742, _941744)), _941746))), _941746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941742), c_Inductive_Ocomplete__lattice__class_Olfp(_941742, _941744)), _941746)))], (8980 ^ _784416) ^ [_941991, _941993, _941995, _941997] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_941991, _941993), _941995), _941997), hAPP(_941995, _941997)) = _941995)], (8982 ^ _784416) ^ [_942059, _942061, _942063, _942065, _942067] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942059, _942061), _942063), _942065), _942067) = _942063, -(hAPP(_942063, _942065) = _942067)], (8988 ^ _784416) ^ [_942168, _942170, _942172, _942174, _942176] : [hAPP(_942172, _942174) = _942176, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942168, _942170), _942172), _942174), _942176) = _942172)], (8994 ^ _784416) ^ [_942283, _942285, _942287, _942289, _942291, _942293] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942283, _942285), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942283, _942285), _942287), _942289), _942291)), _942289), _942293) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942283, _942285), _942287), _942289), _942293))], (8996 ^ _784416) ^ [_942352, _942354, _942356, _942358, _942360] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942352, _942354), _942356), _942358), _942360), _942358) = _942360)], (8998 ^ _784416) ^ [_942419, _942421, _942423, _942425, _942427, _942429] : [_942419 = _942421, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942423, _942425), _942427), _942421), _942429), _942419) = _942429)], (9004 ^ _784416) ^ [_942528, _942530, _942532, _942534, _942536, _942538] : [-(_942528 = _942530), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942532, _942534), _942536), _942530), _942538), _942528) = hAPP(_942536, _942528))], (9010 ^ _784416) ^ [_942588, _942590, _942592, _942594, _942596, _942598, _942600] : [-(_942588 = _942590), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942592, _942594), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942592, _942594), _942596), _942588), _942598)), _942590), _942600) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942592, _942594), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942592, _942594), _942596), _942590), _942600)), _942588), _942598))], (9016 ^ _784416) ^ [_942678, _942680, _942682, _942684, _942686, _942688] : [-(_942678 = _942680), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942682, _942684), _942686), _942680), _942688), _942678) = hAPP(_942686, _942678))], (9022 ^ _784416) ^ [_942740, _942742, _942744, _942746, _942748] : [hAPP(_942740, _942742) = _942744, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_942746, _942748), _942740), _942742), _942744) = _942740)], (9028 ^ _784416) ^ [_942853, _942855] : [class_Orderings_Opreorder(_942853), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942853), _942855), _942855))], (9034 ^ _784416) ^ [_942943, _942945, _942947] : [class_Orderings_Olinorder(_942943), 9037 ^ _784416 : [(9048 ^ _784416) ^ [] : [9049 ^ _784416 : [(9050 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942943), _942945), _942947))], (9052 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942943), _942947), _942945))]], _942945 = _942947], (9038 ^ _784416) ^ [] : [-(_942945 = _942947), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942943), _942945), _942947))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_942943), _942947), _942945)))]]], (9056 ^ _784416) ^ [_943197, _943199, _943201] : [class_Orderings_Olinorder(_943197), 9059 ^ _784416 : [(9070 ^ _784416) ^ [] : [9071 ^ _784416 : [(9072 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943197), _943201), _943199))], (9074 ^ _784416) ^ [] : [_943199 = _943201]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943197), _943199), _943201))], (9060 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943197), _943199), _943201))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943197), _943201), _943199))), -(_943199 = _943201)]]], (9078 ^ _784416) ^ [_943451, _943453, _943455] : [class_Orderings_Olinorder(_943451), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943451), _943453), _943455))), -(_943453 = _943455), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943451), _943455), _943453)))], (9092 ^ _784416) ^ [_943582, _943584, _943586] : [class_Orderings_Olinorder(_943582), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943582), _943584), _943586))), 9099 ^ _784416 : [(9100 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943582), _943586), _943584))), -(_943586 = _943584)], (9106 ^ _784416) ^ [] : [_943586 = _943584, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943582), _943586), _943584))]]], (9112 ^ _784416) ^ [_943841, _943843, _943845] : [class_Orderings_Olinorder(_943841), -(_943843 = _943845), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943841), _943843), _943845))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943841), _943845), _943843)))], (9126 ^ _784416) ^ [_943976, _943978, _943980] : [class_Orderings_Oorder(_943976), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_943976), _943978), _943980)), _943978 = _943980], (9136 ^ _784416) ^ [_944122, _944124, _944126] : [class_Orderings_Opreorder(_944122), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944122), _944124), _944126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944122), _944126), _944124))], (9146 ^ _784416) ^ [_944282, _944284, _944286] : [class_Orderings_Opreorder(_944282), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944282), _944284), _944286)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944282), _944286), _944284))], (9156 ^ _784416) ^ [_944442, _944444, _944446] : [class_Orderings_Oorder(_944442), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944442), _944444), _944446)), _944444 = _944446], (9166 ^ _784416) ^ [_944588, _944590, _944592] : [class_Orderings_Oorder(_944588), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944588), _944590), _944592)), _944592 = _944590], (9176 ^ _784416) ^ [_944734, _944736, _944738] : [class_Orderings_Opreorder(_944734), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944734), _944736), _944738)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944734), _944738), _944736))], (9186 ^ _784416) ^ [_944894, _944896, _944898] : [class_Orderings_Oorder(_944894), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944894), _944896), _944898)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944894), _944898), _944896))], (9196 ^ _784416) ^ [_945054, _945056, _945058, _945060] : [class_Orderings_Oord(_945054), _945056 = _945058, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945054), _945058), _945060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945054), _945056), _945060)))], (9210 ^ _784416) ^ [_945273, _945275, _945277, _945279] : [class_Orderings_Oorder(_945273), _945275 = _945277, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945273), _945279), _945277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945273), _945279), _945275)))], (9224 ^ _784416) ^ [_945492, _945494, _945496, _945498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_945492, tc_HOL_Obool)), _945494), _945496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_945492, tc_HOL_Obool)), _945496), _945498)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_945492, tc_HOL_Obool)), _945494), _945498)))], (9234 ^ _784416) ^ [_945689, _945691, _945693, _945695] : [class_Orderings_Oord(_945689), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945689), _945691), _945693)), _945693 = _945695, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945689), _945691), _945695)))], (9248 ^ _784416) ^ [_945908, _945910, _945912, _945914] : [class_Orderings_Oorder(_945908), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945908), _945910), _945912)), _945910 = _945914, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_945908), _945914), _945912)))], (9262 ^ _784416) ^ [_946127, _946129, _946131, _946133] : [class_Orderings_Opreorder(_946127), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946127), _946129), _946131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946127), _946131), _946133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946127), _946129), _946133)))], (9276 ^ _784416) ^ [_946360, _946362, _946364, _946366] : [class_Orderings_Oorder(_946360), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946360), _946362), _946364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946360), _946366), _946362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946360), _946366), _946364)))], (9290 ^ _784416) ^ [_946593, _946595, _946597] : [class_Orderings_Opreorder(_946593), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946593), _946595), _946597)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946593), _946597), _946595))], (9300 ^ _784416) ^ [_946753, _946755, _946757] : [class_Orderings_Olinorder(_946753), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946753), _946755), _946757))), -(_946755 = _946757), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946753), _946757), _946755)))], (9314 ^ _784416) ^ [_946888, _946890, _946892, _946894, _946896] : [class_Groups_Oordered__ab__group__add(_946888), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_946888), _946890), _946892) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_946888), _946894), _946896), 9321 ^ _784416 : [(9322 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946888), _946890), _946892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946888), _946894), _946896)))], (9328 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946888), _946894), _946896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946888), _946890), _946892)))]]], (9334 ^ _784416) ^ [_947264, _947266, _947268, _947270, _947272, _947274] : [_947264 = _947266, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_947268, _947270), _947272), _947266), _947274), _947264) = _947274)], (9340 ^ _784416) ^ [_947373, _947375, _947377, _947379, _947381, _947383] : [-(_947373 = _947375), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_947377, _947379), _947381), _947375), _947383), _947373) = hAPP(_947381, _947373))], (9346 ^ _784416) ^ [_947437, _947439] : [class_Complete__Lattice_Ocomplete__lattice(_947437), -(c_Inductive_Ocomplete__lattice__class_Olfp(_947437, hAPP(c_COMBK(_947437, _947437), _947439)) = _947439)], (9352 ^ _784416) ^ [_947530, _947532, _947534, _947536] : [-(c_Nitpick_Ofold__graph_H(_947530, _947532, _947534, _947536, c_Orderings_Obot__class_Obot(tc_fun(_947530, tc_HOL_Obool)), _947536))], (9354 ^ _784416) ^ [_947568, _947570, _947572, _947574] : [-(c_Nitpick_Ofold__graph_H(_947568, _947570, _947572, _947574, c_Orderings_Obot__class_Obot(tc_fun(_947568, tc_HOL_Obool)), _947574))], (9356 ^ _784416) ^ [_947606, _947608, _947610, _947612] : [class_Orderings_Oord(_947606), 9359 ^ _784416 : [(9360 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_947608, _947606)), _947610), _947612)), 9363 ^ _784416 : [(9364 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947608, _947606)), _947610), _947612)))], (9366 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947608, _947606)), _947612), _947610))]]], (9368 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_947608, _947606)), _947610), _947612))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947608, _947606)), _947610), _947612)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947608, _947606)), _947612), _947610)))]]], (9378 ^ _784416) ^ [_947998, _948000, _948002] : [class_Orderings_Olinorder(_947998), 9381 ^ _784416 : [(9382 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947998), _948000), _948002))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947998), _948002), _948000)))], (9388 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947998), _948002), _948000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947998), _948000), _948002))]]], (9394 ^ _784416) ^ [_948207, _948209, _948211] : [class_Orderings_Olinorder(_948207), 9397 ^ _784416 : [(9398 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948207), _948209), _948211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948207), _948211), _948209)))], (9404 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948207), _948211), _948209)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948207), _948209), _948211))]]], (9410 ^ _784416) ^ [_948416, _948418, _948420] : [class_Orderings_Olinorder(_948416), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948416), _948418), _948420))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948416), _948420), _948418)))], (9420 ^ _784416) ^ [_948534, _948536, _948538] : [class_Orderings_Oorder(_948534), 9423 ^ _784416 : [(9424 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948534), _948536), _948538)), 9427 ^ _784416 : [(9428 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948534), _948536), _948538)))], (9430 ^ _784416) ^ [] : [_948536 = _948538]]], (9432 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948534), _948536), _948538))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948534), _948536), _948538)), -(_948536 = _948538)]]], (9442 ^ _784416) ^ [_948870, _948872, _948874] : [class_Orderings_Opreorder(_948870), 9445 ^ _784416 : [(9446 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948870), _948872), _948874)), 9449 ^ _784416 : [(9450 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948870), _948872), _948874)))], (9452 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948870), _948874), _948872))]]], (9454 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_948870), _948872), _948874))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948870), _948872), _948874)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948870), _948874), _948872)))]]], (9464 ^ _784416) ^ [_949227, _949229, _949231] : [class_Orderings_Oorder(_949227), 9467 ^ _784416 : [(9478 ^ _784416) ^ [] : [9479 ^ _784416 : [(9480 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949227), _949229), _949231))], (9482 ^ _784416) ^ [] : [_949229 = _949231]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949227), _949229), _949231)))], (9468 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949227), _949229), _949231)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949227), _949229), _949231))), -(_949229 = _949231)]]], (9486 ^ _784416) ^ [_949525, _949527, _949529] : [class_Orderings_Olinorder(_949525), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949525), _949527), _949529))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949525), _949529), _949527)))], (9496 ^ _784416) ^ [_949645, _949647, _949649] : [class_Orderings_Olinorder(_949645), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949645), _949647), _949649))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949645), _949649), _949647)))], (9506 ^ _784416) ^ [_949765, _949767, _949769] : [class_Orderings_Olinorder(_949765), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949765), _949767), _949769))), 9513 ^ _784416 : [(9514 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949765), _949767), _949769)), -(_949767 = _949769)], (9520 ^ _784416) ^ [] : [_949767 = _949769, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949765), _949767), _949769)))]]], (9526 ^ _784416) ^ [_950068, _950070, _950072] : [class_Orderings_Oorder(_950068), -(_950070 = _950072), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950068), _950070), _950072)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950068), _950070), _950072)))], (9540 ^ _784416) ^ [_950284, _950286, _950288] : [class_Orderings_Oorder(_950284), -(_950286 = _950288), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950284), _950288), _950286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950284), _950288), _950286)))], (9554 ^ _784416) ^ [_950500, _950502, _950504] : [class_Orderings_Olinorder(_950500), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950500), _950502), _950504)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950500), _950504), _950502))], (9564 ^ _784416) ^ [_950660, _950662, _950664] : [class_Orderings_Opreorder(_950660), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950660), _950662), _950664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950660), _950662), _950664)))], (9574 ^ _784416) ^ [_950819, _950821, _950823] : [class_Orderings_Olinorder(_950819), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950819), _950821), _950823)), 9581 ^ _784416 : [(9582 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950819), _950821), _950823))), -(_950821 = _950823)], (9588 ^ _784416) ^ [] : [_950821 = _950823, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950819), _950821), _950823))]]], (9594 ^ _784416) ^ [_951075, _951077, _951079] : [class_Orderings_Oorder(_951075), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951075), _951077), _951079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951075), _951077), _951079))), -(_951077 = _951079)], (9608 ^ _784416) ^ [_951247, _951249, _951251] : [class_Orderings_Oorder(_951247), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951247), _951249), _951251)), -(_951249 = _951251), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951247), _951249), _951251)))], (9622 ^ _784416) ^ [_951421, _951423, _951425] : [class_Orderings_Oorder(_951421), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951421), _951423), _951425)), -(_951425 = _951423), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951421), _951423), _951425)))], (9636 ^ _784416) ^ [_951595, _951597, _951599, _951601] : [class_Orderings_Opreorder(_951595), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951595), _951597), _951599)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951595), _951599), _951601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951595), _951597), _951601)))], (9650 ^ _784416) ^ [_951828, _951830, _951832, _951834] : [class_Orderings_Oorder(_951828), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951828), _951830), _951832)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951828), _951834), _951830)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951828), _951834), _951832)))], (9664 ^ _784416) ^ [_952061, _952063, _952065, _952067] : [class_Orderings_Opreorder(_952061), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952061), _952063), _952065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952061), _952065), _952067)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952061), _952063), _952067)))], (9678 ^ _784416) ^ [_952294, _952296, _952298, _952300] : [class_Orderings_Oorder(_952294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952294), _952296), _952298)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952294), _952300), _952296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952294), _952300), _952298)))], (9692 ^ _784416) ^ [_952527, _952529, _952531, _952533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_952527, tc_HOL_Obool)), _952529), _952531)), hBOOL(hAPP(hAPP(c_member(_952527), _952533), _952529)), -(hBOOL(hAPP(hAPP(c_member(_952527), _952533), _952531)))], (9702 ^ _784416) ^ [_952724, _952726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_952724, tc_HOL_Obool)), _952726), c_Orderings_Obot__class_Obot(tc_fun(_952724, tc_HOL_Obool))))], (9704 ^ _784416) ^ [_952764, _952766, _952768, _952770] : [class_Lattices_Osemilattice__sup(_952764), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952764), _952766), _952768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952764), _952766), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_952764), _952770), _952768))))], (9714 ^ _784416) ^ [_952943, _952945, _952947, _952949] : [class_Lattices_Osemilattice__sup(_952943), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952943), _952945), _952947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952943), _952945), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_952943), _952947), _952949))))], (9724 ^ _784416) ^ [_953122, _953124, _953126, _953128] : [class_Lattices_Osemilattice__inf(_953122), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953122), _953124), _953126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953122), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_953122), _953124), _953128)), _953126)))], (9734 ^ _784416) ^ [_953301, _953303, _953305, _953307] : [class_Lattices_Osemilattice__inf(_953301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953301), _953303), _953305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953301), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_953301), _953307), _953303)), _953305)))], (9744 ^ _784416) ^ [_953498, _953500, _953502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_953498, tc_HOL_Obool)), _953500), _953502)), 9747 ^ _784416 : [(9748 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953498, tc_HOL_Obool)), _953500), _953502)))], (9750 ^ _784416) ^ [] : [_953500 = _953502]]], (9752 ^ _784416) ^ [_953647, _953649, _953651] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_953647, tc_HOL_Obool)), _953649), _953651))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953647, tc_HOL_Obool)), _953649), _953651)), -(_953649 = _953651)], (9772 ^ _784416) ^ [_953971, _953973, _953975] : [9773 ^ _784416 : [(9774 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_953971, tc_HOL_Obool)), _953973), _953975))], (9776 ^ _784416) ^ [] : [_953973 = _953975]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953971, tc_HOL_Obool)), _953973), _953975)))], (9762 ^ _784416) ^ [_953843, _953845, _953847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953843, tc_HOL_Obool)), _953845), _953847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_953843, tc_HOL_Obool)), _953845), _953847))), -(_953845 = _953847)], (9780 ^ _784416) ^ [_954130, _954132, _954134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_954130, tc_HOL_Obool)), _954132), _954134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_954130, tc_HOL_Obool)), _954132), _954134)))], (9786 ^ _784416) ^ [_954249, _954251, _954253, _954255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_954249, tc_HOL_Obool)), _954251), _954253)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_954249, tc_HOL_Obool)), _954253), _954255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_954249, tc_HOL_Obool)), _954251), _954255)))], (9796 ^ _784416) ^ [_954446, _954448, _954450, _954452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_954446, tc_HOL_Obool)), _954448), _954450)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_954446, tc_HOL_Obool)), _954450), _954452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_954446, tc_HOL_Obool)), _954448), _954452)))], (9806 ^ _784416) ^ [_954643, _954645, _954647, _954649, _954651] : [class_Orderings_Oorder(_954643), class_Orderings_Olinorder(_954645), c_Orderings_Oorder__class_Ostrict__mono(_954645, _954643, _954647), 9817 ^ _784416 : [(9818 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954643), hAPP(_954647, _954649)), hAPP(_954647, _954651))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954645), _954649), _954651)))], (9824 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954645), _954649), _954651)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_954643), hAPP(_954647, _954649)), hAPP(_954647, _954651))))]]], (9830 ^ _784416) ^ [_955044, _955046, _955048, _955050, _955052] : [class_Orderings_Oorder(_955044), class_Orderings_Oorder(_955046), c_Orderings_Oorder__class_Ostrict__mono(_955046, _955044, _955048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955046), _955050), _955052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955044), hAPP(_955048, _955050)), hAPP(_955048, _955052))))], (9848 ^ _784416) ^ [_955341, _955343, _955345] : [class_Complete__Lattice_Ocomplete__lattice(_955341), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955341), hAPP(_955343, _955345)), _955345)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955341), c_Inductive_Ocomplete__lattice__class_Olfp(_955341, _955343)), _955345)))], (9858 ^ _784416) ^ [_955512, _955514, _955516] : [class_Orderings_Owellorder(_955512), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955512), _955514), c_Orderings_Oord__class_OLeast(_955512, _955516))), hBOOL(hAPP(_955516, _955514))], (9868 ^ _784416) ^ [_955668, _955670, _955672] : [class_Complete__Lattice_Ocomplete__lattice(_955668), _955670 = c_Inductive_Ocomplete__lattice__class_Olfp(_955668, _955672), c_Orderings_Oorder__class_Omono(_955668, _955668, _955672), -(_955670 = hAPP(_955672, _955670))], (9882 ^ _784416) ^ [_955867, _955869] : [class_Complete__Lattice_Ocomplete__lattice(_955867), c_Orderings_Oorder__class_Omono(_955867, _955867, _955869), -(c_Inductive_Ocomplete__lattice__class_Olfp(_955867, _955869) = hAPP(_955869, c_Inductive_Ocomplete__lattice__class_Olfp(_955867, _955869)))], (9892 ^ _784416) ^ [_956014, _956016] : [class_Complete__Lattice_Ocomplete__lattice(_956014), c_Orderings_Oorder__class_Omono(_956014, _956014, _956016), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956014), hAPP(_956016, c_Inductive_Ocomplete__lattice__class_Olfp(_956014, _956016))), c_Inductive_Ocomplete__lattice__class_Olfp(_956014, _956016))))], (9902 ^ _784416) ^ [_956175, _956177] : [class_Complete__Lattice_Ocomplete__lattice(_956175), c_Orderings_Oorder__class_Omono(_956175, _956175, _956177), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956175), c_Inductive_Ocomplete__lattice__class_Olfp(_956175, _956177)), hAPP(_956177, c_Inductive_Ocomplete__lattice__class_Olfp(_956175, _956177)))))], (9912 ^ _784416) ^ [_956336, _956338, _956340, _956342, _956344] : [class_Groups_Oab__group__add(_956336), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_956336), _956338), _956340) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_956336), _956342), _956344), 9919 ^ _784416 : [(9920 ^ _784416) ^ [] : [_956338 = _956340, -(_956342 = _956344)], (9926 ^ _784416) ^ [] : [_956342 = _956344, -(_956338 = _956340)]]], (9932 ^ _784416) ^ [_956649, _956651, _956653, _956655] : [class_Complete__Lattice_Ocomplete__lattice(_956649), _956651 = c_Inductive_Ocomplete__lattice__class_Olfp(_956649, _956653), c_Orderings_Oorder__class_Omono(_956649, _956649, _956653), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956649), hAPP(_956653, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956649), _956651), _956655))), _956655)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956649), _956651), _956655)))], (9950 ^ _784416) ^ [_956954, _956956, _956958, _956960] : [hBOOL(hAPP(hAPP(c_member(_956954), _956956), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_956954, tc_HOL_Obool), _956958))), c_Orderings_Oorder__class_Omono(tc_fun(_956954, tc_HOL_Obool), tc_fun(_956954, tc_HOL_Obool), _956958), 9960 ^ _784416 : [(9961 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_956954), 9959 ^ [_956954, _956956, _956958, _956960]), hAPP(_956958, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_956954, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_956954, tc_HOL_Obool), _956958)), hAPP(c_Set_OCollect(_956954), _956960))))))], (9963 ^ _784416) ^ [] : [hBOOL(hAPP(_956960, 9959 ^ [_956954, _956956, _956958, _956960]))]], -(hBOOL(hAPP(_956960, _956956)))], (9967 ^ _784416) ^ [_957337, _957339, _957341, _957343, _957345] : [_957337 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_957339, tc_HOL_Obool), _957341), c_Orderings_Oorder__class_Omono(tc_fun(_957339, tc_HOL_Obool), tc_fun(_957339, tc_HOL_Obool), _957341), hBOOL(hAPP(hAPP(c_member(_957339), _957343), _957337)), 9981 ^ _784416 : [(9982 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_957339), 9980 ^ [_957337, _957339, _957341, _957343, _957345]), hAPP(_957341, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957339, tc_HOL_Obool)), _957337), hAPP(c_Set_OCollect(_957339), _957345))))))], (9984 ^ _784416) ^ [] : [hBOOL(hAPP(_957345, 9980 ^ [_957337, _957339, _957341, _957343, _957345]))]], -(hBOOL(hAPP(_957345, _957343)))], (9988 ^ _784416) ^ [_957808, _957810, _957812, _957814, _957816, _957818, _957820] : [c_Nitpick_Ofold__graph_H(_957808, _957810, _957812, _957814, _957816, hAPP(hAPP(_957812, _957818), _957820)), 9993 ^ _784416 : [(9994 ^ _784416) ^ [] : [-(_957816 = c_Orderings_Obot__class_Obot(tc_fun(_957808, tc_HOL_Obool)))], (9996 ^ _784416) ^ [] : [-(hAPP(hAPP(_957812, _957818), _957820) = _957814)]], 9999 ^ _784416 : [(10000 ^ _784416) ^ [] : [-(hAPP(hAPP(_957812, _957818), _957820) = hAPP(hAPP(_957812, 9997 ^ [_957808, _957810, _957812, _957814, _957816, _957818, _957820]), 9998 ^ [_957808, _957810, _957812, _957814, _957816, _957818, _957820]))], (10002 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_957808), 9997 ^ [_957808, _957810, _957812, _957814, _957816, _957818, _957820]), _957816)))], (10004 ^ _784416) ^ [] : [-(c_Nitpick_Ofold__graph_H(_957808, _957810, _957812, _957814, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_957808, tc_HOL_Obool)), _957816), hAPP(hAPP(c_Set_Oinsert(_957808), 9997 ^ [_957808, _957810, _957812, _957814, _957816, _957818, _957820]), c_Orderings_Obot__class_Obot(tc_fun(_957808, tc_HOL_Obool)))), 9998 ^ [_957808, _957810, _957812, _957814, _957816, _957818, _957820]))]]], (10006 ^ _784416) ^ [_958245, _958247, _958249, _958251, _958253, _958255, _958257] : [-(c_Nitpick_Ofold__graph_H(_958245, _958247, _958249, _958251, _958253, hAPP(hAPP(_958249, _958255), _958257))), 10007 ^ _784416 : [(10008 ^ _784416) ^ [] : [_958253 = c_Orderings_Obot__class_Obot(tc_fun(_958245, tc_HOL_Obool)), hAPP(hAPP(_958249, _958255), _958257) = _958251], (10014 ^ _784416) ^ [_958474, _958476] : [hAPP(hAPP(_958249, _958255), _958257) = hAPP(hAPP(_958249, _958476), _958474), hBOOL(hAPP(hAPP(c_member(_958245), _958476), _958253)), c_Nitpick_Ofold__graph_H(_958245, _958247, _958249, _958251, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_958245, tc_HOL_Obool)), _958253), hAPP(hAPP(c_Set_Oinsert(_958245), _958476), c_Orderings_Obot__class_Obot(tc_fun(_958245, tc_HOL_Obool)))), _958474)]]], (10026 ^ _784416) ^ [_958766, _958768, _958770, _958772] : [class_Orderings_Oorder(_958766), class_Enum_Oenum(_958768), 10033 ^ _784416 : [(10034 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_958768, _958766)), _958770), _958772)), 10037 ^ _784416 : [(10038 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958768, _958766)), _958770), _958772)))], (10040 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_958768), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _958768), c_fNot), hAPP(hAPP(c_COMBS(_958768, _958766, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_958766, tc_fun(_958766, tc_HOL_Obool), _958768), c_fequal), _958770)), _958772)))))]]], (10042 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_958768, _958766)), _958770), _958772))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958768, _958766)), _958770), _958772)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_958768), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _958768), c_fNot), hAPP(hAPP(c_COMBS(_958768, _958766, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_958766, tc_fun(_958766, tc_HOL_Obool), _958768), c_fequal), _958770)), _958772))))]]], (10052 ^ _784416) ^ [_959310, _959312, _959314, _959316, _959318] : [c_Fun_Oinj__on(_959310, _959312, _959314, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959310, tc_HOL_Obool)), _959316), _959318)), 10055 ^ _784416 : [(10056 ^ _784416) ^ [] : [-(c_Fun_Oinj__on(_959310, _959312, _959314, _959316))], (10058 ^ _784416) ^ [] : [-(c_Fun_Oinj__on(_959310, _959312, _959314, _959318))], (10060 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959312, tc_HOL_Obool)), hAPP(c_Set_Oimage(_959310, _959312, _959314), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_959310, tc_HOL_Obool)), _959316), _959318))), hAPP(c_Set_Oimage(_959310, _959312, _959314), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_959310, tc_HOL_Obool)), _959318), _959316))) = c_Orderings_Obot__class_Obot(tc_fun(_959312, tc_HOL_Obool)))]]], (10062 ^ _784416) ^ [_959577, _959579, _959581, _959583, _959585] : [-(c_Fun_Oinj__on(_959577, _959579, _959581, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959577, tc_HOL_Obool)), _959583), _959585))), c_Fun_Oinj__on(_959577, _959579, _959581, _959583), c_Fun_Oinj__on(_959577, _959579, _959581, _959585), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_959579, tc_HOL_Obool)), hAPP(c_Set_Oimage(_959577, _959579, _959581), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_959577, tc_HOL_Obool)), _959583), _959585))), hAPP(c_Set_Oimage(_959577, _959579, _959581), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_959577, tc_HOL_Obool)), _959585), _959583))) = c_Orderings_Obot__class_Obot(tc_fun(_959579, tc_HOL_Obool))], (10076 ^ _784416) ^ [_959940, _959942, _959944, _959946, _959948] : [c_Fun_Oinj__on(_959940, _959942, _959944, hAPP(hAPP(c_Set_Oinsert(_959940), _959946), _959948)), 10079 ^ _784416 : [(10080 ^ _784416) ^ [] : [-(c_Fun_Oinj__on(_959940, _959942, _959944, _959948))], (10082 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_959942), hAPP(_959944, _959946)), hAPP(c_Set_Oimage(_959940, _959942, _959944), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_959940, tc_HOL_Obool)), _959948), hAPP(hAPP(c_Set_Oinsert(_959940), _959946), c_Orderings_Obot__class_Obot(tc_fun(_959940, tc_HOL_Obool)))))))]]], (10084 ^ _784416) ^ [_960159, _960161, _960163, _960165, _960167] : [-(c_Fun_Oinj__on(_960159, _960161, _960163, hAPP(hAPP(c_Set_Oinsert(_960159), _960165), _960167))), c_Fun_Oinj__on(_960159, _960161, _960163, _960167), -(hBOOL(hAPP(hAPP(c_member(_960161), hAPP(_960163, _960165)), hAPP(c_Set_Oimage(_960159, _960161, _960163), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960159, tc_HOL_Obool)), _960167), hAPP(hAPP(c_Set_Oinsert(_960159), _960165), c_Orderings_Obot__class_Obot(tc_fun(_960159, tc_HOL_Obool))))))))], (10094 ^ _784416) ^ [_960411, _960413, _960415, _960417, _960419] : [-(hAPP(c_Fun_Othe__inv__into(_960411, _960413, _960415, _960417), _960419) = c_HOL_OThe(_960411, hAPP(hAPP(c_COMBS(_960411, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _960411), c_fconj), hAPP(hAPP(c_COMBC(_960411, tc_fun(_960411, tc_HOL_Obool), tc_HOL_Obool), c_member(_960411)), _960415))), hAPP(hAPP(c_COMBC(_960411, _960413, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_960413, tc_fun(_960413, tc_HOL_Obool), _960411), c_fequal), _960417)), _960419))))], (10096 ^ _784416) ^ [_960532, _960534, _960536, _960538] : [c_Partial__Function_Omk__less(_960532, _960534, _960536, _960538), 10099 ^ _784416 : [(10100 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_960534, _960536), _960538)))], (10102 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_960534, _960538), _960536))]]], (10104 ^ _784416) ^ [_960667, _960669, _960671, _960673] : [-(c_Partial__Function_Omk__less(_960667, _960669, _960671, _960673)), hBOOL(hAPP(hAPP(_960669, _960671), _960673)), -(hBOOL(hAPP(hAPP(_960669, _960673), _960671)))], (10114 ^ _784416) ^ [_960833, _960835, _960837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_960833, tc_HOL_Obool)), _960835), _960837)), -(hBOOL(hAPP(hAPP(c_member(_960833), 10117 ^ [_960833, _960835, _960837]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960833, tc_HOL_Obool)), _960837), _960835))))], (10121 ^ _784416) ^ [_961003, _961005, _961007, _961009, _961011, _961013] : [hBOOL(hAPP(hAPP(c_member(_961003), _961005), _961007)), -(hAPP(c_Fun_Ooverride__on(_961003, _961009, _961011, _961013, _961007), _961005) = hAPP(_961013, _961005))], (10127 ^ _784416) ^ [_961120, _961122, _961124, _961126, _961128, _961130] : [-(hBOOL(hAPP(hAPP(c_member(_961120), _961122), _961124))), -(hAPP(c_Fun_Ooverride__on(_961120, _961126, _961128, _961130, _961124), _961122) = hAPP(_961128, _961122))], (10133 ^ _784416) ^ [_961185, _961187, _961189] : [-(c_Fun_Oinj__on(_961185, _961187, _961189, c_Orderings_Obot__class_Obot(tc_fun(_961185, tc_HOL_Obool))))], (10135 ^ _784416) ^ [_961219, _961221] : [-(c_Fun_Oinj__on(_961219, _961219, c_COMBI(_961219), _961221))], (10155 ^ _784416) ^ [_961654, _961656, _961658, _961660] : [10157 ^ _784416 : [(10158 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_961654), 10156 ^ [_961654, _961656, _961658, _961660]), _961660)))], (10161 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_961654), 10159 ^ [_961654, _961656, _961658, _961660]), _961660)))], (10163 ^ _784416) ^ [] : [-(hAPP(_961658, 10156 ^ [_961654, _961656, _961658, _961660]) = hAPP(_961658, 10159 ^ [_961654, _961656, _961658, _961660]))], (10165 ^ _784416) ^ [] : [10156 ^ [_961654, _961656, _961658, _961660] = 10159 ^ [_961654, _961656, _961658, _961660]]], -(c_Fun_Oinj__on(_961654, _961656, _961658, _961660))], (10137 ^ _784416) ^ [_961269, _961271, _961273, _961275] : [c_Fun_Oinj__on(_961269, _961271, _961273, _961275), 10140 ^ _784416 : [(10141 ^ _784416) ^ [_961377] : [hBOOL(hAPP(hAPP(c_member(_961269), _961377), _961275)), 10144 ^ _784416 : [(10145 ^ _784416) ^ [_961479] : [hBOOL(hAPP(hAPP(c_member(_961269), _961479), _961275)), hAPP(_961273, _961377) = hAPP(_961273, _961479), -(_961377 = _961479)]]]]], (10169 ^ _784416) ^ [_962046, _962048, _962050, _962052, _962054, _962056] : [c_Fun_Oinj__on(_962046, _962048, _962050, _962052), hAPP(_962050, _962054) = _962056, hBOOL(hAPP(hAPP(c_member(_962046), _962054), _962052)), -(hAPP(c_Fun_Othe__inv__into(_962046, _962048, _962052, _962050), _962056) = _962054)], (10183 ^ _784416) ^ [_962291, _962293, _962295, _962297, _962299] : [c_Fun_Oinj__on(_962291, _962293, _962295, _962297), hBOOL(hAPP(hAPP(c_member(_962291), _962299), _962297)), -(hAPP(c_Fun_Othe__inv__into(_962291, _962293, _962297, _962295), hAPP(_962295, _962299)) = _962299)], (10193 ^ _784416) ^ [_962472, _962474] : [class_Enum_Oenum(_962472), 10196 ^ _784416 : [(10197 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_962472), _962474)), -(hBOOL(hAPP(_962474, 10200 ^ [_962472, _962474])))], (10204 ^ _784416) ^ [] : [10205 ^ _784416 : [(10206 ^ _784416) ^ [_962652] : [hBOOL(hAPP(_962474, _962652))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_962472), _962474)))]]], (10210 ^ _784416) ^ [_962715, _962717] : [class_Enum_Oenum(_962715), 10213 ^ _784416 : [(10214 ^ _784416) ^ [] : [10215 ^ _784416 : [(10216 ^ _784416) ^ [_962817] : [hBOOL(hAPP(_962717, _962817))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_962715), _962717)))], (10220 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_962715), _962717)), -(hBOOL(hAPP(_962717, 10223 ^ [_962715, _962717])))]]], (10227 ^ _784416) ^ [_962958, _962960, _962962, _962964] : [c_Fun_Oinj__on(_962958, _962960, _962962, _962964), -(hAPP(c_Set_Oimage(_962960, _962958, c_Fun_Othe__inv__into(_962958, _962960, _962964, _962962)), hAPP(c_Set_Oimage(_962958, _962960, _962962), _962964)) = _962964)], (10233 ^ _784416) ^ [_963081, _963083, _963085, _963087] : [c_Fun_Oinj__on(_963081, _963083, _963085, _963087), -(c_Fun_Oinj__on(_963083, _963081, c_Fun_Othe__inv__into(_963081, _963083, _963087, _963085), hAPP(c_Set_Oimage(_963081, _963083, _963085), _963087)))], (10239 ^ _784416) ^ [_963194, _963196, _963198, _963200, _963202, _963204] : [c_Fun_Oinj__on(_963194, _963196, _963198, _963200), -(_963202 = _963204), hBOOL(hAPP(hAPP(c_member(_963194), _963202), _963200)), hBOOL(hAPP(hAPP(c_member(_963194), _963204), _963200)), hAPP(_963198, _963202) = hAPP(_963198, _963204)], (10257 ^ _784416) ^ [_963507, _963509, _963511, _963513, _963515, _963517] : [c_Fun_Oinj__on(_963507, _963509, _963511, _963513), hBOOL(hAPP(hAPP(c_member(_963507), _963515), _963513)), hBOOL(hAPP(hAPP(c_member(_963507), _963517), _963513)), 10268 ^ _784416 : [(10269 ^ _784416) ^ [] : [hAPP(_963511, _963515) = hAPP(_963511, _963517), -(_963515 = _963517)], (10275 ^ _784416) ^ [] : [_963515 = _963517, -(hAPP(_963511, _963515) = hAPP(_963511, _963517))]]], (10281 ^ _784416) ^ [_963908, _963910, _963912, _963914, _963916, _963918] : [c_Fun_Oinj__on(_963908, _963910, _963912, _963914), hAPP(_963912, _963916) = hAPP(_963912, _963918), hBOOL(hAPP(hAPP(c_member(_963908), _963916), _963914)), hBOOL(hAPP(hAPP(c_member(_963908), _963918), _963914)), -(_963916 = _963918)], (10299 ^ _784416) ^ [_964217, _964219, _964221, _964223, _964225] : [c_Fun_Oinj__on(_964217, _964219, _964221, _964223), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_964217, tc_HOL_Obool)), _964225), _964223)), -(c_Fun_Oinj__on(_964217, _964219, _964221, _964225))], (10309 ^ _784416) ^ [_964386, _964388, _964390, _964392, _964394] : [c_Fun_Oinj__on(_964386, _964388, _964390, _964392), c_Fun_Oinj__on(_964386, _964388, _964390, _964394), -(c_Fun_Oinj__on(_964386, _964388, _964390, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964386, tc_HOL_Obool)), _964392), _964394)))], (10319 ^ _784416) ^ [_964561, _964563, _964565, _964567, _964569] : [c_Fun_Oinj__on(_964561, _964563, _964565, _964567), -(c_Fun_Oinj__on(_964561, _964563, _964565, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964561, tc_HOL_Obool)), _964567), _964569)))], (10325 ^ _784416) ^ [_964674, _964676, _964678, _964680, _964682] : [c_Fun_Oinj__on(_964674, _964676, _964678, _964680), hBOOL(hAPP(hAPP(c_member(_964676), _964682), hAPP(c_Set_Oimage(_964674, _964676, _964678), _964680))), -(hAPP(_964678, hAPP(c_Fun_Othe__inv__into(_964674, _964676, _964680, _964678), _964682)) = _964682)], (10335 ^ _784416) ^ [_964869, _964871, _964873, _964875] : [class_Orderings_Oorder(_964869), class_Orderings_Olinorder(_964871), c_Orderings_Oorder__class_Ostrict__mono(_964871, _964869, _964873), -(c_Fun_Oinj__on(_964871, _964869, _964873, _964875))], (10349 ^ _784416) ^ [_965066, _965068, _965070, _965072, _965074, _965076] : [c_Fun_Oinj__on(_965066, _965068, _965070, _965072), hBOOL(hAPP(hAPP(c_member(_965068), _965074), hAPP(c_Set_Oimage(_965066, _965068, _965070), _965072))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_965066, tc_HOL_Obool)), _965072), _965076)), -(hBOOL(hAPP(hAPP(c_member(_965066), hAPP(c_Fun_Othe__inv__into(_965066, _965068, _965072, _965070), _965074)), _965076)))], (10363 ^ _784416) ^ [_965353, _965355, _965357, _965359, _965361] : [c_Fun_Oinj__on(_965353, _965355, _965357, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_965353, tc_HOL_Obool)), _965359), _965361)), 10366 ^ _784416 : [(10367 ^ _784416) ^ [] : [hAPP(c_Set_Oimage(_965353, _965355, _965357), _965359) = hAPP(c_Set_Oimage(_965353, _965355, _965357), _965361), -(_965359 = _965361)], (10373 ^ _784416) ^ [] : [_965359 = _965361, -(hAPP(c_Set_Oimage(_965353, _965355, _965357), _965359) = hAPP(c_Set_Oimage(_965353, _965355, _965357), _965361))]]], (10379 ^ _784416) ^ [_965646, _965648, _965650, _965652, _965654] : [c_Fun_Oinj__on(_965646, _965648, _965650, _965652), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_965646, tc_HOL_Obool)), _965654), _965652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_965648, tc_HOL_Obool)), hAPP(c_Set_Oimage(_965646, _965648, _965650), _965654)), hAPP(c_Set_Oimage(_965646, _965648, _965650), _965652))))], (10389 ^ _784416) ^ [_965859, _965861, _965863, _965865, _965867, _965869] : [c_Fun_Oinj__on(_965859, _965861, _965863, _965865), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_965859, tc_HOL_Obool)), _965867), _965865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_965859, tc_HOL_Obool)), _965869), _965865)), -(hAPP(c_Set_Oimage(_965859, _965861, _965863), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_965859, tc_HOL_Obool)), _965867), _965869)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_965861, tc_HOL_Obool)), hAPP(c_Set_Oimage(_965859, _965861, _965863), _965867)), hAPP(c_Set_Oimage(_965859, _965861, _965863), _965869)))], (10403 ^ _784416) ^ [_966194, _966196, _966198, _966200, _966202, _966204] : [c_Fun_Oinj__on(_966194, _966196, _966198, _966200), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_966194, tc_HOL_Obool)), _966202), _966200)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_966194, tc_HOL_Obool)), _966204), _966200)), -(hAPP(c_Set_Oimage(_966194, _966196, _966198), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966194, tc_HOL_Obool)), _966202), _966204)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966196, tc_HOL_Obool)), hAPP(c_Set_Oimage(_966194, _966196, _966198), _966202)), hAPP(c_Set_Oimage(_966194, _966196, _966198), _966204)))], (10417 ^ _784416) ^ [_966529, _966531, _966533, _966535, _966537, _966539] : [c_Fun_Oinj__on(_966529, _966531, _966533, _966535), -(hBOOL(hAPP(hAPP(c_member(_966531), _966537), hAPP(c_Set_Oimage(_966529, _966531, _966533), _966535)))), -(c_Fun_Oinj__on(_966529, _966531, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_966529, _966531), _966533), _966539), _966537), _966535))], (10427 ^ _784416) ^ [_966685, _966687, _966689, _966691, _966693, _966695] : [-(hBOOL(hAPP(hAPP(c_member(_966685), _966687), _966689))), -(hAPP(c_Fun_Ooverride__on(_966685, _966691, _966693, _966695, _966689), _966687) = hAPP(_966693, _966687))], (10433 ^ _784416) ^ [_966748, _966750, _966752, _966754, _966756, _966758] : [hBOOL(hAPP(hAPP(c_member(_966748), _966750), _966752)), -(hAPP(c_Fun_Ooverride__on(_966748, _966754, _966756, _966758, _966752), _966750) = hAPP(_966758, _966750))], (10439 ^ _784416) ^ [_966871, _966873, _966875, _966877] : [-(c_Fun_Ooverride__on(_966871, _966873, _966875, _966877, c_Orderings_Obot__class_Obot(tc_fun(_966871, tc_HOL_Obool))) = _966875)], (10441 ^ _784416) ^ [_966910, _966912, _966914, _966916] : [-(_966910 = c_Orderings_Obot__class_Obot(tc_fun(_966912, tc_HOL_Obool))), 10444 ^ _784416 : [(10456 ^ _784416) ^ [] : [10457 ^ _784416 : [(10458 ^ _784416) ^ [_967243] : [hAPP(c_Set_Oimage(_966914, _966912, _967243), _966916) = _966910]], 10460 ^ _784416 : [(10461 ^ _784416) ^ [] : [-(c_Fun_Oinj__on(_966912, _966914, 10459 ^ [_966910, _966912, _966914, _966916], _966910))], (10463 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_966914, tc_HOL_Obool)), hAPP(c_Set_Oimage(_966912, _966914, 10459 ^ [_966910, _966912, _966914, _966916]), _966910)), _966916)))]]], (10445 ^ _784416) ^ [] : [-(hAPP(c_Set_Oimage(_966914, _966912, 10452 ^ [_966910, _966912, _966914, _966916]), _966916) = _966910), 10446 ^ _784416 : [(10447 ^ _784416) ^ [_967051] : [c_Fun_Oinj__on(_966912, _966914, _967051, _966910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_966914, tc_HOL_Obool)), hAPP(c_Set_Oimage(_966912, _966914, _967051), _966910)), _966916))]]]]], (10465 ^ _784416) ^ [_967368, _967370, _967372, _967374, _967376] : [-(c_Map_Odom(_967368, _967370, c_Fun_Ooverride__on(_967368, tc_Option_Ooption(_967370), _967372, _967374, _967376)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_967368, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967368, tc_HOL_Obool)), c_Map_Odom(_967368, _967370, _967372)), hAPP(c_Set_OCollect(_967368), hAPP(hAPP(c_COMBC(_967368, tc_fun(_967368, tc_HOL_Obool), tc_HOL_Obool), c_member(_967368)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967368, tc_HOL_Obool)), _967376), c_Map_Odom(_967368, _967370, _967374)))))), hAPP(c_Set_OCollect(_967368), hAPP(hAPP(c_COMBC(_967368, tc_fun(_967368, tc_HOL_Obool), tc_HOL_Obool), c_member(_967368)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_967368, tc_HOL_Obool)), _967376), c_Map_Odom(_967368, _967370, _967374))))))], (10467 ^ _784416) ^ [_967507, _967509, _967511, _967513, _967515, _967517, _967519] : [c_Fun_Oinj__on(_967507, _967509, _967511, hAPP(c_Set_Oimage(_967513, _967507, _967515), _967517)), c_Fun_Oinj__on(_967513, _967507, _967515, _967517), hBOOL(hAPP(hAPP(c_member(_967509), _967519), hAPP(c_Set_Oimage(_967507, _967509, _967511), hAPP(c_Set_Oimage(_967513, _967507, _967515), _967517)))), -(hAPP(c_Fun_Othe__inv__into(_967513, _967509, _967517, hAPP(c_Fun_Ocomp(_967507, _967509, _967513, _967511), _967515)), _967519) = hAPP(hAPP(c_Fun_Ocomp(_967507, _967513, _967509, c_Fun_Othe__inv__into(_967513, _967507, _967517, _967515)), c_Fun_Othe__inv__into(_967507, _967509, hAPP(c_Set_Oimage(_967513, _967507, _967515), _967517), _967511)), _967519))], (10481 ^ _784416) ^ [_967870, _967872, _967874, _967876] : [c_Fun_Oinj__on(_967870, tc_fun(tc_fun(_967870, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_967870, tc_fun(tc_prod(_967870, _967870), tc_HOL_Obool), tc_fun(tc_fun(_967870, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_967870, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_967870, _967870), tc_HOL_Obool), tc_fun(tc_fun(_967870, tc_HOL_Obool), tc_HOL_Obool)), _967870), c_Equiv__Relations_Oquotient(_967870)), hAPP(hAPP(c_COMBC(_967870, tc_fun(_967870, tc_HOL_Obool), tc_fun(_967870, tc_HOL_Obool)), c_Set_Oinsert(_967870)), c_Orderings_Obot__class_Obot(tc_fun(_967870, tc_HOL_Obool))))), _967872), _967874), hBOOL(hAPP(hAPP(c_member(_967870), _967876), _967874)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_967870), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967870, tc_HOL_Obool)), _967874), hAPP(hAPP(c_Set_Oinsert(_967870), _967876), c_Orderings_Obot__class_Obot(tc_fun(_967870, tc_HOL_Obool))))), _967872) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_967870, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_967870), _967874), _967872)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_967870), hAPP(hAPP(c_Set_Oinsert(_967870), _967876), c_Orderings_Obot__class_Obot(tc_fun(_967870, tc_HOL_Obool)))), _967872)))], (10491 ^ _784416) ^ [_968337] : [-(c_Finite__Set_Ofun__left__comm__idem(_968337, tc_fun(_968337, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_968337, tc_HOL_Obool), tc_fun(tc_fun(_968337, tc_HOL_Obool), tc_fun(_968337, tc_HOL_Obool)), _968337), hAPP(c_COMBC(tc_fun(_968337, tc_HOL_Obool), tc_fun(_968337, tc_HOL_Obool), tc_fun(_968337, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_968337, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_968337, tc_fun(_968337, tc_HOL_Obool), tc_fun(_968337, tc_HOL_Obool)), c_Set_Oinsert(_968337)), c_Orderings_Obot__class_Obot(tc_fun(_968337, tc_HOL_Obool))))))], (10493 ^ _784416) ^ [_968430, _968432] : [class_Lattices_Olattice(_968430), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_968430), _968432), _968432) = _968432)], (10499 ^ _784416) ^ [_968521, _968523] : [class_Lattices_Olattice(_968521), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_968521), _968523), _968523) = _968523)], (10505 ^ _784416) ^ [_968612, _968614, _968616, _968618, _968620, _968622] : [hBOOL(hAPP(hAPP(c_member(_968612), _968614), _968616)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_968612, tc_Option_Ooption(_968618)), c_Map_Orestrict__map(_968612, _968618, _968620, _968616)), _968614), _968622) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_968612, tc_Option_Ooption(_968618)), c_Map_Orestrict__map(_968612, _968618, _968620, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968612, tc_HOL_Obool)), _968616), hAPP(hAPP(c_Set_Oinsert(_968612), _968614), c_Orderings_Obot__class_Obot(tc_fun(_968612, tc_HOL_Obool)))))), _968614), _968622))], (10511 ^ _784416) ^ [_968856, _968858, _968860, _968862, _968864, _968866] : [hBOOL(hAPP(hAPP(c_member(_968856), _968858), _968860)), -(c_Map_Orestrict__map(_968856, _968862, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_968856, tc_Option_Ooption(_968862)), _968864), _968858), _968866), _968860) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_968856, tc_Option_Ooption(_968862)), c_Map_Orestrict__map(_968856, _968862, _968864, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968856, tc_HOL_Obool)), _968860), hAPP(hAPP(c_Set_Oinsert(_968856), _968858), c_Orderings_Obot__class_Obot(tc_fun(_968856, tc_HOL_Obool)))))), _968858), _968866))], (10517 ^ _784416) ^ [_969073, _969075, _969077, _969079, _969081, _969083] : [-(hBOOL(hAPP(hAPP(c_member(_969073), _969075), _969077))), -(c_Map_Orestrict__map(_969073, _969079, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_969073, tc_Option_Ooption(_969079)), _969081), _969075), _969083), _969077) = c_Map_Orestrict__map(_969073, _969079, _969081, _969077))], (10523 ^ _784416) ^ [_969150, _969152, _969154] : [10525 ^ _784416 : [(10526 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_969150), 10524 ^ [_969150, _969152, _969154]), _969152)))], (10528 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_969150), 10524 ^ [_969150, _969152, _969154]), _969154))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_969150, tc_HOL_Obool)), _969152), _969154)))], (10532 ^ _784416) ^ [_969354, _969356, _969358, _969360, _969362, _969364, _969366] : [-(hAPP(c_Fun_Ocomp(_969354, _969356, _969358, _969360), hAPP(c_Fun_Ocomp(_969362, _969354, _969358, _969364), _969366)) = hAPP(c_Fun_Ocomp(_969362, _969356, _969358, hAPP(c_Fun_Ocomp(_969354, _969356, _969362, _969360), _969364)), _969366))], (10534 ^ _784416) ^ [_969421, _969423, _969425, _969427, _969429, _969431] : [-(hAPP(hAPP(c_Fun_Ocomp(_969421, _969423, _969425, _969427), _969429), _969431) = hAPP(_969427, hAPP(_969429, _969431)))], (10536 ^ _784416) ^ [_969471, _969473, _969475, _969477, _969479, _969481, _969483, _969485, _969487] : [hAPP(c_Fun_Ocomp(_969471, _969473, _969475, _969477), _969479) = hAPP(c_Fun_Ocomp(_969481, _969473, _969475, _969483), _969485), -(hAPP(_969477, hAPP(_969479, _969487)) = hAPP(_969483, hAPP(_969485, _969487)))], (10542 ^ _784416) ^ [_969618, _969620, _969622, _969624, _969626, _969628, _969630, _969632] : [hAPP(c_Fun_Ocomp(_969618, _969620, _969622, _969624), _969626) = hAPP(c_Fun_Ocomp(_969628, _969620, _969622, _969630), _969632), 10545 ^ _784416 : [(10546 ^ _784416) ^ [_969733] : [-(hAPP(_969624, hAPP(_969626, _969733)) = hAPP(_969630, hAPP(_969632, _969733)))]]], (10548 ^ _784416) ^ [_969772, _969774, _969776, _969778, _969780] : [c_Finite__Set_Ofun__left__comm__idem(_969772, _969774, _969776), -(hAPP(hAPP(_969776, _969778), hAPP(hAPP(_969776, _969778), _969780)) = hAPP(hAPP(_969776, _969778), _969780))], (10554 ^ _784416) ^ [_969893, _969895, _969897, _969899] : [c_Finite__Set_Ofun__left__comm__idem(_969893, _969895, _969897), -(hAPP(c_Fun_Ocomp(_969895, _969895, _969895, hAPP(_969897, _969899)), hAPP(_969897, _969899)) = hAPP(_969897, _969899))], (10560 ^ _784416) ^ [_970010, _970012, _970014, _970016, _970018] : [c_Finite__Set_Ofun__left__comm__idem(_970010, _970012, _970014), -(c_Finite__Set_Ofun__left__comm__idem(_970016, _970012, hAPP(hAPP(c_COMBB(_970010, tc_fun(_970012, _970012), _970016), _970014), _970018)))], (10566 ^ _784416) ^ [_970123, _970125, _970127, _970129, _970131, _970133] : [-(hAPP(hAPP(c_Fun_Ocomp(_970123, _970125, _970127, _970129), _970131), _970133) = hAPP(_970129, hAPP(_970131, _970133)))], (10568 ^ _784416) ^ [_970173, _970175, _970177, _970179] : [-(c_Map_Odom(_970173, _970175, c_Map_Orestrict__map(_970173, _970175, _970177, _970179)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970173, tc_HOL_Obool)), c_Map_Odom(_970173, _970175, _970177)), _970179))], (10570 ^ _784416) ^ [_970226, _970228, _970230, _970232, _970234] : [hBOOL(hAPP(hAPP(c_member(_970226), _970228), _970230)), -(hAPP(c_Map_Orestrict__map(_970226, _970232, _970234, _970230), _970228) = hAPP(_970234, _970228))], (10576 ^ _784416) ^ [_970345, _970347, _970349, _970351, _970353] : [-(c_Map_Orestrict__map(_970345, _970347, _970349, hAPP(hAPP(c_Set_Oinsert(_970345), _970351), _970353)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_970345, tc_Option_Ooption(_970347)), c_Map_Orestrict__map(_970345, _970347, _970349, _970353)), _970351), hAPP(_970349, _970351)))], (10578 ^ _784416) ^ [_970411, _970413, _970415, _970417, _970419] : [-(c_Map_Orestrict__map(_970411, _970413, c_Map_Orestrict__map(_970411, _970413, _970415, _970417), _970419) = c_Map_Orestrict__map(_970411, _970413, _970415, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_970411, tc_HOL_Obool)), _970417), _970419)))], (10580 ^ _784416) ^ [_970468] : [-(c_Finite__Set_Ofun__left__comm__idem(_970468, tc_fun(_970468, tc_HOL_Obool), c_Set_Oinsert(_970468)))], (10582 ^ _784416) ^ [_970497] : [class_Lattices_Osemilattice__sup(_970497), -(c_Finite__Set_Ofun__left__comm__idem(_970497, _970497, c_Lattices_Osemilattice__sup__class_Osup(_970497)))], (10588 ^ _784416) ^ [_970576] : [class_Lattices_Osemilattice__inf(_970576), -(c_Finite__Set_Ofun__left__comm__idem(_970576, _970576, c_Lattices_Osemilattice__inf__class_Oinf(_970576)))], (10594 ^ _784416) ^ [_970655, _970657, _970659, _970661, _970663, _970665] : [-(hAPP(c_Set_Oimage(_970655, _970657, hAPP(c_Fun_Ocomp(_970659, _970657, _970655, _970661), _970663)), _970665) = hAPP(c_Set_Oimage(_970659, _970657, _970661), hAPP(c_Set_Oimage(_970655, _970659, _970663), _970665)))], (10596 ^ _784416) ^ [_970717, _970719, _970721, _970723, _970725, _970727] : [c_Fun_Oinj__on(_970717, _970719, hAPP(c_Fun_Ocomp(_970721, _970719, _970717, _970723), _970725), _970727), -(c_Fun_Oinj__on(_970717, _970721, _970725, _970727))], (10602 ^ _784416) ^ [_970826, _970828, _970830, _970832, _970834, _970836, _970838] : [-(hAPP(c_Fun_Ocomp(_970826, _970828, _970830, _970832), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_970830, _970826), _970834), _970836), _970838)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_970830, _970828), hAPP(c_Fun_Ocomp(_970826, _970828, _970830, _970832), _970834)), _970836), hAPP(_970832, _970838)))], (10604 ^ _784416) ^ [_970904, _970906] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_970904), c_Orderings_Obot__class_Obot(tc_fun(_970904, tc_HOL_Obool))), _970906) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_970904, tc_HOL_Obool), tc_HOL_Obool)))], (10606 ^ _784416) ^ [_970968, _970970, _970972] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_970968, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_970968), _970970), _970972), -(_970970 = c_Orderings_Obot__class_Obot(tc_fun(_970968, tc_HOL_Obool)))], (10612 ^ _784416) ^ [_971085, _971087, _971089] : [_971087 = c_Orderings_Obot__class_Obot(tc_fun(_971085, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_971085, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_971085), _971087), _971089))], (10618 ^ _784416) ^ [_971226, _971228, _971230] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_971226), _971228), _971230) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_971226, tc_HOL_Obool), tc_HOL_Obool)), -(_971228 = c_Orderings_Obot__class_Obot(tc_fun(_971226, tc_HOL_Obool)))], (10624 ^ _784416) ^ [_971343, _971345, _971347] : [_971345 = c_Orderings_Obot__class_Obot(tc_fun(_971343, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_971343), _971345), _971347) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_971343, tc_HOL_Obool), tc_HOL_Obool)))], (10630 ^ _784416) ^ [_971466, _971468, _971470, _971472, _971474, _971476] : [c_Fun_Oinj__on(_971466, _971468, _971470, _971472), 10633 ^ _784416 : [(10634 ^ _784416) ^ [] : [c_Fun_Oinj__on(_971468, _971474, _971476, hAPP(c_Set_Oimage(_971466, _971468, _971470), _971472)), -(c_Fun_Oinj__on(_971466, _971474, hAPP(c_Fun_Ocomp(_971468, _971474, _971466, _971476), _971470), _971472))], (10640 ^ _784416) ^ [] : [c_Fun_Oinj__on(_971466, _971474, hAPP(c_Fun_Ocomp(_971468, _971474, _971466, _971476), _971470), _971472), -(c_Fun_Oinj__on(_971468, _971474, _971476, hAPP(c_Set_Oimage(_971466, _971468, _971470), _971472)))]]], (10646 ^ _784416) ^ [_971758, _971760, _971762, _971764, _971766, _971768] : [c_Fun_Oinj__on(_971758, _971760, _971762, _971764), c_Fun_Oinj__on(_971760, _971766, _971768, hAPP(c_Set_Oimage(_971758, _971760, _971762), _971764)), -(c_Fun_Oinj__on(_971758, _971766, hAPP(c_Fun_Ocomp(_971760, _971766, _971758, _971768), _971762), _971764))], (10656 ^ _784416) ^ [_971945, _971947, _971949, _971951, _971953, _971955] : [c_Fun_Oinj__on(_971945, _971947, hAPP(c_Fun_Ocomp(_971949, _971947, _971945, _971951), _971953), _971955), -(c_Fun_Oinj__on(_971949, _971947, _971951, hAPP(c_Set_Oimage(_971945, _971949, _971953), _971955)))], (10662 ^ _784416) ^ [_972068, _972070, _972072, _972074, _972076, _972078] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_972068, tc_Option_Ooption(_972070)), c_Map_Orestrict__map(_972068, _972070, _972072, _972074)), _972076), _972078) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_972068, tc_Option_Ooption(_972070)), c_Map_Orestrict__map(_972068, _972070, _972072, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_972068, tc_HOL_Obool)), _972074), hAPP(hAPP(c_Set_Oinsert(_972068), _972076), c_Orderings_Obot__class_Obot(tc_fun(_972068, tc_HOL_Obool)))))), _972076), _972078))], (10664 ^ _784416) ^ [_972163, _972165, _972167, _972169, _972171] : [-(c_Map_Odom(_972163, _972165, hAPP(hAPP(c_COMBS(_972163, tc_Option_Ooption(_972165), tc_Option_Ooption(_972165)), hAPP(hAPP(c_COMBS(_972163, tc_Option_Ooption(_972165), tc_fun(tc_Option_Ooption(_972165), tc_Option_Ooption(_972165))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_972165), tc_fun(tc_Option_Ooption(_972165), tc_Option_Ooption(_972165))), _972163), c_If(tc_Option_Ooption(_972165))), _972167)), _972169)), _972171)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972163, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972163, tc_HOL_Obool)), c_Map_Odom(_972163, _972165, _972169)), hAPP(c_Set_OCollect(_972163), _972167))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972163, tc_HOL_Obool)), c_Map_Odom(_972163, _972165, _972171)), hAPP(c_Set_OCollect(_972163), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _972163), c_fNot), _972167)))))], (10666 ^ _784416) ^ [_972336, _972338, _972340, _972342, _972344] : [hBOOL(hAPP(hAPP(c_member(_972336), _972338), _972340)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_972336, tc_Option_Ooption(_972342)), c_Map_Orestrict__map(_972336, _972342, _972344, _972340)), _972338), c_Option_Ooption_ONone(_972342)) = c_Map_Orestrict__map(_972336, _972342, _972344, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_972336, tc_HOL_Obool)), _972340), hAPP(hAPP(c_Set_Oinsert(_972336), _972338), c_Orderings_Obot__class_Obot(tc_fun(_972336, tc_HOL_Obool))))))], (10672 ^ _784416) ^ [_972527, _972529, _972531, _972533, _972535] : [-(hBOOL(hAPP(hAPP(c_member(_972527), _972529), _972531))), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_972527, tc_Option_Ooption(_972533)), c_Map_Orestrict__map(_972527, _972533, _972535, _972531)), _972529), c_Option_Ooption_ONone(_972533)) = c_Map_Orestrict__map(_972527, _972533, _972535, _972531))], (10678 ^ _784416) ^ [_972604, _972606, _972608] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_972604), hAPP(hAPP(c_Set_Oinsert(_972604), _972606), c_Orderings_Obot__class_Obot(tc_fun(_972604, tc_HOL_Obool)))), _972608) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_972604, tc_HOL_Obool)), hAPP(c_Relation_OImage(_972604, _972604, _972608), hAPP(hAPP(c_Set_Oinsert(_972604), _972606), c_Orderings_Obot__class_Obot(tc_fun(_972604, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_972604, tc_HOL_Obool), tc_HOL_Obool))))], (10680 ^ _784416) ^ [_972691, _972693, _972695, _972697] : [hBOOL(hAPP(hAPP(c_member(_972691), _972693), _972695)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_972691, tc_HOL_Obool)), hAPP(c_Relation_OImage(_972691, _972691, _972697), hAPP(hAPP(c_Set_Oinsert(_972691), _972693), c_Orderings_Obot__class_Obot(tc_fun(_972691, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_972691), _972695), _972697))))], (10686 ^ _784416) ^ [_972880, _972882, _972884, _972886, _972888] : [_972880 = c_Option_Ooption_ONone(_972882), -(c_Map_Odom(_972884, _972882, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_972884, tc_Option_Ooption(_972882)), _972886), _972888), _972880)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_972884, tc_HOL_Obool)), c_Map_Odom(_972884, _972882, _972886)), hAPP(hAPP(c_Set_Oinsert(_972884), _972888), c_Orderings_Obot__class_Obot(tc_fun(_972884, tc_HOL_Obool)))))], (10692 ^ _784416) ^ [_973053, _973055, _973057, _973059, _973061] : [-(_973053 = c_Option_Ooption_ONone(_973055)), -(c_Map_Odom(_973057, _973055, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_973057, tc_Option_Ooption(_973055)), _973059), _973061), _973053)) = hAPP(hAPP(c_Set_Oinsert(_973057), _973061), c_Map_Odom(_973057, _973055, _973059)))], (10698 ^ _784416) ^ [_973129, _973131, _973133, _973135, _973137] : [c_Equiv__Relations_Oequiv(_973129, _973131, _973133), hBOOL(hAPP(hAPP(c_member(tc_fun(_973129, tc_HOL_Obool)), _973135), hAPP(hAPP(c_Equiv__Relations_Oquotient(_973129), _973131), _973133))), hBOOL(hAPP(hAPP(c_member(tc_fun(_973129, tc_HOL_Obool)), _973137), hAPP(hAPP(c_Equiv__Relations_Oquotient(_973129), _973131), _973133))), -(_973135 = _973137), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_973129, tc_HOL_Obool)), _973135), _973137) = c_Orderings_Obot__class_Obot(tc_fun(_973129, tc_HOL_Obool)))], (10716 ^ _784416) ^ [_973447, _973449, _973451, _973453, _973455, _973457] : [-(hAPP(hAPP(c_Fun_Ocomp(_973447, _973449, _973451, hAPP(c_COMBK(_973449, _973447), _973453)), _973455), _973457) = _973453)], (10718 ^ _784416) ^ [_973497, _973499, _973501, _973503, _973505, _973507, _973509] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_973497, _973499, _973501, _973503, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973497, tc_HOL_Obool)), _973505), hAPP(hAPP(c_Set_Oinsert(_973497), _973507), c_Orderings_Obot__class_Obot(tc_fun(_973497, tc_HOL_Obool))))), _973509)), hBOOL(hAPP(hAPP(c_member(_973497), _973507), _973505)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_973497, _973499, _973501, _973503, _973505), hAPP(hAPP(_973501, _973507), _973509))))], (10728 ^ _784416) ^ [_973752, _973754, _973756, _973758, _973760, _973762, _973764] : [c_Fun_Oinj__on(_973752, _973754, _973756, hAPP(c_Set_Oimage(_973758, _973752, _973760), _973762)), c_Fun_Oinj__on(_973758, _973752, _973760, _973762), hBOOL(hAPP(hAPP(c_member(_973754), _973764), hAPP(c_Set_Oimage(_973752, _973754, _973756), hAPP(c_Set_Oimage(_973758, _973752, _973760), _973762)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_973758, _973754, _973762, hAPP(c_Fun_Ocomp(_973752, _973754, _973758, _973756), _973760)), _973764) = hAPP(hAPP(c_Fun_Ocomp(_973752, _973758, _973754, c_Hilbert__Choice_Oinv__into(_973758, _973752, _973762, _973760)), c_Hilbert__Choice_Oinv__into(_973752, _973754, hAPP(c_Set_Oimage(_973758, _973752, _973760), _973762), _973756)), _973764))], (10742 ^ _784416) ^ [_974115] : [-(c_Fun_Oinj__on(_974115, tc_fun(_974115, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_974115, tc_fun(_974115, tc_HOL_Obool), tc_fun(_974115, tc_HOL_Obool)), c_Set_Oinsert(_974115)), c_Orderings_Obot__class_Obot(tc_fun(_974115, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_974115, tc_HOL_Obool))))], (10744 ^ _784416) ^ [_974192, _974194, _974196, _974198] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_974192, _974194, hAPP(hAPP(c_Set_Oinsert(_974192), _974196), c_Orderings_Obot__class_Obot(tc_fun(_974192, tc_HOL_Obool)))), _974198)), -(_974196 = _974198)], (10750 ^ _784416) ^ [_974307, _974309, _974311, _974313] : [_974311 = _974313, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_974307, _974309, hAPP(hAPP(c_Set_Oinsert(_974307), _974311), c_Orderings_Obot__class_Obot(tc_fun(_974307, tc_HOL_Obool)))), _974313)))], (10756 ^ _784416) ^ [_974428, _974430] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_974428, tc_HOL_Obool)), _974430)))], (10758 ^ _784416) ^ [_974460, _974462] : [-(hBOOL(hAPP(hAPP(c_member(_974460), _974462), c_Orderings_Otop__class_Otop(tc_fun(_974460, tc_HOL_Obool)))))], (10760 ^ _784416) ^ [_974497, _974499, _974501, _974503, _974505] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_974497, _974497, _974499, _974501, _974503), _974505)), -(hBOOL(hAPP(hAPP(c_member(_974497), _974501), _974503))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_974497, _974499, hAPP(hAPP(c_Set_Oinsert(_974497), _974501), _974503)), _974505)))], (10770 ^ _784416) ^ [_974671, _974673, _974675] : [hAPP(c_Set_Oimage(_974671, _974673, _974675), c_Orderings_Otop__class_Otop(tc_fun(_974671, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_974673, tc_HOL_Obool)), 10773 ^ _784416 : [(10774 ^ _784416) ^ [_974782] : [-(hAPP(_974675, hAPP(c_Hilbert__Choice_Oinv__into(_974671, _974673, c_Orderings_Otop__class_Otop(tc_fun(_974671, tc_HOL_Obool)), _974675), _974782)) = _974782)]]], (10776 ^ _784416) ^ [_974821, _974823, _974825] : [hAPP(_974825, hAPP(c_Hilbert__Choice_Oinv__into(_974821, _974823, c_Orderings_Otop__class_Otop(tc_fun(_974821, tc_HOL_Obool)), _974825), 10777 ^ [_974821, _974823, _974825])) = 10777 ^ [_974821, _974823, _974825], -(hAPP(c_Set_Oimage(_974821, _974823, _974825), c_Orderings_Otop__class_Otop(tc_fun(_974821, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_974823, tc_HOL_Obool)))], (10783 ^ _784416) ^ [_975021, _975023, _975025, _975027] : [hAPP(c_Set_Oimage(_975021, _975023, _975025), c_Orderings_Otop__class_Otop(tc_fun(_975021, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_975023, tc_HOL_Obool)), -(hAPP(_975025, hAPP(c_Hilbert__Choice_Oinv__into(_975021, _975023, c_Orderings_Otop__class_Otop(tc_fun(_975021, tc_HOL_Obool)), _975025), _975027)) = _975027)], (10789 ^ _784416) ^ [_975168, _975170, _975172, _975174] : [hAPP(c_Set_Oimage(_975168, _975170, _975172), c_Orderings_Otop__class_Otop(tc_fun(_975168, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_975170, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_975168, _975170, _975172), hAPP(c_Set_Oimage(_975170, _975168, c_Hilbert__Choice_Oinv__into(_975168, _975170, c_Orderings_Otop__class_Otop(tc_fun(_975168, tc_HOL_Obool)), _975172)), _975174)) = _975174)], (10795 ^ _784416) ^ [_975331, _975333, _975335] : [class_Orderings_Otop(_975331), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_975333, _975331)), _975335) = c_Orderings_Otop__class_Otop(_975331))], (10801 ^ _784416) ^ [_975428, _975430, _975432, _975434, _975436] : [c_Fun_Oinj__on(_975428, _975430, _975432, c_Orderings_Otop__class_Otop(tc_fun(_975428, tc_HOL_Obool))), hAPP(_975432, _975434) = _975436, -(hAPP(c_Hilbert__Choice_Oinv__into(_975428, _975430, c_Orderings_Otop__class_Otop(tc_fun(_975428, tc_HOL_Obool)), _975432), _975436) = _975434)], (10811 ^ _784416) ^ [_975615, _975617, _975619, _975621] : [c_Fun_Oinj__on(_975615, _975617, _975619, c_Orderings_Otop__class_Otop(tc_fun(_975615, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_975615, _975617, c_Orderings_Otop__class_Otop(tc_fun(_975615, tc_HOL_Obool)), _975619), hAPP(_975619, _975621)) = _975621)], (10817 ^ _784416) ^ [_975742, _975744] : [-(hBOOL(hAPP(hAPP(c_member(_975742), _975744), c_Orderings_Otop__class_Otop(tc_fun(_975742, tc_HOL_Obool)))))], (10819 ^ _784416) ^ [_975779] : [-(hAPP(c_Set_OPow(_975779), c_Orderings_Otop__class_Otop(tc_fun(_975779, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_975779, tc_HOL_Obool), tc_HOL_Obool)))], (10821 ^ _784416) ^ [_975820, _975822, _975824] : [hAPP(c_Set_Oimage(_975820, _975822, _975824), c_Orderings_Otop__class_Otop(tc_fun(_975820, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_975822, tc_HOL_Obool)), -(c_Fun_Oinj__on(_975822, _975820, c_Hilbert__Choice_Oinv__into(_975820, _975822, c_Orderings_Otop__class_Otop(tc_fun(_975820, tc_HOL_Obool)), _975824), c_Orderings_Otop__class_Otop(tc_fun(_975822, tc_HOL_Obool))))], (10827 ^ _784416) ^ [_975967, _975969, _975971, _975973] : [c_Fun_Oinj__on(_975967, _975969, _975971, c_Orderings_Otop__class_Otop(tc_fun(_975967, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_975969, _975967, c_Hilbert__Choice_Oinv__into(_975967, _975969, c_Orderings_Otop__class_Otop(tc_fun(_975967, tc_HOL_Obool)), _975971)), hAPP(c_Set_Oimage(_975967, _975969, _975971), _975973)) = _975973)], (10833 ^ _784416) ^ [_976110, _976112, _976114, _976116] : [c_Fun_Oinj__on(_976110, _976112, _976114, c_Orderings_Otop__class_Otop(tc_fun(_976110, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_976112, _976110, c_Hilbert__Choice_Oinv__into(_976110, _976112, c_Orderings_Otop__class_Otop(tc_fun(_976110, tc_HOL_Obool)), _976114)), hAPP(c_Set_Oimage(_976110, _976112, _976114), _976116)) = _976116)], (10839 ^ _784416) ^ [_976253, _976255, _976257] : [c_Fun_Oinj__on(_976253, _976255, _976257, c_Orderings_Otop__class_Otop(tc_fun(_976253, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_976255, _976253, c_Hilbert__Choice_Oinv__into(_976253, _976255, c_Orderings_Otop__class_Otop(tc_fun(_976253, tc_HOL_Obool)), _976257)), c_Orderings_Otop__class_Otop(tc_fun(_976255, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_976253, tc_HOL_Obool)))], (10845 ^ _784416) ^ [_976400, _976402, _976404, _976406, _976408] : [c_Fun_Oinj__on(_976400, _976402, _976404, c_Orderings_Otop__class_Otop(tc_fun(_976400, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_976402, _976406, _976400, hAPP(c_Fun_Ocomp(_976400, _976406, _976402, _976408), c_Hilbert__Choice_Oinv__into(_976400, _976402, c_Orderings_Otop__class_Otop(tc_fun(_976400, tc_HOL_Obool)), _976404))), _976404) = _976408)], (10851 ^ _784416) ^ [_976558] : [c_Orderings_Otop__class_Otop(tc_fun(_976558, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_976558, tc_HOL_Obool))], (10853 ^ _784416) ^ [_976591, _976593] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976591, tc_HOL_Obool)), _976593), c_Orderings_Otop__class_Otop(tc_fun(_976591, tc_HOL_Obool)))))], (10855 ^ _784416) ^ [_976631, _976633] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_976631, tc_HOL_Obool)), _976633), c_Orderings_Otop__class_Otop(tc_fun(_976631, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_976631, tc_HOL_Obool)))], (10857 ^ _784416) ^ [_976677, _976679] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_976677, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_976677, tc_HOL_Obool))), _976679) = c_Orderings_Otop__class_Otop(tc_fun(_976677, tc_HOL_Obool)))], (10859 ^ _784416) ^ [_976723, _976725] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976723, tc_HOL_Obool)), _976725), c_Orderings_Otop__class_Otop(tc_fun(_976723, tc_HOL_Obool))) = _976725)], (10861 ^ _784416) ^ [_976764, _976766] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976764, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_976764, tc_HOL_Obool))), _976766) = _976766)], (10863 ^ _784416) ^ [_976805, _976807, _976809, _976811, _976813] : [c_Fun_Oinj__on(_976805, _976807, _976809, c_Orderings_Otop__class_Otop(tc_fun(_976805, tc_HOL_Obool))), hAPP(_976809, _976811) = hAPP(_976809, _976813), -(_976811 = _976813)], (10873 ^ _784416) ^ [_976972, _976974, _976976, _976978, _976980] : [c_Fun_Oinj__on(_976972, _976974, _976976, c_Orderings_Otop__class_Otop(tc_fun(_976972, tc_HOL_Obool))), 10876 ^ _784416 : [(10877 ^ _784416) ^ [] : [hAPP(_976976, _976978) = hAPP(_976976, _976980), -(_976978 = _976980)], (10883 ^ _784416) ^ [] : [_976978 = _976980, -(hAPP(_976976, _976978) = hAPP(_976976, _976980))]]], (10889 ^ _784416) ^ [_977229, _977231, _977233, _977235, _977237] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_977229, _977231, _977233, _977235, c_Orderings_Obot__class_Obot(tc_fun(_977229, tc_HOL_Obool))), _977237)), -(_977237 = _977235)], (10895 ^ _784416) ^ [_977338, _977340, _977342, _977344] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_977338, _977340, _977342, _977344, c_Orderings_Obot__class_Obot(tc_fun(_977338, tc_HOL_Obool))), _977344)))], (10897 ^ _784416) ^ [_977380, _977382, _977384, _977386] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_977380, _977382, _977384, _977386, c_Orderings_Obot__class_Obot(tc_fun(_977380, tc_HOL_Obool))), _977386)))], (10899 ^ _784416) ^ [_977422] : [-(c_Orderings_Otop__class_Otop(tc_fun(_977422, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_977422), hAPP(c_COMBK(tc_HOL_Obool, _977422), c_fTrue)))], (10901 ^ _784416) ^ [_977461, _977463, _977465, _977467, _977469] : [-(hAPP(c_Set_Oimage(_977461, _977463, hAPP(hAPP(c_COMBB(_977465, _977463, _977461), _977467), _977469)), c_Orderings_Otop__class_Otop(tc_fun(_977461, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_977465, _977463, _977467), hAPP(c_Set_Oimage(_977461, _977465, _977469), c_Orderings_Otop__class_Otop(tc_fun(_977461, tc_HOL_Obool)))))], (10903 ^ _784416) ^ [_977533, _977535, _977537, _977539] : [c_Equiv__Relations_Oequiv(_977533, _977535, _977537), hBOOL(hAPP(hAPP(c_member(_977533), _977539), _977535)), -(hBOOL(hAPP(hAPP(c_member(_977533), _977539), hAPP(c_Relation_OImage(_977533, _977533, _977537), hAPP(hAPP(c_Set_Oinsert(_977533), _977539), c_Orderings_Obot__class_Obot(tc_fun(_977533, tc_HOL_Obool)))))))], (10913 ^ _784416) ^ [_977740, _977742, _977744, _977746] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_977740, tc_Option_Ooption(_977742)), hAPP(c_COMBK(tc_Option_Ooption(_977742), _977740), c_Option_Ooption_ONone(_977742))), _977744), c_Option_Ooption_ONone(_977742)), _977746) = c_Option_Ooption_ONone(_977742))], (10915 ^ _784416) ^ [_977800, _977802] : [class_Orderings_Otop(_977800), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977800), _977802), c_Orderings_Otop__class_Otop(_977800))))], (10921 ^ _784416) ^ [_977893, _977895, _977897, _977899] : [-(hAPP(c_Map_Orestrict__map(_977893, _977895, hAPP(c_COMBK(tc_Option_Ooption(_977895), _977893), c_Option_Ooption_ONone(_977895)), _977897), _977899) = c_Option_Ooption_ONone(_977895))], (10923 ^ _784416) ^ [_977942, _977944] : [class_Lattices_Obounded__lattice__top(_977942), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_977942), c_Orderings_Otop__class_Otop(_977942)), _977944) = c_Orderings_Otop__class_Otop(_977942))], (10929 ^ _784416) ^ [_978041, _978043] : [class_Lattices_Obounded__lattice__top(_978041), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_978041), _978043), c_Orderings_Otop__class_Otop(_978041)) = c_Orderings_Otop__class_Otop(_978041))], (10935 ^ _784416) ^ [_978140, _978142, _978144] : [class_Lattices_Obounded__lattice__top(_978140), 10938 ^ _784416 : [(10939 ^ _784416) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_978140), _978142), _978144) = c_Orderings_Otop__class_Otop(_978140), 10942 ^ _784416 : [(10943 ^ _784416) ^ [] : [-(_978142 = c_Orderings_Otop__class_Otop(_978140))], (10945 ^ _784416) ^ [] : [-(_978144 = c_Orderings_Otop__class_Otop(_978140))]]], (10947 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_978140), _978142), _978144) = c_Orderings_Otop__class_Otop(_978140)), _978142 = c_Orderings_Otop__class_Otop(_978140), _978144 = c_Orderings_Otop__class_Otop(_978140)]]], (10957 ^ _784416) ^ [_978467, _978469] : [class_Lattices_Obounded__lattice__top(_978467), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_978467), _978469), c_Orderings_Otop__class_Otop(_978467)) = _978469)], (10963 ^ _784416) ^ [_978562, _978564] : [class_Lattices_Obounded__lattice__top(_978562), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_978562), c_Orderings_Otop__class_Otop(_978562)), _978564) = _978564)], (10969 ^ _784416) ^ [_978657, _978659, _978661, _978663] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_978657, _978659, _978661), _978663)), _978661 = c_Orderings_Obot__class_Obot(tc_fun(_978657, tc_HOL_Obool))], (10975 ^ _784416) ^ [_978776, _978778, _978780] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_978776, _978778, c_Orderings_Obot__class_Obot(tc_fun(_978776, tc_HOL_Obool))), _978780))], (10977 ^ _784416) ^ [_978835, _978837, _978839, _978841] : [hBOOL(hAPP(hAPP(c_member(_978835), _978837), c_Map_Odom(_978835, _978839, _978841))), hAPP(_978841, _978837) = c_Option_Ooption_ONone(_978839)], (10983 ^ _784416) ^ [_978943, _978945, _978947, _978949] : [-(hAPP(_978949, _978945) = c_Option_Ooption_ONone(_978947)), -(hBOOL(hAPP(hAPP(c_member(_978943), _978945), c_Map_Odom(_978943, _978947, _978949))))], (10989 ^ _784416) ^ [_979001, _979003, _979005, _979007, _979009] : [_979001 = hAPP(_979003, _979005), -(hBOOL(hAPP(hAPP(c_member(_979007), _979001), hAPP(c_Set_Oimage(_979009, _979007, _979003), c_Orderings_Otop__class_Otop(tc_fun(_979009, tc_HOL_Obool))))))], (10995 ^ _784416) ^ [_979128, _979130, _979132, _979134] : [-(hBOOL(hAPP(hAPP(c_member(_979128), hAPP(_979130, _979132)), hAPP(c_Set_Oimage(_979134, _979128, _979130), c_Orderings_Otop__class_Otop(tc_fun(_979134, tc_HOL_Obool))))))], (10997 ^ _784416) ^ [_979175, _979177, _979179, _979181, _979183] : [-(hBOOL(hAPP(hAPP(c_member(_979175), _979177), _979179))), -(hAPP(c_Map_Orestrict__map(_979175, _979181, _979183, _979179), _979177) = c_Option_Ooption_ONone(_979181))], (11003 ^ _784416) ^ [_979234, _979236] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979234, tc_HOL_Obool)), _979236), c_Orderings_Otop__class_Otop(tc_fun(_979234, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_979234, tc_HOL_Obool)))], (11005 ^ _784416) ^ [_979280, _979282, _979284, _979286, _979288] : [hAPP(c_Set_Oimage(_979280, _979282, _979284), c_Orderings_Otop__class_Otop(tc_fun(_979280, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_979282, tc_HOL_Obool)), hAPP(c_Set_Oimage(_979282, _979286, _979288), c_Orderings_Otop__class_Otop(tc_fun(_979282, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_979286, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_979280, _979286, hAPP(c_Fun_Ocomp(_979282, _979286, _979280, _979288), _979284)), c_Orderings_Otop__class_Otop(tc_fun(_979280, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_979286, tc_HOL_Obool)))], (11015 ^ _784416) ^ [_979539, _979541, _979543, _979545, _979547] : [hBOOL(hAPP(hAPP(c_member(_979539), _979541), hAPP(c_Set_Oimage(_979543, _979539, _979545), _979547))), -(hAPP(_979545, hAPP(c_Hilbert__Choice_Oinv__into(_979543, _979539, _979547, _979545), _979541)) = _979541)], (11021 ^ _784416) ^ [_979672, _979674, _979676, _979678, _979680] : [hBOOL(hAPP(hAPP(c_member(_979672), _979674), hAPP(c_Set_Oimage(_979676, _979672, _979678), _979680))), -(hBOOL(hAPP(hAPP(c_member(_979676), hAPP(c_Hilbert__Choice_Oinv__into(_979676, _979672, _979680, _979678), _979674)), _979680)))], (11027 ^ _784416) ^ [_979813, _979815, _979817, _979819, _979821, _979823] : [hAPP(c_Hilbert__Choice_Oinv__into(_979813, _979815, _979817, _979819), _979821) = hAPP(c_Hilbert__Choice_Oinv__into(_979813, _979815, _979817, _979819), _979823), hBOOL(hAPP(hAPP(c_member(_979815), _979821), hAPP(c_Set_Oimage(_979813, _979815, _979819), _979817))), hBOOL(hAPP(hAPP(c_member(_979815), _979823), hAPP(c_Set_Oimage(_979813, _979815, _979819), _979817))), -(_979821 = _979823)], (11041 ^ _784416) ^ [_980106, _980108, _980110, _980112, _980114] : [c_Fun_Oinj__on(_980106, _980108, _980110, c_Orderings_Otop__class_Otop(tc_fun(_980106, tc_HOL_Obool))), 11044 ^ _784416 : [(11045 ^ _784416) ^ [] : [hAPP(c_Set_Oimage(_980106, _980108, _980110), _980112) = hAPP(c_Set_Oimage(_980106, _980108, _980110), _980114), -(_980112 = _980114)], (11051 ^ _784416) ^ [] : [_980112 = _980114, -(hAPP(c_Set_Oimage(_980106, _980108, _980110), _980112) = hAPP(c_Set_Oimage(_980106, _980108, _980110), _980114))]]], (11057 ^ _784416) ^ [_980387, _980389, _980391, _980393, _980395] : [c_Fun_Oinj__on(_980387, _980389, _980391, c_Orderings_Otop__class_Otop(tc_fun(_980387, tc_HOL_Obool))), c_Fun_Oinj__on(_980393, _980387, _980395, c_Orderings_Otop__class_Otop(tc_fun(_980393, tc_HOL_Obool))), -(c_Fun_Oinj__on(_980393, _980389, hAPP(c_Fun_Ocomp(_980387, _980389, _980393, _980391), _980395), c_Orderings_Otop__class_Otop(tc_fun(_980393, tc_HOL_Obool))))], (11067 ^ _784416) ^ [_980586, _980588, _980590, _980592, _980594] : [c_Fun_Oinj__on(_980586, _980588, _980590, _980592), hBOOL(hAPP(hAPP(c_member(_980586), _980594), _980592)), -(hAPP(c_Hilbert__Choice_Oinv__into(_980586, _980588, _980592, _980590), hAPP(_980590, _980594)) = _980594)], (11077 ^ _784416) ^ [_980767, _980769, _980771, _980773, _980775, _980777] : [c_Fun_Oinj__on(_980767, _980769, _980771, _980773), hBOOL(hAPP(hAPP(c_member(_980767), _980775), _980773)), hAPP(_980771, _980775) = _980777, -(hAPP(c_Hilbert__Choice_Oinv__into(_980767, _980769, _980773, _980771), _980777) = _980775)], (11091 ^ _784416) ^ [_981012, _981014, _981016, _981018, _981020, _981022] : [hAPP(c_Set_Oimage(_981012, _981014, _981016), _981018) = _981020, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_981014, tc_HOL_Obool)), _981022), _981020)), -(hAPP(c_Set_Oimage(_981012, _981014, _981016), hAPP(c_Set_Oimage(_981014, _981012, c_Hilbert__Choice_Oinv__into(_981012, _981014, _981018, _981016)), _981022)) = _981022)], (11101 ^ _784416) ^ [_981228, _981230, _981232, _981234, _981236, _981238, _981240] : [-(hBOOL(hAPP(hAPP(c_member(_981228), _981230), _981232))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_981228, _981234, _981236, _981238, _981232), _981240)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_981228, _981234, _981236, _981238, hAPP(hAPP(c_Set_Oinsert(_981228), _981230), _981232)), hAPP(hAPP(_981236, _981230), _981240))))], (11111 ^ _784416) ^ [_981460, _981462, _981464] : [c_Map_Odom(_981460, _981462, _981464) = c_Orderings_Obot__class_Obot(tc_fun(_981460, tc_HOL_Obool)), -(_981464 = hAPP(c_COMBK(tc_Option_Ooption(_981462), _981460), c_Option_Ooption_ONone(_981462)))], (11117 ^ _784416) ^ [_981573, _981575, _981577] : [_981577 = hAPP(c_COMBK(tc_Option_Ooption(_981575), _981573), c_Option_Ooption_ONone(_981575)), -(c_Map_Odom(_981573, _981575, _981577) = c_Orderings_Obot__class_Obot(tc_fun(_981573, tc_HOL_Obool)))], (11123 ^ _784416) ^ [_981692, _981694] : [-(c_Map_Odom(_981692, _981694, hAPP(c_COMBK(tc_Option_Ooption(_981694), _981692), c_Option_Ooption_ONone(_981694))) = c_Orderings_Obot__class_Obot(tc_fun(_981692, tc_HOL_Obool)))], (11125 ^ _784416) ^ [_981736, _981738, _981740] : [-(c_Map_Odom(_981736, _981738, _981740) = hAPP(c_Set_OCollect(_981736), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _981736), c_fNot), hAPP(hAPP(c_COMBC(_981736, tc_Option_Ooption(_981738), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_981738), tc_fun(tc_Option_Ooption(_981738), tc_HOL_Obool), _981736), c_fequal), _981740)), c_Option_Ooption_ONone(_981738)))))], (11127 ^ _784416) ^ [_981831, _981833, _981835, _981837, _981839] : [hBOOL(hAPP(hAPP(c_member(_981831), _981833), _981835)), -(hAPP(c_Map_Orestrict__map(_981831, _981837, _981839, _981835), _981833) = hAPP(_981839, _981833))], (11133 ^ _784416) ^ [_981944, _981946, _981948, _981950, _981952] : [-(hBOOL(hAPP(hAPP(c_member(_981944), _981946), _981948))), -(hAPP(c_Map_Orestrict__map(_981944, _981950, _981952, _981948), _981946) = c_Option_Ooption_ONone(_981950))], (11139 ^ _784416) ^ [_982005, _982007, _982009, _982011] : [c_Fun_Oinj__on(_982005, _982007, _982009, c_Orderings_Otop__class_Otop(tc_fun(_982005, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_982005, _982007, c_Orderings_Otop__class_Otop(tc_fun(_982005, tc_HOL_Obool)), _982009), hAPP(_982009, _982011)) = _982011)], (11145 ^ _784416) ^ [_982132, _982134, _982136, _982138] : [-(hAPP(c_Map_Orestrict__map(_982132, _982134, _982136, c_Orderings_Obot__class_Obot(tc_fun(_982132, tc_HOL_Obool))), _982138) = c_Option_Ooption_ONone(_982134))], (11147 ^ _784416) ^ [_982176, _982178, _982180, _982182] : [c_Fun_Oinj__on(_982176, _982178, _982180, c_Orderings_Otop__class_Otop(tc_fun(_982176, tc_HOL_Obool))), -(c_Fun_Oinj__on(_982176, tc_fun(_982182, _982178), hAPP(hAPP(c_COMBB(_982178, tc_fun(_982182, _982178), _982176), c_COMBK(_982178, _982182)), _982180), c_Orderings_Otop__class_Otop(tc_fun(_982176, tc_HOL_Obool))))], (11153 ^ _784416) ^ [_982323, _982325, _982327, _982329, _982331] : [hAPP(_982323, _982325) = c_Option_Ooption_ONone(_982327), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982329, tc_HOL_Obool)), c_Map_Odom(_982329, _982327, _982323)), hAPP(hAPP(c_Set_Oinsert(_982329), _982325), _982331)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982329, tc_HOL_Obool)), c_Map_Odom(_982329, _982327, _982323)), _982331))], (11159 ^ _784416) ^ [_982492, _982494, _982496, _982498] : [c_Fun_Oinj__on(_982492, _982494, _982496, c_Orderings_Otop__class_Otop(tc_fun(_982492, tc_HOL_Obool))), 11162 ^ _784416 : [(11163 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_982494), _982498), hAPP(c_Set_Oimage(_982492, _982494, _982496), c_Orderings_Otop__class_Otop(tc_fun(_982492, tc_HOL_Obool))))), 11167 ^ _784416 : [(11168 ^ _784416) ^ [] : [-(_982498 = hAPP(_982496, 11166 ^ [_982492, _982494, _982496, _982498]))], (11170 ^ _784416) ^ [_982757] : [_982498 = hAPP(_982496, _982757), -(_982757 = 11166 ^ [_982492, _982494, _982496, _982498])]]], (11176 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_982494), _982498), hAPP(c_Set_Oimage(_982492, _982494, _982496), c_Orderings_Otop__class_Otop(tc_fun(_982492, tc_HOL_Obool)))))), 11177 ^ _784416 : [(11178 ^ _784416) ^ [_982895] : [_982498 = hAPP(_982496, _982895), 11182 ^ _784416 : [(11183 ^ _784416) ^ [] : [-(_982498 = hAPP(_982496, 11181 ^ [_982492, _982494, _982496, _982498, _982895]))], (11185 ^ _784416) ^ [] : [11181 ^ [_982492, _982494, _982496, _982498, _982895] = _982895]]]]]]], (11189 ^ _784416) ^ [_983123, _983125, _983127, _983129, _983131] : [c_Fun_Oinj__on(_983123, _983125, _983127, c_Orderings_Otop__class_Otop(tc_fun(_983123, tc_HOL_Obool))), 11192 ^ _784416 : [(11193 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_983125), hAPP(_983127, _983129)), hAPP(c_Set_Oimage(_983123, _983125, _983127), _983131))), -(hBOOL(hAPP(hAPP(c_member(_983123), _983129), _983131)))], (11199 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_983123), _983129), _983131)), -(hBOOL(hAPP(hAPP(c_member(_983125), hAPP(_983127, _983129)), hAPP(c_Set_Oimage(_983123, _983125, _983127), _983131))))]]], (11205 ^ _784416) ^ [_983434, _983436, _983438, _983440, _983442] : [c_Fun_Oinj__on(_983434, _983436, _983438, c_Orderings_Otop__class_Otop(tc_fun(_983434, tc_HOL_Obool))), 11208 ^ _784416 : [(11209 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983436, tc_HOL_Obool)), hAPP(c_Set_Oimage(_983434, _983436, _983438), _983440)), hAPP(c_Set_Oimage(_983434, _983436, _983438), _983442))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983434, tc_HOL_Obool)), _983440), _983442)))], (11215 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983434, tc_HOL_Obool)), _983440), _983442)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983436, tc_HOL_Obool)), hAPP(c_Set_Oimage(_983434, _983436, _983438), _983440)), hAPP(c_Set_Oimage(_983434, _983436, _983438), _983442))))]]], (11221 ^ _784416) ^ [_983775, _983777, _983779, _983781, _983783] : [c_Fun_Oinj__on(_983775, _983777, _983779, c_Orderings_Otop__class_Otop(tc_fun(_983775, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_983775, _983777, _983779), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_983775, tc_HOL_Obool)), _983781), _983783)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_983777, tc_HOL_Obool)), hAPP(c_Set_Oimage(_983775, _983777, _983779), _983781)), hAPP(c_Set_Oimage(_983775, _983777, _983779), _983783)))], (11227 ^ _784416) ^ [_983958, _983960, _983962, _983964, _983966] : [c_Fun_Oinj__on(_983958, _983960, _983962, c_Orderings_Otop__class_Otop(tc_fun(_983958, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_983958, _983960, _983962), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983958, tc_HOL_Obool)), _983964), _983966)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983960, tc_HOL_Obool)), hAPP(c_Set_Oimage(_983958, _983960, _983962), _983964)), hAPP(c_Set_Oimage(_983958, _983960, _983962), _983966)))], (11233 ^ _784416) ^ [_984141, _984143, _984145, _984147, _984149] : [c_Fun_Oinj__on(_984141, _984143, _984145, _984147), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984141, tc_HOL_Obool)), _984149), _984147)), -(hAPP(c_Set_Oimage(_984143, _984141, c_Hilbert__Choice_Oinv__into(_984141, _984143, _984147, _984145)), hAPP(c_Set_Oimage(_984141, _984143, _984145), _984149)) = _984149)], (11243 ^ _784416) ^ [_984344, _984346, _984348, _984350, _984352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984344, tc_HOL_Obool)), _984346), hAPP(c_Set_Oimage(_984348, _984344, _984350), _984352))), -(c_Fun_Oinj__on(_984344, _984348, c_Hilbert__Choice_Oinv__into(_984348, _984344, _984352, _984350), _984346))], (11249 ^ _784416) ^ [_984475, _984477, _984479, _984481, _984483, _984485, _984487] : [hAPP(c_Fun_Ocomp(_984475, _984477, _984479, _984481), _984483) = _984485, -(hAPP(_984481, hAPP(_984483, _984487)) = hAPP(_984485, _984487))], (11255 ^ _784416) ^ [_984596, _984598, _984600, _984602, _984604] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984596, tc_HOL_Obool)), hAPP(c_Relation_OImage(_984598, _984596, _984600), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_984598, tc_HOL_Obool)), _984602), _984604))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_984596, tc_HOL_Obool)), hAPP(c_Relation_OImage(_984598, _984596, _984600), _984602)), hAPP(c_Relation_OImage(_984598, _984596, _984600), _984604)))))], (11257 ^ _784416) ^ [_984680, _984682, _984684, _984686] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_984680, tc_HOL_Obool)), _984682), hAPP(hAPP(c_Equiv__Relations_Oquotient(_984680), _984684), _984686))), 11261 ^ _784416 : [(11262 ^ _784416) ^ [] : [-(_984682 = hAPP(c_Relation_OImage(_984680, _984680, _984686), hAPP(hAPP(c_Set_Oinsert(_984680), 11260 ^ [_984680, _984682, _984684, _984686]), c_Orderings_Obot__class_Obot(tc_fun(_984680, tc_HOL_Obool)))))], (11264 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_984680), 11260 ^ [_984680, _984682, _984684, _984686]), _984684)))]]], (11266 ^ _784416) ^ [_984908, _984910, _984912, _984914, _984916] : [-(hAPP(c_Relation_OImage(_984908, _984910, _984912), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984908, tc_HOL_Obool)), _984914), _984916)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984910, tc_HOL_Obool)), hAPP(c_Relation_OImage(_984908, _984910, _984912), _984914)), hAPP(c_Relation_OImage(_984908, _984910, _984912), _984916)))], (11268 ^ _784416) ^ [_984982, _984984, _984986, _984988, _984990] : [-(hAPP(c_Relation_OImage(_984982, _984984, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_984982, _984984), tc_HOL_Obool)), _984986), _984988)), _984990) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984984, tc_HOL_Obool)), hAPP(c_Relation_OImage(_984982, _984984, _984986), _984990)), hAPP(c_Relation_OImage(_984982, _984984, _984988), _984990)))], (11270 ^ _784416) ^ [_985059, _985061, _985063, _985065, _985067, _985069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_985059, _985061), tc_HOL_Obool)), _985063), _985065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_985059, tc_HOL_Obool)), _985067), _985069)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_985061, tc_HOL_Obool)), hAPP(c_Relation_OImage(_985059, _985061, _985063), _985067)), hAPP(c_Relation_OImage(_985059, _985061, _985065), _985069))))], (11280 ^ _784416) ^ [_985298, _985300, _985302] : [-(hAPP(c_Relation_OImage(_985298, _985300, _985302), c_Orderings_Obot__class_Obot(tc_fun(_985298, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_985300, tc_HOL_Obool)))], (11282 ^ _784416) ^ [_985342, _985344, _985346] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_985342), _985344), _985346) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_985342, tc_fun(tc_fun(_985342, tc_HOL_Obool), tc_HOL_Obool)), _985344), hAPP(hAPP(c_COMBC(_985342, tc_fun(tc_fun(_985342, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_985342, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_985342, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_985342, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_985342, tc_HOL_Obool), tc_HOL_Obool)), _985342), c_Set_Oinsert(tc_fun(_985342, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_985342, tc_HOL_Obool), tc_fun(_985342, tc_HOL_Obool), _985342), c_Relation_OImage(_985342, _985342, _985346)), hAPP(hAPP(c_COMBC(_985342, tc_fun(_985342, tc_HOL_Obool), tc_fun(_985342, tc_HOL_Obool)), c_Set_Oinsert(_985342)), c_Orderings_Obot__class_Obot(tc_fun(_985342, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_985342, tc_HOL_Obool), tc_HOL_Obool)))))], (11284 ^ _784416) ^ [_985498, _985500, _985502, _985504] : [c_Fun_Oinj__on(_985498, _985500, _985502, c_Orderings_Otop__class_Otop(tc_fun(_985498, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_985498, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_985498, _985500, _985502), hAPP(hAPP(c_Set_Oinsert(_985500), _985504), c_Orderings_Obot__class_Obot(tc_fun(_985500, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_985498), c_HOL_OThe(_985498, hAPP(hAPP(c_COMBC(_985498, _985500, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_985500, tc_fun(_985500, tc_HOL_Obool), _985498), c_fequal), _985502)), _985504))), c_Orderings_Obot__class_Obot(tc_fun(_985498, tc_HOL_Obool))))))], (11290 ^ _784416) ^ [_985731, _985733, _985735, _985737, _985739] : [c_Fun_Oinj__on(_985731, _985733, _985735, c_Orderings_Otop__class_Otop(tc_fun(_985731, tc_HOL_Obool))), 11296 ^ _784416 : [(11297 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_985733), 11295 ^ [_985731, _985733, _985735, _985737, _985739]), hAPP(c_Set_Oimage(_985731, _985733, _985735), c_Orderings_Otop__class_Otop(tc_fun(_985731, tc_HOL_Obool))))))], (11299 ^ _784416) ^ [] : [hBOOL(hAPP(_985737, hAPP(c_Hilbert__Choice_Oinv__into(_985731, _985733, c_Orderings_Otop__class_Otop(tc_fun(_985731, tc_HOL_Obool)), _985735), 11295 ^ [_985731, _985733, _985735, _985737, _985739])))]], -(hBOOL(hAPP(_985737, _985739)))], (11303 ^ _784416) ^ [_986057, _986059, _986061, _986063, _986065, _986067] : [hAPP(_986057, _986059) = _986061, hBOOL(hAPP(hAPP(c_member(_986063), _986061), _986065)), -(hBOOL(hAPP(hAPP(c_member(_986067), _986059), hAPP(c_Set_Ovimage(_986067, _986063, _986057), _986065))))], (11313 ^ _784416) ^ [_986250, _986252, _986254, _986256, _986258, _986260] : [hBOOL(hAPP(hAPP(c_member(_986250), _986252), _986254)), hBOOL(hAPP(hAPP(_986256, _986252), _986258)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_986250, tc_fun(_986260, tc_HOL_Obool)), _986254), _986256), _986258)))], (11323 ^ _784416) ^ [_986471, _986473, _986475, _986477, _986479] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_986471, _986473, _986475), _986477), _986479)), -(hBOOL(hAPP(_986477, hAPP(_986475, _986479))))], (11329 ^ _784416) ^ [_986578, _986580, _986582, _986584, _986586] : [hBOOL(hAPP(_986584, hAPP(_986582, _986586))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_986578, _986580, _986582), _986584), _986586)))], (11335 ^ _784416) ^ [_986715, _986717, _986719, _986721, _986723] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_986715, tc_fun(_986717, tc_HOL_Obool)), _986719), _986721), _986723)), 11339 ^ _784416 : [(11340 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_986715), 11338 ^ [_986715, _986717, _986719, _986721, _986723]), _986719)))], (11342 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_986721, 11338 ^ [_986715, _986717, _986719, _986721, _986723]), _986723)))]]], (11344 ^ _784416) ^ [_986903, _986905, _986907, _986909, _986911] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_986903, tc_fun(_986905, tc_HOL_Obool)), _986907), _986909), _986911))), 11345 ^ _784416 : [(11346 ^ _784416) ^ [_986975] : [hBOOL(hAPP(hAPP(c_member(_986903), _986975), _986907)), hBOOL(hAPP(hAPP(_986909, _986975), _986911))]]], (11354 ^ _784416) ^ [_987127, _987129] : [-(hAPP(c_Set_Ovimage(_987127, _987127, c_COMBI(_987127)), _987129) = _987129)], (11356 ^ _784416) ^ [_987161, _987163, _987165, _987167, _987169, _987171] : [-(hAPP(c_Relation_OImage(_987161, _987163, _987165), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_987167, tc_fun(_987161, tc_HOL_Obool)), _987169), _987171)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_987167, tc_fun(_987163, tc_HOL_Obool)), _987169), hAPP(hAPP(c_COMBB(tc_fun(_987161, tc_HOL_Obool), tc_fun(_987163, tc_HOL_Obool), _987167), c_Relation_OImage(_987161, _987163, _987165)), _987171)))], (11358 ^ _784416) ^ [_987245, _987247, _987249, _987251, _987253, _987255] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_987245, tc_fun(_987247, tc_HOL_Obool)), _987249), hAPP(c_Fun_Ocomp(_987251, tc_fun(_987247, tc_HOL_Obool), _987245, _987253), _987255)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_987251, tc_fun(_987247, tc_HOL_Obool)), hAPP(c_Set_Oimage(_987245, _987251, _987255), _987249)), _987253))], (11360 ^ _784416) ^ [_987344, _987346, _987348, _987350, _987352] : [hBOOL(hAPP(hAPP(c_member(_987344), _987346), hAPP(c_Set_Ovimage(_987344, _987348, _987350), _987352))), -(hBOOL(hAPP(hAPP(c_member(_987348), hAPP(_987350, _987346)), _987352)))], (11366 ^ _784416) ^ [_987471, _987473, _987475, _987477, _987479] : [hBOOL(hAPP(hAPP(c_member(_987475), hAPP(_987477, _987473)), _987479)), -(hBOOL(hAPP(hAPP(c_member(_987471), _987473), hAPP(c_Set_Ovimage(_987471, _987475, _987477), _987479))))], (11372 ^ _784416) ^ [_987604, _987606, _987608, _987610, _987612] : [hBOOL(hAPP(hAPP(c_member(_987604), _987606), hAPP(c_Set_Ovimage(_987604, _987608, _987610), _987612))), -(hBOOL(hAPP(hAPP(c_member(_987608), hAPP(_987610, _987606)), _987612)))], (11378 ^ _784416) ^ [_987735, _987737, _987739, _987741, _987743] : [hBOOL(hAPP(hAPP(c_member(_987735), hAPP(_987737, _987739)), _987741)), -(hBOOL(hAPP(hAPP(c_member(_987743), _987739), hAPP(c_Set_Ovimage(_987743, _987735, _987737), _987741))))], (11384 ^ _784416) ^ [_987866, _987868, _987870] : [-(hAPP(c_Set_Ovimage(_987866, _987868, _987870), c_Orderings_Obot__class_Obot(tc_fun(_987868, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_987866, tc_HOL_Obool)))], (11386 ^ _784416) ^ [_987910, _987912, _987914, _987916, _987918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_987910, tc_HOL_Obool)), _987912), _987914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_987916, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_987916, _987910, _987918), _987912)), hAPP(c_Set_Ovimage(_987916, _987910, _987918), _987914))))], (11392 ^ _784416) ^ [_988061, _988063, _988065] : [-(hAPP(c_Set_Ovimage(_988061, _988063, _988065), c_Orderings_Otop__class_Otop(tc_fun(_988063, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_988061, tc_HOL_Obool)))], (11394 ^ _784416) ^ [_988105, _988107, _988109, _988111, _988113] : [-(hAPP(c_Set_Ovimage(_988105, _988107, _988109), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_988107, tc_HOL_Obool)), _988111), _988113)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_988105, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_988105, _988107, _988109), _988111)), hAPP(c_Set_Ovimage(_988105, _988107, _988109), _988113)))], (11396 ^ _784416) ^ [_988179, _988181, _988183, _988185, _988187] : [-(hAPP(c_Set_Ovimage(_988179, _988181, _988183), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_988181, tc_HOL_Obool)), _988185), _988187)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_988179, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_988179, _988181, _988183), _988185)), hAPP(c_Set_Ovimage(_988179, _988181, _988183), _988187)))], (11398 ^ _784416) ^ [_988253, _988255, _988257, _988259, _988261, _988263] : [-(hAPP(c_Set_Ovimage(_988253, _988255, hAPP(c_Fun_Ocomp(_988257, _988255, _988253, _988259), _988261)), _988263) = hAPP(c_Set_Ovimage(_988253, _988257, _988261), hAPP(c_Set_Ovimage(_988257, _988255, _988259), _988263)))], (11400 ^ _784416) ^ [_988315, _988317, _988319, _988321, _988323] : [-(hAPP(c_Set_Ovimage(_988315, _988317, _988319), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_988317, tc_HOL_Obool)), _988321), _988323)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_988315, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_988315, _988317, _988319), _988321)), hAPP(c_Set_Ovimage(_988315, _988317, _988319), _988323)))], (11402 ^ _784416) ^ [_988389, _988391, _988393, _988395] : [-(hAPP(c_Set_Ovimage(_988389, _988391, _988393), hAPP(c_Set_OCollect(_988391), _988395)) = hAPP(c_Set_OCollect(_988389), hAPP(hAPP(c_COMBB(_988391, tc_HOL_Obool, _988389), _988395), _988393)))], (11404 ^ _784416) ^ [_988445, _988447, _988449, _988451] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_988445, tc_HOL_Obool)), hAPP(c_Set_Oimage(_988447, _988445, _988449), hAPP(c_Set_Ovimage(_988447, _988445, _988449), _988451))), _988451)))], (11406 ^ _784416) ^ [_988498, _988500, _988502, _988504] : [hAPP(c_Set_Oimage(_988498, _988500, _988502), c_Orderings_Otop__class_Otop(tc_fun(_988498, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_988500, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_988498, _988500, _988502), hAPP(c_Set_Ovimage(_988498, _988500, _988502), _988504)) = _988504)], (11412 ^ _784416) ^ [_988662, _988664, _988666, _988668] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_988662, tc_fun(_988664, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_988662, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_988664, tc_HOL_Obool), tc_fun(_988664, tc_HOL_Obool), _988662), hAPP(c_COMBC(_988664, tc_fun(_988664, tc_HOL_Obool), tc_HOL_Obool), c_member(_988664))), _988666)), _988668)), -(hBOOL(hAPP(hAPP(c_member(_988664), _988668), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_988662, tc_fun(_988664, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_988662, tc_HOL_Obool))), _988666))))], (11418 ^ _784416) ^ [_988881, _988883, _988885, _988887] : [hBOOL(hAPP(hAPP(c_member(_988883), _988887), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_988881, tc_fun(_988883, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_988881, tc_HOL_Obool))), _988885))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_988881, tc_fun(_988883, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_988881, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_988883, tc_HOL_Obool), tc_fun(_988883, tc_HOL_Obool), _988881), hAPP(c_COMBC(_988883, tc_fun(_988883, tc_HOL_Obool), tc_HOL_Obool), c_member(_988883))), _988885)), _988887)))], (11424 ^ _784416) ^ [_989106, _989108, _989110, _989112] : [-(hAPP(c_Relation_OImage(_989106, _989108, _989110), _989112) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989106, tc_fun(_989108, tc_HOL_Obool)), _989112), hAPP(hAPP(c_COMBB(tc_fun(_989106, tc_HOL_Obool), tc_fun(_989108, tc_HOL_Obool), _989106), c_Relation_OImage(_989106, _989108, _989110)), hAPP(hAPP(c_COMBC(_989106, tc_fun(_989106, tc_HOL_Obool), tc_fun(_989106, tc_HOL_Obool)), c_Set_Oinsert(_989106)), c_Orderings_Obot__class_Obot(tc_fun(_989106, tc_HOL_Obool))))))], (11426 ^ _784416) ^ [_989197, _989199, _989201, _989203] : [-(hAPP(c_Set_Ovimage(_989197, _989199, _989201), _989203) = hAPP(c_Set_OCollect(_989197), hAPP(hAPP(c_COMBC(_989197, tc_fun(_989199, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_989199, tc_fun(tc_fun(_989199, tc_HOL_Obool), tc_HOL_Obool), _989197), c_member(_989199)), _989201)), _989203)))], (11428 ^ _784416) ^ [_989293, _989295, _989297, _989299, _989301] : [hBOOL(hAPP(hAPP(c_member(_989293), _989295), hAPP(c_Set_Ovimage(_989293, _989297, _989299), hAPP(hAPP(c_Set_Oinsert(_989297), _989301), c_Orderings_Obot__class_Obot(tc_fun(_989297, tc_HOL_Obool)))))), -(hAPP(_989299, _989295) = _989301)], (11434 ^ _784416) ^ [_989432, _989434, _989436, _989438, _989440] : [hAPP(_989438, _989434) = _989440, -(hBOOL(hAPP(hAPP(c_member(_989432), _989434), hAPP(c_Set_Ovimage(_989432, _989436, _989438), hAPP(hAPP(c_Set_Oinsert(_989436), _989440), c_Orderings_Obot__class_Obot(tc_fun(_989436, tc_HOL_Obool)))))))], (11440 ^ _784416) ^ [_989577, _989579, _989581, _989583, _989585] : [-(hAPP(c_Set_Ovimage(_989577, _989579, _989581), hAPP(hAPP(c_Set_Oinsert(_989579), _989583), _989585)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_989577, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_989577, _989579, _989581), hAPP(hAPP(c_Set_Oinsert(_989579), _989583), c_Orderings_Obot__class_Obot(tc_fun(_989579, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_989577, _989579, _989581), _989585)))], (11442 ^ _784416) ^ [_989661, _989663, _989665, _989667, _989669] : [hAPP(c_Set_Oimage(_989661, _989663, _989665), c_Orderings_Otop__class_Otop(tc_fun(_989661, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_989663, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989661, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_989661, _989663, _989665), _989667)), _989669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989663, tc_HOL_Obool)), _989667), hAPP(c_Set_Oimage(_989661, _989663, _989665), _989669))))], (11452 ^ _784416) ^ [_989904, _989906, _989908, _989910] : [-(hAPP(c_Set_Oimage(_989904, _989906, _989908), hAPP(c_Set_Ovimage(_989904, _989906, _989908), _989910)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_989906, tc_HOL_Obool)), _989910), hAPP(c_Set_Oimage(_989904, _989906, _989908), c_Orderings_Otop__class_Otop(tc_fun(_989904, tc_HOL_Obool)))))], (11454 ^ _784416) ^ [_989970, _989972, _989974, _989976] : [c_Fun_Oinj__on(_989970, _989972, _989974, c_Orderings_Otop__class_Otop(tc_fun(_989970, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_989970, _989972, _989974), hAPP(c_Set_Oimage(_989970, _989972, _989974), _989976)) = _989976)], (11460 ^ _784416) ^ [_990108, _990110, _990112, _990114] : [hBOOL(hAPP(hAPP(c_member(_990108), _990110), _990112)), -(hAPP(c_Set_Ovimage(_990114, _990108, hAPP(c_COMBK(_990108, _990114), _990110)), _990112) = c_Orderings_Otop__class_Otop(tc_fun(_990114, tc_HOL_Obool)))], (11466 ^ _784416) ^ [_990233, _990235, _990237, _990239] : [-(hBOOL(hAPP(hAPP(c_member(_990233), _990235), _990237))), -(hAPP(c_Set_Ovimage(_990239, _990233, hAPP(c_COMBK(_990233, _990239), _990235)), _990237) = c_Orderings_Obot__class_Obot(tc_fun(_990239, tc_HOL_Obool)))], (11472 ^ _784416) ^ [_990300, _990302, _990304, _990306, _990308] : [c_Fun_Oinj__on(_990300, _990302, _990304, c_Orderings_Otop__class_Otop(tc_fun(_990300, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990302, tc_HOL_Obool)), _990306), hAPP(c_Set_Oimage(_990300, _990302, _990304), _990308))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990300, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_990300, _990302, _990304), _990306)), _990308)))], (11482 ^ _784416) ^ [_990523, _990525, _990527, _990529, _990531, _990533] : [hBOOL(hAPP(hAPP(c_member(_990523), _990525), _990527)), hBOOL(hAPP(hAPP(c_member(_990529), _990531), hAPP(_990533, _990525))), -(hBOOL(hAPP(hAPP(c_member(_990529), _990531), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990523, tc_fun(_990529, tc_HOL_Obool)), _990527), _990533))))], (11492 ^ _784416) ^ [_990740, _990742, _990744, _990746] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_990740, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990742, tc_fun(tc_fun(_990740, tc_HOL_Obool), tc_HOL_Obool)), _990744), hAPP(hAPP(c_COMBB(tc_fun(_990740, tc_HOL_Obool), tc_fun(tc_fun(_990740, tc_HOL_Obool), tc_HOL_Obool), _990742), c_Set_OPow(_990740)), _990746))), hAPP(c_Set_OPow(_990740), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990742, tc_fun(_990740, tc_HOL_Obool)), _990744), _990746)))))], (11494 ^ _784416) ^ [_990835, _990837, _990839, _990841] : [-(hAPP(c_Set_Ovimage(_990835, _990837, _990839), _990841) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990837, tc_fun(_990835, tc_HOL_Obool)), _990841), hAPP(hAPP(c_COMBB(tc_fun(_990837, tc_HOL_Obool), tc_fun(_990835, tc_HOL_Obool), _990837), c_Set_Ovimage(_990835, _990837, _990839)), hAPP(hAPP(c_COMBC(_990837, tc_fun(_990837, tc_HOL_Obool), tc_fun(_990837, tc_HOL_Obool)), c_Set_Oinsert(_990837)), c_Orderings_Obot__class_Obot(tc_fun(_990837, tc_HOL_Obool))))))], (11496 ^ _784416) ^ [_990926, _990928, _990930, _990932] : [-(hAPP(c_Set_Oimage(_990926, _990928, _990930), _990932) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990926, tc_fun(_990928, tc_HOL_Obool)), _990932), hAPP(hAPP(c_COMBC(_990926, tc_fun(_990928, tc_HOL_Obool), tc_fun(_990928, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_990928, tc_fun(tc_fun(_990928, tc_HOL_Obool), tc_fun(_990928, tc_HOL_Obool)), _990926), c_Set_Oinsert(_990928)), _990930)), c_Orderings_Obot__class_Obot(tc_fun(_990928, tc_HOL_Obool)))))], (11498 ^ _784416) ^ [_991016, _991018, _991020, _991022, _991024, _991026] : [c_Equiv__Relations_Oequiv(_991016, _991018, _991020), c_Equiv__Relations_Ocongruent(_991016, tc_fun(_991022, tc_HOL_Obool), _991020, _991024), hBOOL(hAPP(hAPP(c_member(_991016), _991026), _991018)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991016, tc_fun(_991022, tc_HOL_Obool)), hAPP(c_Relation_OImage(_991016, _991016, _991020), hAPP(hAPP(c_Set_Oinsert(_991016), _991026), c_Orderings_Obot__class_Obot(tc_fun(_991016, tc_HOL_Obool))))), _991024) = hAPP(_991024, _991026))], (11512 ^ _784416) ^ [_991317, _991319, _991321, _991323, _991325, _991327, _991329, _991331, _991333, _991335] : [c_Equiv__Relations_Oequiv(_991317, _991319, _991321), c_Equiv__Relations_Oequiv(_991323, _991325, _991327), c_Equiv__Relations_Ocongruent2(_991317, _991323, tc_fun(_991329, tc_HOL_Obool), _991321, _991327, _991331), hBOOL(hAPP(hAPP(c_member(_991317), _991333), _991319)), hBOOL(hAPP(hAPP(c_member(_991323), _991335), _991325)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991317, tc_fun(_991329, tc_HOL_Obool)), hAPP(c_Relation_OImage(_991317, _991317, _991321), hAPP(hAPP(c_Set_Oinsert(_991317), _991333), c_Orderings_Obot__class_Obot(tc_fun(_991317, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_991323, tc_fun(_991329, tc_HOL_Obool)), tc_fun(_991329, tc_HOL_Obool), _991317), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991323, tc_fun(_991329, tc_HOL_Obool)), hAPP(c_Relation_OImage(_991323, _991323, _991327), hAPP(hAPP(c_Set_Oinsert(_991323), _991335), c_Orderings_Obot__class_Obot(tc_fun(_991323, tc_HOL_Obool)))))), _991331)) = hAPP(hAPP(_991331, _991333), _991335))], (11534 ^ _784416) ^ [_991900, _991902, _991904, _991906, _991908] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991900, tc_fun(_991902, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_991900), _991904), _991906)), _991908) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_991902, tc_HOL_Obool)), hAPP(_991908, _991904)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991900, tc_fun(_991902, tc_HOL_Obool)), _991906), _991908)))], (11536 ^ _784416) ^ [_991995, _991997, _991999, _992001, _992003] : [_991995 = c_Orderings_Obot__class_Obot(tc_fun(_991997, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_991999, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991997, tc_fun(_991999, tc_HOL_Obool)), _991995), _992001)), _992003) = _992003)], (11542 ^ _784416) ^ [_992128, _992130, _992132, _992134, _992136] : [-(_992128 = c_Orderings_Obot__class_Obot(tc_fun(_992130, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_992132, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992130, tc_fun(_992132, tc_HOL_Obool)), _992128), _992134)), _992136) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992130, tc_fun(_992132, tc_HOL_Obool)), _992128), hAPP(hAPP(c_COMBC(_992130, tc_fun(_992132, tc_HOL_Obool), tc_fun(_992132, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_992132, tc_HOL_Obool), tc_fun(tc_fun(_992132, tc_HOL_Obool), tc_fun(_992132, tc_HOL_Obool)), _992130), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_992132, tc_HOL_Obool))), _992134)), _992136)))], (11548 ^ _784416) ^ [_992273, _992275, _992277, _992279, _992281] : [_992273 = c_Orderings_Obot__class_Obot(tc_fun(_992275, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_992277, tc_HOL_Obool)), _992279), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992275, tc_fun(_992277, tc_HOL_Obool)), _992273), _992281)) = _992279)], (11554 ^ _784416) ^ [_992406, _992408, _992410, _992412, _992414] : [-(_992406 = c_Orderings_Obot__class_Obot(tc_fun(_992408, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_992410, tc_HOL_Obool)), _992412), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992408, tc_fun(_992410, tc_HOL_Obool)), _992406), _992414)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992408, tc_fun(_992410, tc_HOL_Obool)), _992406), hAPP(hAPP(c_COMBB(tc_fun(_992410, tc_HOL_Obool), tc_fun(_992410, tc_HOL_Obool), _992408), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_992410, tc_HOL_Obool)), _992412)), _992414)))], (11560 ^ _784416) ^ [_992514, _992516, _992518, _992520, _992522, _992524, _992526, _992528] : [c_Equiv__Relations_Oequiv(_992514, _992516, _992518), c_Equiv__Relations_Ocongruent2(_992514, _992520, _992522, _992518, _992524, _992526), hBOOL(hAPP(hAPP(c_member(_992514), _992528), _992516)), -(c_Equiv__Relations_Ocongruent(_992520, _992522, _992524, hAPP(_992526, _992528)))], (11591 ^ _784416) ^ [_993225, _993227, _993229, _993231, _993233] : [11593 ^ _784416 : [(11594 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_993227), 11592 ^ [_993225, _993227, _993229, _993231, _993233]), _993229)))], (11597 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_993225), 11595 ^ [_993225, _993227, _993229, _993231, _993233]), hAPP(_993231, 11592 ^ [_993225, _993227, _993229, _993231, _993233]))))], (11599 ^ _784416) ^ [] : [hBOOL(hAPP(_993233, 11595 ^ [_993225, _993227, _993229, _993231, _993233]))]], 11600 ^ _784416 : [(11601 ^ _784416) ^ [_993535] : [hBOOL(hAPP(hAPP(c_member(_993225), _993535), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993227, tc_fun(_993225, tc_HOL_Obool)), _993229), _993231))), -(hBOOL(hAPP(_993233, _993535)))]]], (11574 ^ _784416) ^ [_992789, _992791, _992793, _992795, _992797] : [11576 ^ _784416 : [(11577 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_992789), 11575 ^ [_992789, _992791, _992793, _992795, _992797]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992791, tc_fun(_992789, tc_HOL_Obool)), _992793), _992795))))], (11579 ^ _784416) ^ [] : [hBOOL(hAPP(_992797, 11575 ^ [_992789, _992791, _992793, _992795, _992797]))]], 11580 ^ _784416 : [(11581 ^ _784416) ^ [_993011] : [hBOOL(hAPP(hAPP(c_member(_992791), _993011), _992793)), 11584 ^ _784416 : [(11585 ^ _784416) ^ [_993108] : [hBOOL(hAPP(hAPP(c_member(_992789), _993108), hAPP(_992795, _993011))), -(hBOOL(hAPP(_992797, _993108)))]]]]], (11607 ^ _784416) ^ [_993670, _993672, _993674, _993676, _993678, _993680] : [class_Complete__Lattice_Ocomplete__lattice(_993670), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993672, _993670), _993674), hAPP(hAPP(c_COMBB(tc_fun(_993676, _993670), _993670, _993672), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993676, _993670), _993678)), _993680)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993676, _993670), _993678), hAPP(hAPP(c_COMBB(tc_fun(_993672, _993670), _993670, _993676), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993672, _993670), _993674)), hAPP(c_COMBC(_993672, _993676, _993670), _993680))))], (11613 ^ _784416) ^ [_993879, _993881, _993883, _993885, _993887, _993889] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993879, tc_fun(_993881, tc_HOL_Obool)), _993883), hAPP(hAPP(c_COMBC(_993879, tc_fun(_993885, tc_fun(_993881, tc_HOL_Obool)), tc_fun(_993881, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_993885, tc_HOL_Obool), tc_fun(tc_fun(_993885, tc_fun(_993881, tc_HOL_Obool)), tc_fun(_993881, tc_HOL_Obool)), _993879), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993885, tc_fun(_993881, tc_HOL_Obool))), _993887)), _993889)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993885, tc_fun(_993881, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993879, tc_fun(_993885, tc_HOL_Obool)), _993883), _993887)), _993889))], (11615 ^ _784416) ^ [_993998, _994000, _994002, _994004, _994006, _994008] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993998, tc_fun(_994000, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_994002, tc_fun(_993998, tc_HOL_Obool)), _994004), _994006)), _994008) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_994002, tc_fun(_994000, tc_HOL_Obool)), _994004), hAPP(hAPP(c_COMBC(_994002, tc_fun(_993998, tc_fun(_994000, tc_HOL_Obool)), tc_fun(_994000, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_993998, tc_HOL_Obool), tc_fun(tc_fun(_993998, tc_fun(_994000, tc_HOL_Obool)), tc_fun(_994000, tc_HOL_Obool)), _994002), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993998, tc_fun(_994000, tc_HOL_Obool))), _994006)), _994008)))], (11617 ^ _784416) ^ [_994117, _994119, _994121, _994123, _994125, _994127] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_994117, tc_fun(_994119, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_994121, tc_fun(_994117, tc_HOL_Obool)), _994123), _994125)), _994127) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_994121, tc_fun(_994119, tc_HOL_Obool)), _994123), hAPP(hAPP(c_COMBC(_994121, tc_fun(_994117, tc_fun(_994119, tc_HOL_Obool)), tc_fun(_994119, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_994117, tc_HOL_Obool), tc_fun(tc_fun(_994117, tc_fun(_994119, tc_HOL_Obool)), tc_fun(_994119, tc_HOL_Obool)), _994121), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_994117, tc_fun(_994119, tc_HOL_Obool))), _994125)), _994127)))], (11619 ^ _784416) ^ [_994236, _994238, _994240, _994242, _994244, _994246, _994248, _994250, _994252] : [c_Equiv__Relations_Oequiv(_994236, _994238, _994240), c_Equiv__Relations_Oequiv(_994242, _994244, _994246), c_Equiv__Relations_Ocongruent2(_994236, _994242, tc_fun(_994248, tc_HOL_Obool), _994240, _994246, _994250), hBOOL(hAPP(hAPP(c_member(_994242), _994252), _994244)), -(c_Equiv__Relations_Ocongruent(_994236, tc_fun(_994248, tc_HOL_Obool), _994240, hAPP(hAPP(c_COMBB(tc_fun(_994242, tc_fun(_994248, tc_HOL_Obool)), tc_fun(_994248, tc_HOL_Obool), _994236), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_994242, tc_fun(_994248, tc_HOL_Obool)), hAPP(c_Relation_OImage(_994242, _994242, _994246), hAPP(hAPP(c_Set_Oinsert(_994242), _994252), c_Orderings_Obot__class_Obot(tc_fun(_994242, tc_HOL_Obool)))))), _994250)))], (11637 ^ _784416) ^ [_994663, _994665, _994667, _994669, _994671] : [class_Complete__Lattice_Ocomplete__lattice(_994663), 11640 ^ _784416 : [(11651 ^ _784416) ^ [] : [11653 ^ _784416 : [(11654 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_994665), 11652 ^ [_994663, _994665, _994667, _994669, _994671]), _994667)))], (11656 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994663), hAPP(_994669, 11652 ^ [_994663, _994665, _994667, _994669, _994671])), _994671))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994663), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_994665, _994663), _994667), _994669)), _994671)))], (11641 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994663), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_994665, _994663), _994667), _994669)), _994671)), 11644 ^ _784416 : [(11645 ^ _784416) ^ [_994844] : [hBOOL(hAPP(hAPP(c_member(_994665), _994844), _994667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994663), hAPP(_994669, _994844)), _994671)))]]]]], (11660 ^ _784416) ^ [_995157, _995159, _995161, _995163, _995165] : [class_Complete__Lattice_Ocomplete__lattice(_995157), class_Orderings_Olinorder(_995157), 11667 ^ _784416 : [(11668 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995157), _995159), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_995161, _995157), _995163), _995165))), 11672 ^ _784416 : [(11673 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_995161), 11671 ^ [_995157, _995159, _995161, _995163, _995165]), _995163)))], (11675 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995157), _995159), hAPP(_995165, 11671 ^ [_995157, _995159, _995161, _995163, _995165]))))]]], (11677 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995157), _995159), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_995161, _995157), _995163), _995165)))), 11678 ^ _784416 : [(11679 ^ _784416) ^ [_995505] : [hBOOL(hAPP(hAPP(c_member(_995161), _995505), _995163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995157), _995159), hAPP(_995165, _995505)))]]]]], (11687 ^ _784416) ^ [_995699, _995701, _995703, _995705, _995707] : [hBOOL(hAPP(hAPP(c_member(_995699), _995701), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_995703, tc_fun(_995699, tc_HOL_Obool)), _995705), _995707))), 11691 ^ _784416 : [(11692 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_995703), 11690 ^ [_995699, _995701, _995703, _995705, _995707]), _995705)))], (11694 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_995699), _995701), hAPP(_995707, 11690 ^ [_995699, _995701, _995703, _995705, _995707]))))]]], (11696 ^ _784416) ^ [_995907, _995909, _995911, _995913, _995915] : [-(hBOOL(hAPP(hAPP(c_member(_995907), _995909), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_995911, tc_fun(_995907, tc_HOL_Obool)), _995913), _995915)))), 11697 ^ _784416 : [(11698 ^ _784416) ^ [_995989] : [hBOOL(hAPP(hAPP(c_member(_995911), _995989), _995913)), hBOOL(hAPP(hAPP(c_member(_995907), _995909), hAPP(_995915, _995989)))]]], (11706 ^ _784416) ^ [_996156, _996158, _996160, _996162] : [class_Complete__Lattice_Ocomplete__lattice(_996156), -(_996158 = c_Orderings_Obot__class_Obot(tc_fun(_996160, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_996160, _996156), _996158), hAPP(c_COMBK(_996156, _996160), _996162)) = _996162)], (11726 ^ _784416) ^ [_996540, _996542, _996544, _996546] : [11728 ^ _784416 : [(11729 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_996540), 11727 ^ [_996540, _996542, _996544, _996546]), _996544)))], (11731 ^ _784416) ^ [] : [hAPP(_996546, 11727 ^ [_996540, _996542, _996544, _996546]) = c_Orderings_Obot__class_Obot(tc_fun(_996542, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_996540, tc_fun(_996542, tc_HOL_Obool)), _996544), _996546) = c_Orderings_Obot__class_Obot(tc_fun(_996542, tc_HOL_Obool)))], (11716 ^ _784416) ^ [_996311, _996313, _996315, _996317] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_996311, tc_fun(_996313, tc_HOL_Obool)), _996315), _996317) = c_Orderings_Obot__class_Obot(tc_fun(_996313, tc_HOL_Obool)), 11719 ^ _784416 : [(11720 ^ _784416) ^ [_996427] : [hBOOL(hAPP(hAPP(c_member(_996311), _996427), _996315)), -(hAPP(_996317, _996427) = c_Orderings_Obot__class_Obot(tc_fun(_996313, tc_HOL_Obool)))]]], (11735 ^ _784416) ^ [_996785, _996787, _996789, _996791] : [_996785 = c_Orderings_Obot__class_Obot(tc_fun(_996787, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_996787, tc_fun(_996789, tc_HOL_Obool)), _996785), hAPP(c_COMBK(tc_fun(_996789, tc_HOL_Obool), _996787), _996791)) = c_Orderings_Obot__class_Obot(tc_fun(_996789, tc_HOL_Obool)))], (11741 ^ _784416) ^ [_996922, _996924, _996926, _996928] : [-(_996922 = c_Orderings_Obot__class_Obot(tc_fun(_996924, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_996924, tc_fun(_996926, tc_HOL_Obool)), _996922), hAPP(c_COMBK(tc_fun(_996926, tc_HOL_Obool), _996924), _996928)) = _996928)], (11747 ^ _784416) ^ [_996990, _996992, _996994] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_996990, tc_fun(_996992, tc_HOL_Obool)), _996994), hAPP(c_COMBK(tc_fun(_996992, tc_HOL_Obool), _996990), c_Orderings_Obot__class_Obot(tc_fun(_996992, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_996992, tc_HOL_Obool)))], (11759 ^ _784416) ^ [_997298, _997300, _997302, _997304] : [11761 ^ _784416 : [(11762 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_997300), 11760 ^ [_997298, _997300, _997302, _997304]), _997302)))], (11764 ^ _784416) ^ [] : [hAPP(_997304, 11760 ^ [_997298, _997300, _997302, _997304]) = c_Orderings_Obot__class_Obot(tc_fun(_997298, tc_HOL_Obool))]], -(c_Orderings_Obot__class_Obot(tc_fun(_997298, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_997300, tc_fun(_997298, tc_HOL_Obool)), _997302), _997304))], (11749 ^ _784416) ^ [_997069, _997071, _997073, _997075] : [c_Orderings_Obot__class_Obot(tc_fun(_997069, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_997071, tc_fun(_997069, tc_HOL_Obool)), _997073), _997075), 11752 ^ _784416 : [(11753 ^ _784416) ^ [_997185] : [hBOOL(hAPP(hAPP(c_member(_997071), _997185), _997073)), -(hAPP(_997075, _997185) = c_Orderings_Obot__class_Obot(tc_fun(_997069, tc_HOL_Obool)))]]], (11778 ^ _784416) ^ [_997810, _997812, _997814, _997816, _997818] : [11780 ^ _784416 : [(11781 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_997812), 11779 ^ [_997810, _997812, _997814, _997816, _997818]), _997814)))], (11783 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997810, tc_HOL_Obool)), hAPP(_997816, 11779 ^ [_997810, _997812, _997814, _997816, _997818])), _997818))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997810, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_997812, tc_fun(_997810, tc_HOL_Obool)), _997814), _997816)), _997818)))], (11768 ^ _784416) ^ [_997552, _997554, _997556, _997558, _997560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997552, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_997554, tc_fun(_997552, tc_HOL_Obool)), _997556), _997558)), _997560)), 11771 ^ _784416 : [(11772 ^ _784416) ^ [_997685] : [hBOOL(hAPP(hAPP(c_member(_997554), _997685), _997556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_997552, tc_HOL_Obool)), hAPP(_997558, _997685)), _997560)))]]], (11787 ^ _784416) ^ [_998073, _998075, _998077, _998079, _998081, _998083] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998073, tc_fun(_998075, tc_HOL_Obool)), _998077), hAPP(hAPP(c_COMBB(_998079, tc_fun(_998075, tc_HOL_Obool), _998073), _998081), _998083)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998079, tc_fun(_998075, tc_HOL_Obool)), hAPP(c_Set_Oimage(_998073, _998079, _998083), _998077)), _998081))], (11789 ^ _784416) ^ [_998150, _998152, _998154, _998156, _998158, _998160] : [-(hAPP(c_Set_Oimage(_998150, _998152, _998154), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998156, tc_fun(_998150, tc_HOL_Obool)), _998158), _998160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998156, tc_fun(_998152, tc_HOL_Obool)), _998158), hAPP(hAPP(c_COMBB(tc_fun(_998150, tc_HOL_Obool), tc_fun(_998152, tc_HOL_Obool), _998156), c_Set_Oimage(_998150, _998152, _998154)), _998160)))], (11791 ^ _784416) ^ [_998234, _998236, _998238, _998240, _998242, _998244] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998234, tc_fun(_998236, tc_HOL_Obool)), hAPP(c_Set_Oimage(_998238, _998234, _998240), _998242)), _998244) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998238, tc_fun(_998236, tc_HOL_Obool)), _998242), hAPP(hAPP(c_COMBB(_998234, tc_fun(_998236, tc_HOL_Obool), _998238), _998244), _998240)))], (11793 ^ _784416) ^ [_998311, _998313, _998315, _998317, _998319] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998311, tc_fun(_998313, tc_HOL_Obool)), _998315), hAPP(hAPP(c_COMBS(_998311, tc_fun(_998313, tc_HOL_Obool), tc_fun(_998313, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_998313, tc_HOL_Obool), tc_fun(tc_fun(_998313, tc_HOL_Obool), tc_fun(_998313, tc_HOL_Obool)), _998311), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_998313, tc_HOL_Obool))), _998317)), _998319)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_998313, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998311, tc_fun(_998313, tc_HOL_Obool)), _998315), _998317)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998311, tc_fun(_998313, tc_HOL_Obool)), _998315), _998319)))], (11795 ^ _784416) ^ [_998432, _998434, _998436, _998438, _998440] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998432, tc_fun(_998434, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_998432, tc_HOL_Obool)), _998436), _998438)), _998440) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_998434, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998432, tc_fun(_998434, tc_HOL_Obool)), _998436), _998440)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998432, tc_fun(_998434, tc_HOL_Obool)), _998438), _998440)))], (11797 ^ _784416) ^ [_998521, _998523, _998525, _998527, _998529] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998521, tc_fun(_998523, tc_HOL_Obool)), _998525), hAPP(hAPP(c_COMBB(tc_fun(_998523, tc_HOL_Obool), tc_fun(_998523, tc_HOL_Obool), _998521), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998523, tc_HOL_Obool)), _998527)), _998529)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998523, tc_HOL_Obool)), _998527), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998521, tc_fun(_998523, tc_HOL_Obool)), _998525), _998529)))], (11799 ^ _784416) ^ [_998611, _998613, _998615, _998617, _998619] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998611, tc_fun(_998613, tc_HOL_Obool)), _998615), hAPP(hAPP(c_COMBC(_998611, tc_fun(_998613, tc_HOL_Obool), tc_fun(_998613, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_998613, tc_HOL_Obool), tc_fun(tc_fun(_998613, tc_HOL_Obool), tc_fun(_998613, tc_HOL_Obool)), _998611), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998613, tc_HOL_Obool))), _998617)), _998619)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998613, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998611, tc_fun(_998613, tc_HOL_Obool)), _998615), _998617)), _998619))], (11801 ^ _784416) ^ [_998720, _998722, _998724, _998726, _998728] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998720, tc_HOL_Obool)), _998722), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998724, tc_fun(_998720, tc_HOL_Obool)), _998726), _998728)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998724, tc_fun(_998720, tc_HOL_Obool)), _998726), hAPP(hAPP(c_COMBB(tc_fun(_998720, tc_HOL_Obool), tc_fun(_998720, tc_HOL_Obool), _998724), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998720, tc_HOL_Obool)), _998722)), _998728)))], (11803 ^ _784416) ^ [_998810, _998812, _998814, _998816, _998818] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998810, tc_HOL_Obool)), _998812), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998814, tc_fun(_998810, tc_HOL_Obool)), _998816), _998818)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998814, tc_fun(_998810, tc_HOL_Obool)), _998816), hAPP(hAPP(c_COMBB(tc_fun(_998810, tc_HOL_Obool), tc_fun(_998810, tc_HOL_Obool), _998814), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998810, tc_HOL_Obool)), _998812)), _998818)))], (11805 ^ _784416) ^ [_998900, _998902, _998904, _998906, _998908] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998900, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998902, tc_fun(_998900, tc_HOL_Obool)), _998904), _998906)), _998908) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_998902, tc_fun(_998900, tc_HOL_Obool)), _998904), hAPP(hAPP(c_COMBC(_998902, tc_fun(_998900, tc_HOL_Obool), tc_fun(_998900, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_998900, tc_HOL_Obool), tc_fun(tc_fun(_998900, tc_HOL_Obool), tc_fun(_998900, tc_HOL_Obool)), _998902), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_998900, tc_HOL_Obool))), _998906)), _998908)))], (11807 ^ _784416) ^ [_999009, _999011, _999013, _999015, _999017, _999019, _999021] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_999009, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999011, tc_fun(_999009, tc_HOL_Obool)), _999013), _999015)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999017, tc_fun(_999009, tc_HOL_Obool)), _999019), _999021)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999011, tc_fun(_999009, tc_HOL_Obool)), _999013), hAPP(hAPP(c_COMBB(tc_fun(_999017, tc_fun(_999009, tc_HOL_Obool)), tc_fun(_999009, tc_HOL_Obool), _999011), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999017, tc_fun(_999009, tc_HOL_Obool)), _999019)), hAPP(hAPP(c_COMBC(_999011, tc_fun(_999017, tc_fun(_999009, tc_HOL_Obool)), tc_fun(_999017, tc_fun(_999009, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_999009, tc_HOL_Obool), tc_fun(_999009, tc_HOL_Obool)), tc_fun(tc_fun(_999017, tc_fun(_999009, tc_HOL_Obool)), tc_fun(_999017, tc_fun(_999009, tc_HOL_Obool))), _999011), c_COMBB(tc_fun(_999009, tc_HOL_Obool), tc_fun(_999009, tc_HOL_Obool), _999017)), hAPP(hAPP(c_COMBB(tc_fun(_999009, tc_HOL_Obool), tc_fun(tc_fun(_999009, tc_HOL_Obool), tc_fun(_999009, tc_HOL_Obool)), _999011), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_999009, tc_HOL_Obool))), _999015))), _999021))))], (11809 ^ _784416) ^ [_999212, _999214, _999216, _999218, _999220, _999222] : [class_Complete__Lattice_Ocomplete__lattice(_999212), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999214, tc_fun(_999216, _999212)), _999218), _999220), _999222) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999214, _999212), _999218), hAPP(hAPP(c_COMBC(_999214, _999216, _999212), _999220), _999222)))], (11815 ^ _784416) ^ [_999363, _999365, _999367, _999369, _999371] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999363, tc_fun(_999365, tc_HOL_Obool)), _999367), hAPP(hAPP(c_COMBC(_999363, tc_fun(_999365, tc_HOL_Obool), tc_fun(_999365, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_999365, tc_HOL_Obool), tc_fun(tc_fun(_999365, tc_HOL_Obool), tc_fun(_999365, tc_HOL_Obool)), _999363), c_Groups_Ominus__class_Ominus(tc_fun(_999365, tc_HOL_Obool))), _999369)), _999371)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_999365, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999363, tc_fun(_999365, tc_HOL_Obool)), _999367), _999369)), _999371))], (11817 ^ _784416) ^ [_999472, _999474, _999476, _999478, _999480] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_999472, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999474, tc_fun(_999472, tc_HOL_Obool)), _999476), _999478)), _999480) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999474, tc_fun(_999472, tc_HOL_Obool)), _999476), hAPP(hAPP(c_COMBC(_999474, tc_fun(_999472, tc_HOL_Obool), tc_fun(_999472, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_999472, tc_HOL_Obool), tc_fun(tc_fun(_999472, tc_HOL_Obool), tc_fun(_999472, tc_HOL_Obool)), _999474), c_Groups_Ominus__class_Ominus(tc_fun(_999472, tc_HOL_Obool))), _999478)), _999480)))], (11819 ^ _784416) ^ [_999581, _999583, _999585, _999587, _999589, _999591] : [-(hAPP(c_Set_Ovimage(_999581, _999583, _999585), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999587, tc_fun(_999583, tc_HOL_Obool)), _999589), _999591)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999587, tc_fun(_999581, tc_HOL_Obool)), _999589), hAPP(hAPP(c_COMBB(tc_fun(_999583, tc_HOL_Obool), tc_fun(_999581, tc_HOL_Obool), _999587), c_Set_Ovimage(_999581, _999583, _999585)), _999591)))], (11821 ^ _784416) ^ [_999665, _999667, _999669, _999671, _999673] : [class_Complete__Lattice_Ocomplete__lattice(_999665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999667, tc_HOL_Obool)), _999669), _999671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999665), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999667, _999665), _999669), _999673)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999667, _999665), _999671), _999673))))], (11831 ^ _784416) ^ [_999874, _999876, _999878, _999880, _999882] : [class_Complete__Lattice_Ocomplete__lattice(_999874), hBOOL(hAPP(hAPP(c_member(_999876), _999878), _999880)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999874), hAPP(_999882, _999878)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_999876, _999874), _999880), _999882))))], (11841 ^ _784416) ^ [_1000065, _1000067, _1000069, _1000071, _1000073, _1000075] : [hBOOL(hAPP(hAPP(c_member(_1000065), _1000067), _1000069)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1000065, tc_fun(_1000071, tc_HOL_Obool)), _1000069), hAPP(hAPP(c_COMBB(tc_fun(_1000071, tc_HOL_Obool), tc_fun(_1000071, tc_HOL_Obool), _1000065), hAPP(c_Set_Oinsert(_1000071), _1000073)), _1000075)) = hAPP(hAPP(c_Set_Oinsert(_1000071), _1000073), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1000065, tc_fun(_1000071, tc_HOL_Obool)), _1000069), _1000075)))], (11847 ^ _784416) ^ [_1000270, _1000272, _1000274, _1000276, _1000278] : [hBOOL(hAPP(hAPP(c_member(_1000270), _1000272), _1000274)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1000276, tc_HOL_Obool)), hAPP(_1000278, _1000272)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1000270, tc_fun(_1000276, tc_HOL_Obool)), _1000274), _1000278))))], (11853 ^ _784416) ^ [_1000417, _1000419, _1000421, _1000423, _1000425] : [hBOOL(hAPP(hAPP(c_member(_1000417), _1000419), _1000421)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000423, tc_HOL_Obool)), hAPP(_1000425, _1000419)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1000417, tc_fun(_1000423, tc_HOL_Obool)), _1000421), _1000425)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1000417, tc_fun(_1000423, tc_HOL_Obool)), _1000421), _1000425))], (11859 ^ _784416) ^ [_1000608, _1000610, _1000612, _1000614, _1000616] : [_1000608 = c_Orderings_Obot__class_Obot(tc_fun(_1000610, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1000612), _1000614), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1000610, tc_fun(_1000612, tc_HOL_Obool)), _1000608), _1000616)) = hAPP(hAPP(c_Set_Oinsert(_1000612), _1000614), c_Orderings_Obot__class_Obot(tc_fun(_1000612, tc_HOL_Obool))))], (11865 ^ _784416) ^ [_1000761, _1000763, _1000765, _1000767, _1000769] : [-(_1000761 = c_Orderings_Obot__class_Obot(tc_fun(_1000763, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1000765), _1000767), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1000763, tc_fun(_1000765, tc_HOL_Obool)), _1000761), _1000769)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1000763, tc_fun(_1000765, tc_HOL_Obool)), _1000761), hAPP(hAPP(c_COMBB(tc_fun(_1000765, tc_HOL_Obool), tc_fun(_1000765, tc_HOL_Obool), _1000763), hAPP(c_Set_Oinsert(_1000765), _1000767)), _1000769)))], (11871 ^ _784416) ^ [_1000863, _1000865] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1000863, tc_fun(_1000863, tc_HOL_Obool)), _1000865), hAPP(hAPP(c_COMBC(_1000863, tc_fun(_1000863, tc_HOL_Obool), tc_fun(_1000863, tc_HOL_Obool)), c_Set_Oinsert(_1000863)), c_Orderings_Obot__class_Obot(tc_fun(_1000863, tc_HOL_Obool)))) = _1000865)], (11873 ^ _784416) ^ [_1000941, _1000943, _1000945, _1000947, _1000949] : [_1000941 = c_Orderings_Obot__class_Obot(tc_fun(_1000943, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1000943, tc_fun(_1000945, tc_HOL_Obool)), _1000941), hAPP(hAPP(c_COMBB(tc_fun(_1000945, tc_HOL_Obool), tc_fun(_1000945, tc_HOL_Obool), _1000943), hAPP(c_Set_Oinsert(_1000945), _1000947)), _1000949)) = c_Orderings_Obot__class_Obot(tc_fun(_1000945, tc_HOL_Obool)))], (11879 ^ _784416) ^ [_1001104, _1001106, _1001108, _1001110, _1001112] : [-(_1001104 = c_Orderings_Obot__class_Obot(tc_fun(_1001106, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001106, tc_fun(_1001108, tc_HOL_Obool)), _1001104), hAPP(hAPP(c_COMBB(tc_fun(_1001108, tc_HOL_Obool), tc_fun(_1001108, tc_HOL_Obool), _1001106), hAPP(c_Set_Oinsert(_1001108), _1001110)), _1001112)) = hAPP(hAPP(c_Set_Oinsert(_1001108), _1001110), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001106, tc_fun(_1001108, tc_HOL_Obool)), _1001104), _1001112)))], (11885 ^ _784416) ^ [_1001224, _1001226, _1001228, _1001230, _1001232] : [_1001224 = c_Orderings_Obot__class_Obot(tc_fun(_1001226, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001226, tc_fun(_1001228, tc_HOL_Obool)), _1001224), hAPP(hAPP(c_COMBB(tc_fun(_1001228, tc_HOL_Obool), tc_fun(_1001228, tc_HOL_Obool), _1001226), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1001228, tc_HOL_Obool)), _1001230)), _1001232)) = c_Orderings_Obot__class_Obot(tc_fun(_1001228, tc_HOL_Obool)))], (11891 ^ _784416) ^ [_1001393, _1001395, _1001397, _1001399, _1001401] : [-(_1001393 = c_Orderings_Obot__class_Obot(tc_fun(_1001395, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001395, tc_fun(_1001397, tc_HOL_Obool)), _1001393), hAPP(hAPP(c_COMBB(tc_fun(_1001397, tc_HOL_Obool), tc_fun(_1001397, tc_HOL_Obool), _1001395), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1001397, tc_HOL_Obool)), _1001399)), _1001401)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1001397, tc_HOL_Obool)), _1001399), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001395, tc_fun(_1001397, tc_HOL_Obool)), _1001393), _1001401)))], (11897 ^ _784416) ^ [_1001519, _1001521, _1001523, _1001525, _1001527] : [_1001519 = c_Orderings_Obot__class_Obot(tc_fun(_1001521, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001521, tc_fun(_1001523, tc_HOL_Obool)), _1001519), hAPP(hAPP(c_COMBC(_1001521, tc_fun(_1001523, tc_HOL_Obool), tc_fun(_1001523, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1001523, tc_HOL_Obool), tc_fun(tc_fun(_1001523, tc_HOL_Obool), tc_fun(_1001523, tc_HOL_Obool)), _1001521), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1001523, tc_HOL_Obool))), _1001525)), _1001527)) = c_Orderings_Obot__class_Obot(tc_fun(_1001523, tc_HOL_Obool)))], (11903 ^ _784416) ^ [_1001726, _1001728, _1001730, _1001732, _1001734] : [-(_1001726 = c_Orderings_Obot__class_Obot(tc_fun(_1001728, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001728, tc_fun(_1001730, tc_HOL_Obool)), _1001726), hAPP(hAPP(c_COMBC(_1001728, tc_fun(_1001730, tc_HOL_Obool), tc_fun(_1001730, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1001730, tc_HOL_Obool), tc_fun(tc_fun(_1001730, tc_HOL_Obool), tc_fun(_1001730, tc_HOL_Obool)), _1001728), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1001730, tc_HOL_Obool))), _1001732)), _1001734)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1001730, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001728, tc_fun(_1001730, tc_HOL_Obool)), _1001726), _1001732)), _1001734))], (11909 ^ _784416) ^ [_1001853, _1001855, _1001857, _1001859, _1001861, _1001863, _1001865, _1001867, _1001869, _1001871, _1001873] : [c_Equiv__Relations_Oequiv(_1001853, _1001855, _1001857), c_Equiv__Relations_Oequiv(_1001859, _1001861, _1001863), c_Equiv__Relations_Ocongruent2(_1001853, _1001859, tc_fun(_1001865, tc_HOL_Obool), _1001857, _1001863, _1001867), hBOOL(hAPP(hAPP(c_member(tc_fun(_1001853, tc_HOL_Obool)), _1001869), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1001853), _1001855), _1001857))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1001859, tc_HOL_Obool)), _1001871), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1001859), _1001861), _1001863))), 11931 ^ _784416 : [(11932 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1001853), 11930 ^ [_1001853, _1001855, _1001857, _1001859, _1001861, _1001863, _1001865, _1001867, _1001869, _1001871, _1001873]), _1001855)))], (11935 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1001859), 11933 ^ [_1001853, _1001855, _1001857, _1001859, _1001861, _1001863, _1001865, _1001867, _1001869, _1001871, _1001873]), _1001861)))], (11937 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1001865, tc_HOL_Obool)), hAPP(hAPP(_1001867, 11930 ^ [_1001853, _1001855, _1001857, _1001859, _1001861, _1001863, _1001865, _1001867, _1001869, _1001871, _1001873]), 11933 ^ [_1001853, _1001855, _1001857, _1001859, _1001861, _1001863, _1001865, _1001867, _1001869, _1001871, _1001873])), _1001873))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1001865, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001853, tc_fun(_1001865, tc_HOL_Obool)), _1001869), hAPP(hAPP(c_COMBB(tc_fun(_1001859, tc_fun(_1001865, tc_HOL_Obool)), tc_fun(_1001865, tc_HOL_Obool), _1001853), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001859, tc_fun(_1001865, tc_HOL_Obool)), _1001871)), _1001867))), _1001873)))], (11941 ^ _784416) ^ [_1002855, _1002857, _1002859, _1002861, _1002863, _1002865, _1002867] : [c_Equiv__Relations_Oequiv(_1002855, _1002857, _1002859), c_Equiv__Relations_Ocongruent(_1002855, tc_fun(_1002861, tc_HOL_Obool), _1002859, _1002863), hBOOL(hAPP(hAPP(c_member(tc_fun(_1002855, tc_HOL_Obool)), _1002865), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1002855), _1002857), _1002859))), 11955 ^ _784416 : [(11956 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1002855), 11954 ^ [_1002855, _1002857, _1002859, _1002861, _1002863, _1002865, _1002867]), _1002857)))], (11958 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1002861, tc_HOL_Obool)), hAPP(_1002863, 11954 ^ [_1002855, _1002857, _1002859, _1002861, _1002863, _1002865, _1002867])), _1002867))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1002861, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1002855, tc_fun(_1002861, tc_HOL_Obool)), _1002865), _1002863)), _1002867)))], (11962 ^ _784416) ^ [_1003366, _1003368, _1003370, _1003372, _1003374, _1003376] : [c_Equiv__Relations_Oequiv(_1003366, _1003368, _1003370), hBOOL(hAPP(hAPP(c_member(_1003366), _1003372), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1003366, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1003366, _1003366, _1003370), hAPP(hAPP(c_Set_Oinsert(_1003366), _1003374), c_Orderings_Obot__class_Obot(tc_fun(_1003366, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1003366, _1003366, _1003370), hAPP(hAPP(c_Set_Oinsert(_1003366), _1003376), c_Orderings_Obot__class_Obot(tc_fun(_1003366, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1003366, _1003366)), hAPP(hAPP(c_Product__Type_OPair(_1003366, _1003366), _1003374), _1003376)), _1003370)))], (11972 ^ _784416) ^ [_1003667, _1003669, _1003671, _1003673, _1003675] : [c_Equiv__Relations_Oequiv(_1003667, _1003669, _1003671), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1003667, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1003667, _1003667, _1003671), hAPP(hAPP(c_Set_Oinsert(_1003667), _1003673), c_Orderings_Obot__class_Obot(tc_fun(_1003667, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1003667, _1003667, _1003671), hAPP(hAPP(c_Set_Oinsert(_1003667), _1003675), c_Orderings_Obot__class_Obot(tc_fun(_1003667, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1003667), _1003673), _1003669)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1003667, _1003667)), hAPP(hAPP(c_Product__Type_OPair(_1003667, _1003667), _1003675), _1003673)), _1003671)))], (11986 ^ _784416) ^ [_1004020, _1004022, _1004024, _1004026, _1004028] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1004020, _1004022, hAPP(hAPP(c_Set_Oinsert(_1004020), _1004024), _1004026)), _1004028)), 11991 ^ _784416 : [(11992 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1004020), _1004024), _1004026) = hAPP(hAPP(c_Set_Oinsert(_1004020), 11989 ^ [_1004020, _1004022, _1004024, _1004026, _1004028]), 11990 ^ [_1004020, _1004022, _1004024, _1004026, _1004028]))], (11994 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1004020, _1004020, _1004022, 11989 ^ [_1004020, _1004022, _1004024, _1004026, _1004028], 11990 ^ [_1004020, _1004022, _1004024, _1004026, _1004028]), _1004028)))], (11996 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1004020), 11989 ^ [_1004020, _1004022, _1004024, _1004026, _1004028]), 11990 ^ [_1004020, _1004022, _1004024, _1004026, _1004028]))]]], (11998 ^ _784416) ^ [_1004437, _1004439, _1004441, _1004443, _1004445] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1004437, _1004439, hAPP(hAPP(c_Set_Oinsert(_1004437), _1004441), _1004443)), _1004445)), 12003 ^ _784416 : [(12004 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1004437), _1004441), _1004443) = hAPP(hAPP(c_Set_Oinsert(_1004437), 12001 ^ [_1004437, _1004439, _1004441, _1004443, _1004445]), 12002 ^ [_1004437, _1004439, _1004441, _1004443, _1004445]))], (12006 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1004437, _1004437, _1004439, 12001 ^ [_1004437, _1004439, _1004441, _1004443, _1004445], 12002 ^ [_1004437, _1004439, _1004441, _1004443, _1004445]), _1004445)))], (12008 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1004437), 12001 ^ [_1004437, _1004439, _1004441, _1004443, _1004445]), 12002 ^ [_1004437, _1004439, _1004441, _1004443, _1004445]))]]], (12010 ^ _784416) ^ [_1004828, _1004830, _1004832, _1004834, _1004836] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1004828, _1004830, hAPP(hAPP(c_Set_Oinsert(_1004828), _1004832), _1004834)), _1004836))), 12011 ^ _784416 : [(12012 ^ _784416) ^ [_1004932, _1004934] : [hAPP(hAPP(c_Set_Oinsert(_1004828), _1004832), _1004834) = hAPP(hAPP(c_Set_Oinsert(_1004828), _1004934), _1004932), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1004828, _1004828, _1004830, _1004934, _1004932), _1004836)), -(hBOOL(hAPP(hAPP(c_member(_1004828), _1004934), _1004932)))]]], (12024 ^ _784416) ^ [_1005189, _1005191, _1005193, _1005195, _1005197] : [c_Equiv__Relations_Oequiv(_1005189, _1005191, _1005193), hBOOL(hAPP(hAPP(c_member(_1005189), _1005195), _1005191)), hBOOL(hAPP(hAPP(c_member(_1005189), _1005197), _1005191)), 12035 ^ _784416 : [(12036 ^ _784416) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1005189), hAPP(hAPP(c_Set_Oinsert(_1005189), _1005195), c_Orderings_Obot__class_Obot(tc_fun(_1005189, tc_HOL_Obool)))), _1005193) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1005189), hAPP(hAPP(c_Set_Oinsert(_1005189), _1005197), c_Orderings_Obot__class_Obot(tc_fun(_1005189, tc_HOL_Obool)))), _1005193), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1005189, _1005189)), hAPP(hAPP(c_Product__Type_OPair(_1005189, _1005189), _1005195), _1005197)), _1005193)))], (12042 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1005189, _1005189)), hAPP(hAPP(c_Product__Type_OPair(_1005189, _1005189), _1005195), _1005197)), _1005193)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1005189), hAPP(hAPP(c_Set_Oinsert(_1005189), _1005195), c_Orderings_Obot__class_Obot(tc_fun(_1005189, tc_HOL_Obool)))), _1005193) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1005189), hAPP(hAPP(c_Set_Oinsert(_1005189), _1005197), c_Orderings_Obot__class_Obot(tc_fun(_1005189, tc_HOL_Obool)))), _1005193))]]], (12048 ^ _784416) ^ [_1005743, _1005745, _1005747, _1005749, _1005751] : [c_Equiv__Relations_Oequiv(_1005743, _1005745, _1005747), hBOOL(hAPP(hAPP(c_member(tc_prod(_1005743, _1005743)), hAPP(hAPP(c_Product__Type_OPair(_1005743, _1005743), _1005749), _1005751)), _1005747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1005743, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1005743, _1005743, _1005747), hAPP(hAPP(c_Set_Oinsert(_1005743), _1005749), c_Orderings_Obot__class_Obot(tc_fun(_1005743, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1005743, _1005743, _1005747), hAPP(hAPP(c_Set_Oinsert(_1005743), _1005751), c_Orderings_Obot__class_Obot(tc_fun(_1005743, tc_HOL_Obool)))))))], (12058 ^ _784416) ^ [_1006045, _1006047, _1006049, _1006051] : [c_Map_Odom(_1006045, _1006047, _1006049) = hAPP(hAPP(c_Set_Oinsert(_1006045), _1006051), c_Orderings_Obot__class_Obot(tc_fun(_1006045, tc_HOL_Obool))), -(_1006049 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1006045, tc_Option_Ooption(_1006047)), hAPP(c_COMBK(tc_Option_Ooption(_1006047), _1006045), c_Option_Ooption_ONone(_1006047))), _1006051), hAPP(c_Option_Ooption_OSome(_1006047), 12061 ^ [_1006045, _1006047, _1006049, _1006051])))], (12065 ^ _784416) ^ [_1006230, _1006232, _1006234, _1006236] : [12066 ^ _784416 : [(12067 ^ _784416) ^ [_1006319] : [_1006234 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1006230, tc_Option_Ooption(_1006232)), hAPP(c_COMBK(tc_Option_Ooption(_1006232), _1006230), c_Option_Ooption_ONone(_1006232))), _1006236), hAPP(c_Option_Ooption_OSome(_1006232), _1006319))]], -(c_Map_Odom(_1006230, _1006232, _1006234) = hAPP(hAPP(c_Set_Oinsert(_1006230), _1006236), c_Orderings_Obot__class_Obot(tc_fun(_1006230, tc_HOL_Obool))))], (12071 ^ _784416) ^ [_1006418, _1006420, _1006422, _1006424, _1006426, _1006428, _1006430, _1006432] : [hBOOL(hAPP(hAPP(c_member(_1006418), _1006420), _1006422)), hBOOL(hAPP(hAPP(hAPP(_1006424, _1006420), _1006426), _1006428)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1006418, tc_fun(_1006430, tc_fun(_1006432, tc_HOL_Obool))), _1006422), _1006424), _1006426), _1006428)))], (12081 ^ _784416) ^ [_1006662, _1006664, _1006666, _1006668] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1006662, tc_fun(_1006664, tc_HOL_Obool))), _1006666), _1006668)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1006662, _1006664)), hAPP(hAPP(c_Product__Type_OPair(_1006662, _1006664), _1006666), _1006668)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1006662, _1006664), tc_HOL_Obool)))))], (12087 ^ _784416) ^ [_1006819, _1006821, _1006823, _1006825] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1006819, _1006821)), hAPP(hAPP(c_Product__Type_OPair(_1006819, _1006821), _1006823), _1006825)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1006819, _1006821), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1006819, tc_fun(_1006821, tc_HOL_Obool))), _1006823), _1006825)))], (12093 ^ _784416) ^ [_1007003, _1007005, _1007007, _1007009] : [hAPP(hAPP(c_COMBC(_1007003, tc_fun(tc_prod(_1007003, _1007005), tc_HOL_Obool), tc_fun(_1007005, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1007005, tc_fun(tc_fun(tc_prod(_1007003, _1007005), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1007003, _1007005), tc_HOL_Obool), tc_fun(_1007005, tc_HOL_Obool)), _1007003), c_COMBC(_1007005, tc_fun(tc_prod(_1007003, _1007005), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1007005, tc_prod(_1007003, _1007005)), tc_fun(_1007005, tc_fun(tc_fun(tc_prod(_1007003, _1007005), tc_HOL_Obool), tc_HOL_Obool)), _1007003), hAPP(c_COMBB(tc_prod(_1007003, _1007005), tc_fun(tc_fun(tc_prod(_1007003, _1007005), tc_HOL_Obool), tc_HOL_Obool), _1007005), c_member(tc_prod(_1007003, _1007005)))), c_Product__Type_OPair(_1007003, _1007005)))), _1007007) = hAPP(hAPP(c_COMBC(_1007003, tc_fun(tc_prod(_1007003, _1007005), tc_HOL_Obool), tc_fun(_1007005, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1007005, tc_fun(tc_fun(tc_prod(_1007003, _1007005), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1007003, _1007005), tc_HOL_Obool), tc_fun(_1007005, tc_HOL_Obool)), _1007003), c_COMBC(_1007005, tc_fun(tc_prod(_1007003, _1007005), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1007005, tc_prod(_1007003, _1007005)), tc_fun(_1007005, tc_fun(tc_fun(tc_prod(_1007003, _1007005), tc_HOL_Obool), tc_HOL_Obool)), _1007003), hAPP(c_COMBB(tc_prod(_1007003, _1007005), tc_fun(tc_fun(tc_prod(_1007003, _1007005), tc_HOL_Obool), tc_HOL_Obool), _1007005), c_member(tc_prod(_1007003, _1007005)))), c_Product__Type_OPair(_1007003, _1007005)))), _1007009), -(_1007007 = _1007009)], (12099 ^ _784416) ^ [_1007552, _1007554, _1007556, _1007558] : [_1007556 = _1007558, -(hAPP(hAPP(c_COMBC(_1007552, tc_fun(tc_prod(_1007552, _1007554), tc_HOL_Obool), tc_fun(_1007554, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1007554, tc_fun(tc_fun(tc_prod(_1007552, _1007554), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1007552, _1007554), tc_HOL_Obool), tc_fun(_1007554, tc_HOL_Obool)), _1007552), c_COMBC(_1007554, tc_fun(tc_prod(_1007552, _1007554), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1007554, tc_prod(_1007552, _1007554)), tc_fun(_1007554, tc_fun(tc_fun(tc_prod(_1007552, _1007554), tc_HOL_Obool), tc_HOL_Obool)), _1007552), hAPP(c_COMBB(tc_prod(_1007552, _1007554), tc_fun(tc_fun(tc_prod(_1007552, _1007554), tc_HOL_Obool), tc_HOL_Obool), _1007554), c_member(tc_prod(_1007552, _1007554)))), c_Product__Type_OPair(_1007552, _1007554)))), _1007556) = hAPP(hAPP(c_COMBC(_1007552, tc_fun(tc_prod(_1007552, _1007554), tc_HOL_Obool), tc_fun(_1007554, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1007554, tc_fun(tc_fun(tc_prod(_1007552, _1007554), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1007552, _1007554), tc_HOL_Obool), tc_fun(_1007554, tc_HOL_Obool)), _1007552), c_COMBC(_1007554, tc_fun(tc_prod(_1007552, _1007554), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1007554, tc_prod(_1007552, _1007554)), tc_fun(_1007554, tc_fun(tc_fun(tc_prod(_1007552, _1007554), tc_HOL_Obool), tc_HOL_Obool)), _1007552), hAPP(c_COMBB(tc_prod(_1007552, _1007554), tc_fun(tc_fun(tc_prod(_1007552, _1007554), tc_HOL_Obool), tc_HOL_Obool), _1007554), c_member(tc_prod(_1007552, _1007554)))), c_Product__Type_OPair(_1007552, _1007554)))), _1007558))], (12105 ^ _784416) ^ [_1008134, _1008136, _1008138, _1008140, _1008142, _1008144] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1008134, tc_fun(_1008136, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1008134, tc_fun(tc_prod(_1008134, _1008136), tc_HOL_Obool), tc_fun(_1008136, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1008136, tc_fun(tc_fun(tc_prod(_1008134, _1008136), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1008134, _1008136), tc_HOL_Obool), tc_fun(_1008136, tc_HOL_Obool)), _1008134), c_COMBC(_1008136, tc_fun(tc_prod(_1008134, _1008136), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1008136, tc_prod(_1008134, _1008136)), tc_fun(_1008136, tc_fun(tc_fun(tc_prod(_1008134, _1008136), tc_HOL_Obool), tc_HOL_Obool)), _1008134), hAPP(c_COMBB(tc_prod(_1008134, _1008136), tc_fun(tc_fun(tc_prod(_1008134, _1008136), tc_HOL_Obool), tc_HOL_Obool), _1008136), c_member(tc_prod(_1008134, _1008136)))), c_Product__Type_OPair(_1008134, _1008136)))), _1008138)), hAPP(hAPP(c_COMBC(_1008134, tc_fun(tc_prod(_1008134, _1008136), tc_HOL_Obool), tc_fun(_1008136, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1008136, tc_fun(tc_fun(tc_prod(_1008134, _1008136), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1008134, _1008136), tc_HOL_Obool), tc_fun(_1008136, tc_HOL_Obool)), _1008134), c_COMBC(_1008136, tc_fun(tc_prod(_1008134, _1008136), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1008136, tc_prod(_1008134, _1008136)), tc_fun(_1008136, tc_fun(tc_fun(tc_prod(_1008134, _1008136), tc_HOL_Obool), tc_HOL_Obool)), _1008134), hAPP(c_COMBB(tc_prod(_1008134, _1008136), tc_fun(tc_fun(tc_prod(_1008134, _1008136), tc_HOL_Obool), tc_HOL_Obool), _1008136), c_member(tc_prod(_1008134, _1008136)))), c_Product__Type_OPair(_1008134, _1008136)))), _1008140)), _1008142), _1008144)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1008134, _1008136)), hAPP(hAPP(c_Product__Type_OPair(_1008134, _1008136), _1008142), _1008144)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1008134, _1008136), tc_HOL_Obool)), _1008138), _1008140))))], (12111 ^ _784416) ^ [_1008791, _1008793, _1008795, _1008797, _1008799, _1008801] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1008791, _1008793)), hAPP(hAPP(c_Product__Type_OPair(_1008791, _1008793), _1008799), _1008801)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1008791, _1008793), tc_HOL_Obool)), _1008795), _1008797))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1008791, tc_fun(_1008793, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1008791, tc_fun(tc_prod(_1008791, _1008793), tc_HOL_Obool), tc_fun(_1008793, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1008793, tc_fun(tc_fun(tc_prod(_1008791, _1008793), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1008791, _1008793), tc_HOL_Obool), tc_fun(_1008793, tc_HOL_Obool)), _1008791), c_COMBC(_1008793, tc_fun(tc_prod(_1008791, _1008793), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1008793, tc_prod(_1008791, _1008793)), tc_fun(_1008793, tc_fun(tc_fun(tc_prod(_1008791, _1008793), tc_HOL_Obool), tc_HOL_Obool)), _1008791), hAPP(c_COMBB(tc_prod(_1008791, _1008793), tc_fun(tc_fun(tc_prod(_1008791, _1008793), tc_HOL_Obool), tc_HOL_Obool), _1008793), c_member(tc_prod(_1008791, _1008793)))), c_Product__Type_OPair(_1008791, _1008793)))), _1008795)), hAPP(hAPP(c_COMBC(_1008791, tc_fun(tc_prod(_1008791, _1008793), tc_HOL_Obool), tc_fun(_1008793, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1008793, tc_fun(tc_fun(tc_prod(_1008791, _1008793), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1008791, _1008793), tc_HOL_Obool), tc_fun(_1008793, tc_HOL_Obool)), _1008791), c_COMBC(_1008793, tc_fun(tc_prod(_1008791, _1008793), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1008793, tc_prod(_1008791, _1008793)), tc_fun(_1008793, tc_fun(tc_fun(tc_prod(_1008791, _1008793), tc_HOL_Obool), tc_HOL_Obool)), _1008791), hAPP(c_COMBB(tc_prod(_1008791, _1008793), tc_fun(tc_fun(tc_prod(_1008791, _1008793), tc_HOL_Obool), tc_HOL_Obool), _1008793), c_member(tc_prod(_1008791, _1008793)))), c_Product__Type_OPair(_1008791, _1008793)))), _1008797)), _1008799), _1008801)))], (12117 ^ _784416) ^ [_1009481, _1009483, _1009485, _1009487, _1009489, _1009491] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1009481, tc_fun(_1009483, tc_fun(_1009485, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1009481, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1009483, _1009485), tc_HOL_Obool), tc_fun(_1009483, tc_fun(_1009485, tc_HOL_Obool)), _1009481), hAPP(c_COMBC(_1009483, tc_fun(tc_prod(_1009483, _1009485), tc_HOL_Obool), tc_fun(_1009485, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1009485, tc_fun(tc_fun(tc_prod(_1009483, _1009485), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1009483, _1009485), tc_HOL_Obool), tc_fun(_1009485, tc_HOL_Obool)), _1009483), c_COMBC(_1009485, tc_fun(tc_prod(_1009483, _1009485), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1009485, tc_prod(_1009483, _1009485)), tc_fun(_1009485, tc_fun(tc_fun(tc_prod(_1009483, _1009485), tc_HOL_Obool), tc_HOL_Obool)), _1009483), hAPP(c_COMBB(tc_prod(_1009483, _1009485), tc_fun(tc_fun(tc_prod(_1009483, _1009485), tc_HOL_Obool), tc_HOL_Obool), _1009485), c_member(tc_prod(_1009483, _1009485)))), c_Product__Type_OPair(_1009483, _1009485))))), _1009487)), _1009489), _1009491)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1009483, _1009485)), hAPP(hAPP(c_Product__Type_OPair(_1009483, _1009485), _1009489), _1009491)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1009481, tc_fun(tc_prod(_1009483, _1009485), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1009481, tc_HOL_Obool))), _1009487))))], (12123 ^ _784416) ^ [_1009964, _1009966, _1009968, _1009970, _1009972, _1009974] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1009966, _1009968)), hAPP(hAPP(c_Product__Type_OPair(_1009966, _1009968), _1009972), _1009974)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1009964, tc_fun(tc_prod(_1009966, _1009968), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1009964, tc_HOL_Obool))), _1009970))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1009964, tc_fun(_1009966, tc_fun(_1009968, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1009964, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1009966, _1009968), tc_HOL_Obool), tc_fun(_1009966, tc_fun(_1009968, tc_HOL_Obool)), _1009964), hAPP(c_COMBC(_1009966, tc_fun(tc_prod(_1009966, _1009968), tc_HOL_Obool), tc_fun(_1009968, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1009968, tc_fun(tc_fun(tc_prod(_1009966, _1009968), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1009966, _1009968), tc_HOL_Obool), tc_fun(_1009968, tc_HOL_Obool)), _1009966), c_COMBC(_1009968, tc_fun(tc_prod(_1009966, _1009968), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1009968, tc_prod(_1009966, _1009968)), tc_fun(_1009968, tc_fun(tc_fun(tc_prod(_1009966, _1009968), tc_HOL_Obool), tc_HOL_Obool)), _1009966), hAPP(c_COMBB(tc_prod(_1009966, _1009968), tc_fun(tc_fun(tc_prod(_1009966, _1009968), tc_HOL_Obool), tc_HOL_Obool), _1009968), c_member(tc_prod(_1009966, _1009968)))), c_Product__Type_OPair(_1009966, _1009968))))), _1009970)), _1009972), _1009974)))], (12129 ^ _784416) ^ [_1010483, _1010485, _1010487, _1010489, _1010491, _1010493, _1010495] : [hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1010483, tc_Option_Ooption(_1010485)), _1010487), _1010489), hAPP(c_Option_Ooption_OSome(_1010485), _1010491)), _1010493) = hAPP(c_Option_Ooption_OSome(_1010485), _1010495), 12134 ^ _784416 : [(12135 ^ _784416) ^ [] : [-(_1010493 = _1010489)], (12137 ^ _784416) ^ [] : [-(_1010491 = _1010495)]], 12138 ^ _784416 : [(12139 ^ _784416) ^ [] : [_1010493 = _1010489], (12141 ^ _784416) ^ [] : [-(hAPP(_1010487, _1010493) = hAPP(c_Option_Ooption_OSome(_1010485), _1010495))]]], (12143 ^ _784416) ^ [_1010761, _1010763, _1010765, _1010767, _1010769, _1010771, _1010773] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1010761, tc_Option_Ooption(_1010763)), _1010765), _1010767), hAPP(c_Option_Ooption_OSome(_1010763), _1010769)), _1010771) = hAPP(c_Option_Ooption_OSome(_1010763), _1010773)), 12144 ^ _784416 : [(12145 ^ _784416) ^ [] : [_1010771 = _1010767, _1010769 = _1010773], (12151 ^ _784416) ^ [] : [-(_1010771 = _1010767), hAPP(_1010765, _1010771) = hAPP(c_Option_Ooption_OSome(_1010763), _1010773)]]], (12159 ^ _784416) ^ [_1011078, _1011080, _1011082, _1011084, _1011086] : [hAPP(_1011078, _1011080) = hAPP(c_Option_Ooption_OSome(_1011082), _1011084), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1011086, tc_Option_Ooption(_1011082)), _1011078), _1011080), hAPP(c_Option_Ooption_OSome(_1011082), _1011084)) = _1011078)], (12165 ^ _784416) ^ [_1011215, _1011217, _1011219, _1011221, _1011223, _1011225, _1011227] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1011215, tc_Option_Ooption(_1011217)), _1011219), _1011221), hAPP(c_Option_Ooption_OSome(_1011217), _1011223)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1011215, tc_Option_Ooption(_1011217)), _1011225), _1011221), hAPP(c_Option_Ooption_OSome(_1011217), _1011227)), -(_1011223 = _1011227)], (12171 ^ _784416) ^ [_1011378, _1011380, _1011382, _1011384, _1011386, _1011388] : [c_Equiv__Relations_Ocongruent(_1011378, _1011380, _1011382, _1011384), hBOOL(hAPP(hAPP(c_member(tc_prod(_1011378, _1011378)), hAPP(hAPP(c_Product__Type_OPair(_1011378, _1011378), _1011386), _1011388)), _1011382)), -(hAPP(_1011384, _1011386) = hAPP(_1011384, _1011388))], (12181 ^ _784416) ^ [_1011577, _1011579, _1011581, _1011583, _1011585, _1011587, _1011589, _1011591, _1011593, _1011595] : [c_Equiv__Relations_Ocongruent2(_1011577, _1011579, _1011581, _1011583, _1011585, _1011587), hBOOL(hAPP(hAPP(c_member(tc_prod(_1011577, _1011577)), hAPP(hAPP(c_Product__Type_OPair(_1011577, _1011577), _1011589), _1011591)), _1011583)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1011579, _1011579)), hAPP(hAPP(c_Product__Type_OPair(_1011579, _1011579), _1011593), _1011595)), _1011585)), -(hAPP(hAPP(_1011587, _1011589), _1011593) = hAPP(hAPP(_1011587, _1011591), _1011595))], (12195 ^ _784416) ^ [_1011935, _1011937, _1011939, _1011941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1011935, tc_fun(_1011937, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1011935, tc_fun(tc_prod(_1011935, _1011937), tc_HOL_Obool), tc_fun(_1011937, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1011937, tc_fun(tc_fun(tc_prod(_1011935, _1011937), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1011935, _1011937), tc_HOL_Obool), tc_fun(_1011937, tc_HOL_Obool)), _1011935), c_COMBC(_1011937, tc_fun(tc_prod(_1011935, _1011937), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1011937, tc_prod(_1011935, _1011937)), tc_fun(_1011937, tc_fun(tc_fun(tc_prod(_1011935, _1011937), tc_HOL_Obool), tc_HOL_Obool)), _1011935), hAPP(c_COMBB(tc_prod(_1011935, _1011937), tc_fun(tc_fun(tc_prod(_1011935, _1011937), tc_HOL_Obool), tc_HOL_Obool), _1011937), c_member(tc_prod(_1011935, _1011937)))), c_Product__Type_OPair(_1011935, _1011937)))), _1011939)), hAPP(hAPP(c_COMBC(_1011935, tc_fun(tc_prod(_1011935, _1011937), tc_HOL_Obool), tc_fun(_1011937, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1011937, tc_fun(tc_fun(tc_prod(_1011935, _1011937), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1011935, _1011937), tc_HOL_Obool), tc_fun(_1011937, tc_HOL_Obool)), _1011935), c_COMBC(_1011937, tc_fun(tc_prod(_1011935, _1011937), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1011937, tc_prod(_1011935, _1011937)), tc_fun(_1011937, tc_fun(tc_fun(tc_prod(_1011935, _1011937), tc_HOL_Obool), tc_HOL_Obool)), _1011935), hAPP(c_COMBB(tc_prod(_1011935, _1011937), tc_fun(tc_fun(tc_prod(_1011935, _1011937), tc_HOL_Obool), tc_HOL_Obool), _1011937), c_member(tc_prod(_1011935, _1011937)))), c_Product__Type_OPair(_1011935, _1011937)))), _1011941))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1011935, _1011937), tc_HOL_Obool)), _1011939), _1011941)))], (12201 ^ _784416) ^ [_1012536, _1012538, _1012540, _1012542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1012536, _1012538), tc_HOL_Obool)), _1012540), _1012542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1012536, tc_fun(_1012538, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1012536, tc_fun(tc_prod(_1012536, _1012538), tc_HOL_Obool), tc_fun(_1012538, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1012538, tc_fun(tc_fun(tc_prod(_1012536, _1012538), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1012536, _1012538), tc_HOL_Obool), tc_fun(_1012538, tc_HOL_Obool)), _1012536), c_COMBC(_1012538, tc_fun(tc_prod(_1012536, _1012538), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1012538, tc_prod(_1012536, _1012538)), tc_fun(_1012538, tc_fun(tc_fun(tc_prod(_1012536, _1012538), tc_HOL_Obool), tc_HOL_Obool)), _1012536), hAPP(c_COMBB(tc_prod(_1012536, _1012538), tc_fun(tc_fun(tc_prod(_1012536, _1012538), tc_HOL_Obool), tc_HOL_Obool), _1012538), c_member(tc_prod(_1012536, _1012538)))), c_Product__Type_OPair(_1012536, _1012538)))), _1012540)), hAPP(hAPP(c_COMBC(_1012536, tc_fun(tc_prod(_1012536, _1012538), tc_HOL_Obool), tc_fun(_1012538, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1012538, tc_fun(tc_fun(tc_prod(_1012536, _1012538), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1012536, _1012538), tc_HOL_Obool), tc_fun(_1012538, tc_HOL_Obool)), _1012536), c_COMBC(_1012538, tc_fun(tc_prod(_1012536, _1012538), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1012538, tc_prod(_1012536, _1012538)), tc_fun(_1012538, tc_fun(tc_fun(tc_prod(_1012536, _1012538), tc_HOL_Obool), tc_HOL_Obool)), _1012536), hAPP(c_COMBB(tc_prod(_1012536, _1012538), tc_fun(tc_fun(tc_prod(_1012536, _1012538), tc_HOL_Obool), tc_HOL_Obool), _1012538), c_member(tc_prod(_1012536, _1012538)))), c_Product__Type_OPair(_1012536, _1012538)))), _1012542))))], (12207 ^ _784416) ^ [_1013170, _1013172, _1013174, _1013176, _1013178, _1013180] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013170, tc_fun(_1013172, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1013170, tc_fun(tc_prod(_1013170, _1013172), tc_HOL_Obool), tc_fun(_1013172, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1013172, tc_fun(tc_fun(tc_prod(_1013170, _1013172), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1013170, _1013172), tc_HOL_Obool), tc_fun(_1013172, tc_HOL_Obool)), _1013170), c_COMBC(_1013172, tc_fun(tc_prod(_1013170, _1013172), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1013172, tc_prod(_1013170, _1013172)), tc_fun(_1013172, tc_fun(tc_fun(tc_prod(_1013170, _1013172), tc_HOL_Obool), tc_HOL_Obool)), _1013170), hAPP(c_COMBB(tc_prod(_1013170, _1013172), tc_fun(tc_fun(tc_prod(_1013170, _1013172), tc_HOL_Obool), tc_HOL_Obool), _1013172), c_member(tc_prod(_1013170, _1013172)))), c_Product__Type_OPair(_1013170, _1013172)))), _1013174)), hAPP(hAPP(c_COMBC(_1013170, tc_fun(tc_prod(_1013170, _1013172), tc_HOL_Obool), tc_fun(_1013172, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1013172, tc_fun(tc_fun(tc_prod(_1013170, _1013172), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1013170, _1013172), tc_HOL_Obool), tc_fun(_1013172, tc_HOL_Obool)), _1013170), c_COMBC(_1013172, tc_fun(tc_prod(_1013170, _1013172), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1013172, tc_prod(_1013170, _1013172)), tc_fun(_1013172, tc_fun(tc_fun(tc_prod(_1013170, _1013172), tc_HOL_Obool), tc_HOL_Obool)), _1013170), hAPP(c_COMBB(tc_prod(_1013170, _1013172), tc_fun(tc_fun(tc_prod(_1013170, _1013172), tc_HOL_Obool), tc_HOL_Obool), _1013172), c_member(tc_prod(_1013170, _1013172)))), c_Product__Type_OPair(_1013170, _1013172)))), _1013176)), _1013178), _1013180)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1013170, _1013172)), hAPP(hAPP(c_Product__Type_OPair(_1013170, _1013172), _1013178), _1013180)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1013170, _1013172), tc_HOL_Obool)), _1013174), _1013176))))], (12213 ^ _784416) ^ [_1013827, _1013829, _1013831, _1013833, _1013835, _1013837] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1013827, _1013829)), hAPP(hAPP(c_Product__Type_OPair(_1013827, _1013829), _1013835), _1013837)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1013827, _1013829), tc_HOL_Obool)), _1013831), _1013833))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013827, tc_fun(_1013829, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1013827, tc_fun(tc_prod(_1013827, _1013829), tc_HOL_Obool), tc_fun(_1013829, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1013829, tc_fun(tc_fun(tc_prod(_1013827, _1013829), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1013827, _1013829), tc_HOL_Obool), tc_fun(_1013829, tc_HOL_Obool)), _1013827), c_COMBC(_1013829, tc_fun(tc_prod(_1013827, _1013829), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1013829, tc_prod(_1013827, _1013829)), tc_fun(_1013829, tc_fun(tc_fun(tc_prod(_1013827, _1013829), tc_HOL_Obool), tc_HOL_Obool)), _1013827), hAPP(c_COMBB(tc_prod(_1013827, _1013829), tc_fun(tc_fun(tc_prod(_1013827, _1013829), tc_HOL_Obool), tc_HOL_Obool), _1013829), c_member(tc_prod(_1013827, _1013829)))), c_Product__Type_OPair(_1013827, _1013829)))), _1013831)), hAPP(hAPP(c_COMBC(_1013827, tc_fun(tc_prod(_1013827, _1013829), tc_HOL_Obool), tc_fun(_1013829, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1013829, tc_fun(tc_fun(tc_prod(_1013827, _1013829), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1013827, _1013829), tc_HOL_Obool), tc_fun(_1013829, tc_HOL_Obool)), _1013827), c_COMBC(_1013829, tc_fun(tc_prod(_1013827, _1013829), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1013829, tc_prod(_1013827, _1013829)), tc_fun(_1013829, tc_fun(tc_fun(tc_prod(_1013827, _1013829), tc_HOL_Obool), tc_HOL_Obool)), _1013827), hAPP(c_COMBB(tc_prod(_1013827, _1013829), tc_fun(tc_fun(tc_prod(_1013827, _1013829), tc_HOL_Obool), tc_HOL_Obool), _1013829), c_member(tc_prod(_1013827, _1013829)))), c_Product__Type_OPair(_1013827, _1013829)))), _1013833)), _1013835), _1013837)))], (12219 ^ _784416) ^ [_1014490, _1014492, _1014494] : [class_Enum_Oenum(_1014490), class_Enum_Oenum(_1014492), 12226 ^ _784416 : [(12227 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1014492, _1014490)), _1014494)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1014492), hAPP(hAPP(c_COMBB(tc_fun(_1014490, tc_HOL_Obool), tc_HOL_Obool, _1014492), c_Enum_Oenum__class_Oenum__all(_1014490)), hAPP(hAPP(c_COMBB(tc_fun(_1014490, tc_prod(_1014492, _1014490)), tc_fun(_1014490, tc_HOL_Obool), _1014492), hAPP(c_COMBB(tc_prod(_1014492, _1014490), tc_HOL_Obool, _1014490), _1014494)), c_Product__Type_OPair(_1014492, _1014490))))))], (12233 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1014492), hAPP(hAPP(c_COMBB(tc_fun(_1014490, tc_HOL_Obool), tc_HOL_Obool, _1014492), c_Enum_Oenum__class_Oenum__all(_1014490)), hAPP(hAPP(c_COMBB(tc_fun(_1014490, tc_prod(_1014492, _1014490)), tc_fun(_1014490, tc_HOL_Obool), _1014492), hAPP(c_COMBB(tc_prod(_1014492, _1014490), tc_HOL_Obool, _1014490), _1014494)), c_Product__Type_OPair(_1014492, _1014490))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1014492, _1014490)), _1014494)))]]], (12239 ^ _784416) ^ [_1014929, _1014931, _1014933] : [class_Enum_Oenum(_1014929), class_Enum_Oenum(_1014931), 12246 ^ _784416 : [(12247 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1014931, _1014929)), _1014933)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1014931), hAPP(hAPP(c_COMBB(tc_fun(_1014929, tc_HOL_Obool), tc_HOL_Obool, _1014931), c_Enum_Oenum__class_Oenum__ex(_1014929)), hAPP(hAPP(c_COMBB(tc_fun(_1014929, tc_prod(_1014931, _1014929)), tc_fun(_1014929, tc_HOL_Obool), _1014931), hAPP(c_COMBB(tc_prod(_1014931, _1014929), tc_HOL_Obool, _1014929), _1014933)), c_Product__Type_OPair(_1014931, _1014929))))))], (12253 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1014931), hAPP(hAPP(c_COMBB(tc_fun(_1014929, tc_HOL_Obool), tc_HOL_Obool, _1014931), c_Enum_Oenum__class_Oenum__ex(_1014929)), hAPP(hAPP(c_COMBB(tc_fun(_1014929, tc_prod(_1014931, _1014929)), tc_fun(_1014929, tc_HOL_Obool), _1014931), hAPP(c_COMBB(tc_prod(_1014931, _1014929), tc_HOL_Obool, _1014929), _1014933)), c_Product__Type_OPair(_1014931, _1014929))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1014931, _1014929)), _1014933)))]]], (12259 ^ _784416) ^ [_1015368, _1015370, _1015372, _1015374, _1015376] : [hAPP(_1015368, _1015370) = hAPP(c_Option_Ooption_OSome(_1015372), _1015374), -(hBOOL(hAPP(hAPP(c_member(_1015376), _1015370), c_Map_Odom(_1015376, _1015372, _1015368))))], (12265 ^ _784416) ^ [_1015485, _1015487, _1015489, _1015491, _1015493, _1015495] : [-(hBOOL(hAPP(hAPP(c_member(_1015485), _1015487), _1015489))), -(hAPP(c_Set_Oimage(_1015485, tc_Option_Ooption(_1015491), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1015485, tc_Option_Ooption(_1015491)), _1015493), _1015487), hAPP(c_Option_Ooption_OSome(_1015491), _1015495))), _1015489) = hAPP(c_Set_Oimage(_1015485, tc_Option_Ooption(_1015491), _1015493), _1015489))], (12271 ^ _784416) ^ [_1015573, _1015575, _1015577, _1015579, _1015581] : [hAPP(_1015573, _1015575) = hAPP(c_Option_Ooption_OSome(_1015577), _1015579), -(hAPP(hAPP(c_Set_Oinsert(_1015581), _1015575), c_Map_Odom(_1015581, _1015577, _1015573)) = c_Map_Odom(_1015581, _1015577, _1015573))], (12277 ^ _784416) ^ [_1015704, _1015706, _1015708, _1015710, _1015712, _1015714] : [hBOOL(hAPP(hAPP(c_member(_1015704), _1015706), _1015708)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1015704, _1015710)), hAPP(hAPP(c_Product__Type_OPair(_1015704, _1015710), _1015706), _1015712)), _1015714)), -(hBOOL(hAPP(hAPP(c_member(_1015710), _1015712), hAPP(c_Relation_OImage(_1015704, _1015710, _1015714), _1015708))))], (12287 ^ _784416) ^ [_1015953, _1015955, _1015957, _1015959, _1015961] : [hBOOL(hAPP(hAPP(c_member(_1015953), _1015955), hAPP(c_Relation_OImage(_1015957, _1015953, _1015959), _1015961))), 12291 ^ _784416 : [(12292 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1015957), 12290 ^ [_1015953, _1015955, _1015957, _1015959, _1015961]), _1015961)))], (12294 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1015957, _1015953)), hAPP(hAPP(c_Product__Type_OPair(_1015957, _1015953), 12290 ^ [_1015953, _1015955, _1015957, _1015959, _1015961]), _1015955)), _1015959)))]]], (12296 ^ _784416) ^ [_1016169, _1016171, _1016173, _1016175, _1016177] : [-(hBOOL(hAPP(hAPP(c_member(_1016169), _1016171), hAPP(c_Relation_OImage(_1016173, _1016169, _1016175), _1016177)))), 12297 ^ _784416 : [(12298 ^ _784416) ^ [_1016255] : [hBOOL(hAPP(hAPP(c_member(_1016173), _1016255), _1016177)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1016173, _1016169)), hAPP(hAPP(c_Product__Type_OPair(_1016173, _1016169), _1016255), _1016171)), _1016175))]]], (12306 ^ _784416) ^ [_1016435, _1016437, _1016439] : [-(c_Map_Odom(_1016435, _1016437, hAPP(hAPP(c_COMBB(_1016437, tc_Option_Ooption(_1016437), _1016435), c_Option_Ooption_OSome(_1016437)), _1016439)) = c_Orderings_Otop__class_Otop(tc_fun(_1016435, tc_HOL_Obool)))], (12308 ^ _784416) ^ [_1016506, _1016508, _1016510, _1016512, _1016514] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1016506, tc_Option_Ooption(_1016508)), _1016510), _1016512), hAPP(c_Option_Ooption_OSome(_1016508), _1016514)) = hAPP(c_COMBK(tc_Option_Ooption(_1016508), _1016506), c_Option_Ooption_ONone(_1016508))], (12310 ^ _784416) ^ [_1016566, _1016568] : [class_Enum_Oenum(_1016566), 12313 ^ _784416 : [(12314 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1016566)), _1016568)), 12317 ^ _784416 : [(12318 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1016568, c_Option_Ooption_ONone(_1016566))))], (12320 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1016566), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1016566), tc_HOL_Obool, _1016566), _1016568), c_Option_Ooption_OSome(_1016566)))))]]], (12322 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1016566)), _1016568))), hBOOL(hAPP(_1016568, c_Option_Ooption_ONone(_1016566))), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1016566), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1016566), tc_HOL_Obool, _1016566), _1016568), c_Option_Ooption_OSome(_1016566))))]]], (12332 ^ _784416) ^ [_1016927, _1016929] : [class_Enum_Oenum(_1016927), 12335 ^ _784416 : [(12346 ^ _784416) ^ [] : [12347 ^ _784416 : [(12348 ^ _784416) ^ [] : [hBOOL(hAPP(_1016929, c_Option_Ooption_ONone(_1016927)))], (12350 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1016927), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1016927), tc_HOL_Obool, _1016927), _1016929), c_Option_Ooption_OSome(_1016927))))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1016927)), _1016929)))], (12336 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1016927)), _1016929)), -(hBOOL(hAPP(_1016929, c_Option_Ooption_ONone(_1016927)))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1016927), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1016927), tc_HOL_Obool, _1016927), _1016929), c_Option_Ooption_OSome(_1016927)))))]]], (12354 ^ _784416) ^ [_1017285, _1017287, _1017289, _1017291, _1017293] : [hBOOL(hAPP(hAPP(c_member(_1017285), _1017287), hAPP(c_Relation_OImage(_1017289, _1017285, _1017291), hAPP(hAPP(c_Set_Oinsert(_1017289), _1017293), c_Orderings_Obot__class_Obot(tc_fun(_1017289, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1017289, _1017285)), hAPP(hAPP(c_Product__Type_OPair(_1017289, _1017285), _1017293), _1017287)), _1017291)))], (12360 ^ _784416) ^ [_1017456, _1017458, _1017460, _1017462, _1017464] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1017460, _1017456)), hAPP(hAPP(c_Product__Type_OPair(_1017460, _1017456), _1017464), _1017458)), _1017462)), -(hBOOL(hAPP(hAPP(c_member(_1017456), _1017458), hAPP(c_Relation_OImage(_1017460, _1017456, _1017462), hAPP(hAPP(c_Set_Oinsert(_1017460), _1017464), c_Orderings_Obot__class_Obot(tc_fun(_1017460, tc_HOL_Obool)))))))], (12366 ^ _784416) ^ [_1017633, _1017635, _1017637, _1017639, _1017641] : [c_Equiv__Relations_Oequiv(_1017633, _1017635, _1017637), hBOOL(hAPP(hAPP(c_member(tc_prod(_1017633, _1017633)), hAPP(hAPP(c_Product__Type_OPair(_1017633, _1017633), _1017639), _1017641)), _1017637)), -(hAPP(c_Relation_OImage(_1017633, _1017633, _1017637), hAPP(hAPP(c_Set_Oinsert(_1017633), _1017639), c_Orderings_Obot__class_Obot(tc_fun(_1017633, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1017633, _1017633, _1017637), hAPP(hAPP(c_Set_Oinsert(_1017633), _1017641), c_Orderings_Obot__class_Obot(tc_fun(_1017633, tc_HOL_Obool)))))], (12376 ^ _784416) ^ [_1017894, _1017896, _1017898, _1017900, _1017902, _1017904, _1017906] : [c_Equiv__Relations_Oequiv(_1017894, _1017896, _1017898), hBOOL(hAPP(hAPP(c_member(tc_fun(_1017894, tc_HOL_Obool)), _1017900), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1017894), _1017896), _1017898))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1017894, tc_HOL_Obool)), _1017902), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1017894), _1017896), _1017898))), hBOOL(hAPP(hAPP(c_member(_1017894), _1017904), _1017900)), hBOOL(hAPP(hAPP(c_member(_1017894), _1017906), _1017902)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1017894, _1017894)), hAPP(hAPP(c_Product__Type_OPair(_1017894, _1017894), _1017904), _1017906)), _1017898)), -(_1017900 = _1017902)], (12402 ^ _784416) ^ [_1018431, _1018433, _1018435, _1018437, _1018439, _1018441, _1018443] : [c_Equiv__Relations_Oequiv(_1018431, _1018433, _1018435), hBOOL(hAPP(hAPP(c_member(tc_fun(_1018431, tc_HOL_Obool)), _1018437), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1018431), _1018433), _1018435))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1018431, tc_HOL_Obool)), _1018439), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1018431), _1018433), _1018435))), hBOOL(hAPP(hAPP(c_member(_1018431), _1018441), _1018437)), hBOOL(hAPP(hAPP(c_member(_1018431), _1018443), _1018439)), 12421 ^ _784416 : [(12422 ^ _784416) ^ [] : [_1018437 = _1018439, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1018431, _1018431)), hAPP(hAPP(c_Product__Type_OPair(_1018431, _1018431), _1018441), _1018443)), _1018435)))], (12428 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1018431, _1018431)), hAPP(hAPP(c_Product__Type_OPair(_1018431, _1018431), _1018441), _1018443)), _1018435)), -(_1018437 = _1018439)]]], (12434 ^ _784416) ^ [_1019075, _1019077, _1019079, _1019081] : [-(hAPP(c_Relation_OImage(_1019075, _1019077, _1019079), hAPP(hAPP(c_Set_Oinsert(_1019075), _1019081), c_Orderings_Obot__class_Obot(tc_fun(_1019075, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1019077), hAPP(hAPP(c_COMBC(_1019077, tc_fun(tc_prod(_1019075, _1019077), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1019075, _1019077), tc_fun(tc_fun(tc_prod(_1019075, _1019077), tc_HOL_Obool), tc_HOL_Obool), _1019077), c_member(tc_prod(_1019075, _1019077))), hAPP(c_Product__Type_OPair(_1019075, _1019077), _1019081))), _1019079)))], (12436 ^ _784416) ^ [_1019178, _1019180, _1019182, _1019184, _1019186] : [c_Equiv__Relations_Oequiv(_1019178, _1019180, _1019182), 12439 ^ _784416 : [(12440 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1019178, _1019178)), hAPP(hAPP(c_Product__Type_OPair(_1019178, _1019178), _1019184), _1019186)), _1019182)), 12443 ^ _784416 : [(12444 ^ _784416) ^ [] : [-(hAPP(c_Relation_OImage(_1019178, _1019178, _1019182), hAPP(hAPP(c_Set_Oinsert(_1019178), _1019184), c_Orderings_Obot__class_Obot(tc_fun(_1019178, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1019178, _1019178, _1019182), hAPP(hAPP(c_Set_Oinsert(_1019178), _1019186), c_Orderings_Obot__class_Obot(tc_fun(_1019178, tc_HOL_Obool)))))], (12446 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1019178), _1019184), _1019180)))], (12448 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1019178), _1019186), _1019180)))]]], (12450 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1019178, _1019178)), hAPP(hAPP(c_Product__Type_OPair(_1019178, _1019178), _1019184), _1019186)), _1019182))), hAPP(c_Relation_OImage(_1019178, _1019178, _1019182), hAPP(hAPP(c_Set_Oinsert(_1019178), _1019184), c_Orderings_Obot__class_Obot(tc_fun(_1019178, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1019178, _1019178, _1019182), hAPP(hAPP(c_Set_Oinsert(_1019178), _1019186), c_Orderings_Obot__class_Obot(tc_fun(_1019178, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1019178), _1019184), _1019180)), hBOOL(hAPP(hAPP(c_member(_1019178), _1019186), _1019180))]]], (12464 ^ _784416) ^ [_1019778, _1019780, _1019782, _1019784, _1019786] : [c_Equiv__Relations_Oequiv(_1019778, _1019780, _1019782), hBOOL(hAPP(hAPP(c_member(_1019778), _1019784), _1019780)), hBOOL(hAPP(hAPP(c_member(_1019778), _1019786), _1019780)), 12475 ^ _784416 : [(12476 ^ _784416) ^ [] : [hAPP(c_Relation_OImage(_1019778, _1019778, _1019782), hAPP(hAPP(c_Set_Oinsert(_1019778), _1019784), c_Orderings_Obot__class_Obot(tc_fun(_1019778, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1019778, _1019778, _1019782), hAPP(hAPP(c_Set_Oinsert(_1019778), _1019786), c_Orderings_Obot__class_Obot(tc_fun(_1019778, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1019778, _1019778)), hAPP(hAPP(c_Product__Type_OPair(_1019778, _1019778), _1019784), _1019786)), _1019782)))], (12482 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1019778, _1019778)), hAPP(hAPP(c_Product__Type_OPair(_1019778, _1019778), _1019784), _1019786)), _1019782)), -(hAPP(c_Relation_OImage(_1019778, _1019778, _1019782), hAPP(hAPP(c_Set_Oinsert(_1019778), _1019784), c_Orderings_Obot__class_Obot(tc_fun(_1019778, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1019778, _1019778, _1019782), hAPP(hAPP(c_Set_Oinsert(_1019778), _1019786), c_Orderings_Obot__class_Obot(tc_fun(_1019778, tc_HOL_Obool)))))]]], (12488 ^ _784416) ^ [_1020326, _1020328, _1020330, _1020332, _1020334] : [hAPP(c_Relation_OImage(_1020326, _1020326, _1020328), hAPP(hAPP(c_Set_Oinsert(_1020326), _1020330), c_Orderings_Obot__class_Obot(tc_fun(_1020326, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1020326, _1020326, _1020328), hAPP(hAPP(c_Set_Oinsert(_1020326), _1020332), c_Orderings_Obot__class_Obot(tc_fun(_1020326, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1020326, _1020334, _1020328), hBOOL(hAPP(hAPP(c_member(_1020326), _1020332), _1020334)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1020326, _1020326)), hAPP(hAPP(c_Product__Type_OPair(_1020326, _1020326), _1020330), _1020332)), _1020328)))], (12502 ^ _784416) ^ [_1020674, _1020676] : [c_Nitpick_Orefl_H(_1020674, _1020676), 12505 ^ _784416 : [(12506 ^ _784416) ^ [_1020752] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1020674, _1020674)), hAPP(hAPP(c_Product__Type_OPair(_1020674, _1020674), _1020752), _1020752)), _1020676)))]]], (12508 ^ _784416) ^ [_1020794, _1020796] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1020794, _1020794)), hAPP(hAPP(c_Product__Type_OPair(_1020794, _1020794), 12509 ^ [_1020794, _1020796]), 12509 ^ [_1020794, _1020796])), _1020796)), -(c_Nitpick_Orefl_H(_1020794, _1020796))], (12515 ^ _784416) ^ [_1020961, _1020963, _1020965, _1020967, _1020969, _1020971, _1020973] : [c_Equiv__Relations_Oequiv(_1020961, _1020963, _1020965), c_Equiv__Relations_Ocongruent(_1020961, tc_fun(_1020967, tc_HOL_Obool), _1020965, _1020969), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1020961, tc_fun(_1020967, tc_HOL_Obool)), _1020971), _1020969) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1020961, tc_fun(_1020967, tc_HOL_Obool)), _1020973), _1020969), hBOOL(hAPP(hAPP(c_member(tc_fun(_1020961, tc_HOL_Obool)), _1020971), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1020961), _1020963), _1020965))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1020961, tc_HOL_Obool)), _1020973), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1020961), _1020963), _1020965))), 12537 ^ _784416 : [(12538 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1020961), 12536 ^ [_1020961, _1020963, _1020965, _1020967, _1020969, _1020971, _1020973]), _1020963)))], (12541 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1020961), 12539 ^ [_1020961, _1020963, _1020965, _1020967, _1020969, _1020971, _1020973]), _1020963)))], (12543 ^ _784416) ^ [] : [-(hAPP(_1020969, 12536 ^ [_1020961, _1020963, _1020965, _1020967, _1020969, _1020971, _1020973]) = hAPP(_1020969, 12539 ^ [_1020961, _1020963, _1020965, _1020967, _1020969, _1020971, _1020973]))], (12545 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1020961, _1020961)), hAPP(hAPP(c_Product__Type_OPair(_1020961, _1020961), 12536 ^ [_1020961, _1020963, _1020965, _1020967, _1020969, _1020971, _1020973]), 12539 ^ [_1020961, _1020963, _1020965, _1020967, _1020969, _1020971, _1020973])), _1020965))]], -(_1020971 = _1020973)], (12549 ^ _784416) ^ [_1021931] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1021931), tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(_1021931)), c_Option_Ooption_ONone(_1021931)), hAPP(c_Set_Oimage(_1021931, tc_Option_Ooption(_1021931), c_Option_Ooption_OSome(_1021931)), c_Orderings_Otop__class_Otop(tc_fun(_1021931, tc_HOL_Obool)))))], (12551 ^ _784416) ^ [_1022004, _1022006] : [c_Relation_Oirrefl(_1022004, _1022006), 12554 ^ _784416 : [(12555 ^ _784416) ^ [_1022086] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1022004, _1022004)), hAPP(hAPP(c_Product__Type_OPair(_1022004, _1022004), _1022086), _1022086)), _1022006))]]], (12557 ^ _784416) ^ [_1022126, _1022128] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1022126, _1022126)), hAPP(hAPP(c_Product__Type_OPair(_1022126, _1022126), 12558 ^ [_1022126, _1022128]), 12558 ^ [_1022126, _1022128])), _1022128))), -(c_Relation_Oirrefl(_1022126, _1022128))], (12564 ^ _784416) ^ [_1022197, _1022199, _1022201, _1022203, _1022205] : [hAPP(_1022197, _1022199) = c_Option_Ooption_ONone(_1022201), -(c_Map_Oran(_1022203, _1022201, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1022203, tc_Option_Ooption(_1022201)), _1022197), _1022199), hAPP(c_Option_Ooption_OSome(_1022201), _1022205))) = hAPP(hAPP(c_Set_Oinsert(_1022201), _1022205), c_Map_Oran(_1022203, _1022201, _1022197)))], (12570 ^ _784416) ^ [_1022372, _1022374] : [c_Option_Ooption_ONone(_1022372) = hAPP(c_Option_Ooption_OSome(_1022372), _1022374)], (12572 ^ _784416) ^ [_1022416, _1022418] : [hAPP(c_Option_Ooption_OSome(_1022416), _1022418) = c_Option_Ooption_ONone(_1022416)], (12574 ^ _784416) ^ [_1022457, _1022459] : [-(_1022457 = hAPP(c_Option_Ooption_OSome(_1022459), 12575 ^ [_1022457, _1022459])), -(_1022457 = c_Option_Ooption_ONone(_1022459))], (12581 ^ _784416) ^ [_1022503, _1022505] : [_1022503 = c_Option_Ooption_ONone(_1022505), 12584 ^ _784416 : [(12585 ^ _784416) ^ [_1022575] : [_1022503 = hAPP(c_Option_Ooption_OSome(_1022505), _1022575)]]], (12587 ^ _784416) ^ [_1022618, _1022620] : [-(_1022618 = c_Option_Ooption_ONone(_1022620)), -(_1022618 = hAPP(c_Option_Ooption_OSome(_1022620), 12590 ^ [_1022618, _1022620]))], (12594 ^ _784416) ^ [_1022664, _1022666] : [12595 ^ _784416 : [(12596 ^ _784416) ^ [_1022712] : [_1022664 = hAPP(c_Option_Ooption_OSome(_1022666), _1022712)]], _1022664 = c_Option_Ooption_ONone(_1022666)], (12600 ^ _784416) ^ [_1022771, _1022773, _1022775, _1022777, _1022779, _1022781] : [12601 ^ _784416 : [(12602 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1022771, _1022773), _1022775))], (12604 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1022777, _1022773), _1022775))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1022779, tc_fun(_1022781, tc_HOL_Obool))), _1022777), _1022771), _1022773), _1022775)))], (12608 ^ _784416) ^ [_1022954, _1022956, _1022958, _1022960, _1022962, _1022964] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1022954, tc_fun(_1022956, tc_HOL_Obool))), _1022958), _1022960), _1022962), _1022964)), -(hBOOL(hAPP(hAPP(_1022958, _1022962), _1022964))), -(hBOOL(hAPP(hAPP(_1022960, _1022962), _1022964)))], (12618 ^ _784416) ^ [_1023112, _1023114, _1023116, _1023118, _1023120, _1023122] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1023112, tc_fun(_1023114, tc_HOL_Obool))), _1023116), _1023118), _1023120), _1023122)), 12621 ^ _784416 : [(12622 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1023116, _1023120), _1023122)))], (12624 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1023118, _1023120), _1023122)))]]], (12626 ^ _784416) ^ [_1023285, _1023287, _1023289, _1023291, _1023293, _1023295] : [hBOOL(hAPP(hAPP(_1023285, _1023287), _1023289)), hBOOL(hAPP(hAPP(_1023291, _1023287), _1023289)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1023293, tc_fun(_1023295, tc_HOL_Obool))), _1023285), _1023291), _1023287), _1023289)))], (12636 ^ _784416) ^ [_1023506, _1023508, _1023510, _1023512] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1023506, tc_fun(_1023508, tc_HOL_Obool))), _1023510), _1023512))], (12638 ^ _784416) ^ [_1023578, _1023580, _1023582, _1023584, _1023586, _1023588, _1023590] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1023578, tc_fun(_1023580, tc_fun(_1023582, tc_HOL_Obool))), _1023584), _1023586), _1023588), _1023590)), 12642 ^ _784416 : [(12643 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1023578), 12641 ^ [_1023578, _1023580, _1023582, _1023584, _1023586, _1023588, _1023590]), _1023584)))], (12645 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1023586, 12641 ^ [_1023578, _1023580, _1023582, _1023584, _1023586, _1023588, _1023590]), _1023588), _1023590)))]]], (12647 ^ _784416) ^ [_1023796, _1023798, _1023800, _1023802, _1023804, _1023806, _1023808] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1023796, tc_fun(_1023798, tc_fun(_1023800, tc_HOL_Obool))), _1023802), _1023804), _1023806), _1023808))), 12648 ^ _784416 : [(12649 ^ _784416) ^ [_1023881] : [hBOOL(hAPP(hAPP(c_member(_1023796), _1023881), _1023802)), hBOOL(hAPP(hAPP(hAPP(_1023804, _1023881), _1023806), _1023808))]]], (12657 ^ _784416) ^ [_1024049, _1024051, _1024053, _1024055, _1024057, _1024059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1024049, tc_fun(_1024051, tc_HOL_Obool))), _1024053), _1024055)), hBOOL(hAPP(hAPP(_1024053, _1024057), _1024059)), -(hBOOL(hAPP(hAPP(_1024055, _1024057), _1024059)))], (12667 ^ _784416) ^ [_1024240, _1024242, _1024244, _1024246, _1024248, _1024250] : [hBOOL(hAPP(hAPP(_1024240, _1024242), _1024244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1024246, tc_fun(_1024248, tc_HOL_Obool))), _1024240), _1024250)), -(hBOOL(hAPP(hAPP(_1024250, _1024242), _1024244)))], (12677 ^ _784416) ^ [_1024431, _1024433, _1024435, _1024437, _1024439, _1024441] : [hBOOL(hAPP(hAPP(_1024431, _1024433), _1024435)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1024437, tc_fun(_1024439, tc_HOL_Obool))), _1024441), _1024431), _1024433), _1024435)))], (12683 ^ _784416) ^ [_1024564, _1024566, _1024568, _1024570, _1024572, _1024574] : [hBOOL(hAPP(hAPP(_1024564, _1024566), _1024568)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1024570, tc_fun(_1024572, tc_HOL_Obool))), _1024564), _1024574), _1024566), _1024568)))], (12689 ^ _784416) ^ [_1024697, _1024699, _1024701, _1024703, _1024705, _1024707] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1024697, tc_fun(_1024699, tc_HOL_Obool))), _1024701), _1024703), _1024705), _1024707)), -(hBOOL(hAPP(hAPP(_1024703, _1024705), _1024707)))], (12695 ^ _784416) ^ [_1024830, _1024832, _1024834, _1024836, _1024838, _1024840] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1024830, tc_fun(_1024832, tc_HOL_Obool))), _1024834), _1024836), _1024838), _1024840)), -(hBOOL(hAPP(hAPP(_1024834, _1024838), _1024840)))], (12701 ^ _784416) ^ [_1024963, _1024965] : [-(c_Fun_Oinj__on(_1024963, tc_Option_Ooption(_1024963), c_Option_Ooption_OSome(_1024963), _1024965))], (12703 ^ _784416) ^ [_1025012, _1025014, _1025016] : [hAPP(c_Option_Ooption_OSome(_1025012), _1025014) = hAPP(c_Option_Ooption_OSome(_1025012), _1025016), -(_1025014 = _1025016)], (12709 ^ _784416) ^ [_1025107, _1025109, _1025111] : [_1025109 = _1025111, -(hAPP(c_Option_Ooption_OSome(_1025107), _1025109) = hAPP(c_Option_Ooption_OSome(_1025107), _1025111))], (12715 ^ _784416) ^ [_1025208, _1025210, _1025212, _1025214, _1025216] : [hAPP(_1025208, _1025210) = hAPP(c_Option_Ooption_OSome(_1025212), _1025214), -(hBOOL(hAPP(hAPP(c_member(_1025212), _1025214), c_Map_Oran(_1025216, _1025212, _1025208))))], (12721 ^ _784416) ^ [_1025329, _1025331] : [-(c_Map_Oran(_1025329, _1025331, hAPP(c_COMBK(tc_Option_Ooption(_1025331), _1025329), c_Option_Ooption_ONone(_1025331))) = c_Orderings_Obot__class_Obot(tc_fun(_1025331, tc_HOL_Obool)))], (12723 ^ _784416) ^ [_1025373, _1025375] : [-(c_Option_Oset(_1025373, hAPP(c_Option_Ooption_OSome(_1025373), _1025375)) = hAPP(hAPP(c_Set_Oinsert(_1025373), _1025375), c_Orderings_Obot__class_Obot(tc_fun(_1025373, tc_HOL_Obool))))], (12725 ^ _784416) ^ [_1025419, _1025421, _1025423] : [_1025419 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1025421, _1025421), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1025421, _1025421), tc_HOL_Obool)), _1025419), _1025423)))], (12731 ^ _784416) ^ [_1025555, _1025557] : [c_Equiv__Relations_Oequiv(_1025555, c_Orderings_Otop__class_Otop(tc_fun(_1025555, tc_HOL_Obool)), _1025557), -(c_Equiv__Relations_Oequivp(_1025555, hAPP(hAPP(c_COMBC(_1025555, tc_fun(tc_prod(_1025555, _1025555), tc_HOL_Obool), tc_fun(_1025555, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1025555, tc_fun(tc_fun(tc_prod(_1025555, _1025555), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1025555, _1025555), tc_HOL_Obool), tc_fun(_1025555, tc_HOL_Obool)), _1025555), c_COMBC(_1025555, tc_fun(tc_prod(_1025555, _1025555), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1025555, tc_prod(_1025555, _1025555)), tc_fun(_1025555, tc_fun(tc_fun(tc_prod(_1025555, _1025555), tc_HOL_Obool), tc_HOL_Obool)), _1025555), hAPP(c_COMBB(tc_prod(_1025555, _1025555), tc_fun(tc_fun(tc_prod(_1025555, _1025555), tc_HOL_Obool), tc_HOL_Obool), _1025555), c_member(tc_prod(_1025555, _1025555)))), c_Product__Type_OPair(_1025555, _1025555)))), _1025557)))], (12737 ^ _784416) ^ [_1025876, _1025878] : [c_Equiv__Relations_Oequivp(_1025876, hAPP(hAPP(c_COMBC(_1025876, tc_fun(tc_prod(_1025876, _1025876), tc_HOL_Obool), tc_fun(_1025876, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1025876, tc_fun(tc_fun(tc_prod(_1025876, _1025876), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1025876, _1025876), tc_HOL_Obool), tc_fun(_1025876, tc_HOL_Obool)), _1025876), c_COMBC(_1025876, tc_fun(tc_prod(_1025876, _1025876), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1025876, tc_prod(_1025876, _1025876)), tc_fun(_1025876, tc_fun(tc_fun(tc_prod(_1025876, _1025876), tc_HOL_Obool), tc_HOL_Obool)), _1025876), hAPP(c_COMBB(tc_prod(_1025876, _1025876), tc_fun(tc_fun(tc_prod(_1025876, _1025876), tc_HOL_Obool), tc_HOL_Obool), _1025876), c_member(tc_prod(_1025876, _1025876)))), c_Product__Type_OPair(_1025876, _1025876)))), _1025878)), -(c_Equiv__Relations_Oequiv(_1025876, c_Orderings_Otop__class_Otop(tc_fun(_1025876, tc_HOL_Obool)), _1025878))], (12743 ^ _784416) ^ [_1026203, _1026205, _1026207, _1026209, _1026211] : [hBOOL(hAPP(hAPP(c_member(_1026203), _1026205), hAPP(c_Relation_OImage(_1026207, _1026203, _1026209), _1026211))), 12747 ^ _784416 : [(12748 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1026207, _1026203)), hAPP(hAPP(c_Product__Type_OPair(_1026207, _1026203), 12746 ^ [_1026203, _1026205, _1026207, _1026209, _1026211]), _1026205)), _1026209)))], (12750 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1026207), 12746 ^ [_1026203, _1026205, _1026207, _1026209, _1026211]), _1026211)))]]], (12752 ^ _784416) ^ [_1026427, _1026429, _1026431, _1026433] : [-(hAPP(c_Relation_OField(_1026427), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1026427, _1026427)), hAPP(hAPP(c_Product__Type_OPair(_1026427, _1026427), _1026429), _1026431)), _1026433)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1026427, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1026427), _1026429), hAPP(hAPP(c_Set_Oinsert(_1026427), _1026431), c_Orderings_Obot__class_Obot(tc_fun(_1026427, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1026427), _1026433)))], (12754 ^ _784416) ^ [_1026518, _1026520, _1026522, _1026524, _1026526] : [hBOOL(hAPP(hAPP(c_member(_1026518), _1026520), c_Map_Oran(_1026522, _1026518, c_Map_Orestrict__map(_1026522, _1026518, _1026524, _1026526)))), 12758 ^ _784416 : [(12759 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1026522), 12757 ^ [_1026518, _1026520, _1026522, _1026524, _1026526]), _1026526)))], (12761 ^ _784416) ^ [] : [-(hAPP(_1026524, 12757 ^ [_1026518, _1026520, _1026522, _1026524, _1026526]) = hAPP(c_Option_Ooption_OSome(_1026518), _1026520))]]], (12763 ^ _784416) ^ [_1026720, _1026722] : [-(c_Relation_OId__on(_1026720, _1026722) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1026720, tc_fun(tc_prod(_1026720, _1026720), tc_HOL_Obool)), _1026722), hAPP(hAPP(c_COMBC(_1026720, tc_fun(tc_prod(_1026720, _1026720), tc_HOL_Obool), tc_fun(tc_prod(_1026720, _1026720), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1026720, _1026720), tc_fun(tc_fun(tc_prod(_1026720, _1026720), tc_HOL_Obool), tc_fun(tc_prod(_1026720, _1026720), tc_HOL_Obool)), _1026720), c_Set_Oinsert(tc_prod(_1026720, _1026720))), hAPP(hAPP(c_COMBS(_1026720, _1026720, tc_prod(_1026720, _1026720)), c_Product__Type_OPair(_1026720, _1026720)), c_COMBI(_1026720)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1026720, _1026720), tc_HOL_Obool)))))], (12765 ^ _784416) ^ [_1026859, _1026861] : [c_Option_Oset(_1026859, _1026861) = c_Orderings_Obot__class_Obot(tc_fun(_1026859, tc_HOL_Obool)), -(_1026861 = c_Option_Ooption_ONone(_1026859))], (12771 ^ _784416) ^ [_1026952, _1026954] : [_1026954 = c_Option_Ooption_ONone(_1026952), -(c_Option_Oset(_1026952, _1026954) = c_Orderings_Obot__class_Obot(tc_fun(_1026952, tc_HOL_Obool)))], (12777 ^ _784416) ^ [_1027051] : [-(c_Option_Oset(_1027051, c_Option_Ooption_ONone(_1027051)) = c_Orderings_Obot__class_Obot(tc_fun(_1027051, tc_HOL_Obool)))], (12779 ^ _784416) ^ [_1027084] : [-(c_Equiv__Relations_Oequivp(_1027084, c_fequal))], (12797 ^ _784416) ^ [_1027420, _1027422] : [-(c_Equiv__Relations_Oequivp(_1027420, _1027422)), 12802 ^ _784416 : [(12803 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1027422, 12798 ^ [_1027420, _1027422]), 12799 ^ [_1027420, _1027422])))], (12805 ^ _784416) ^ [] : [hAPP(_1027422, 12798 ^ [_1027420, _1027422]) = hAPP(_1027422, 12799 ^ [_1027420, _1027422])]], 12806 ^ _784416 : [(12807 ^ _784416) ^ [] : [-(hAPP(_1027422, 12798 ^ [_1027420, _1027422]) = hAPP(_1027422, 12799 ^ [_1027420, _1027422]))], (12809 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1027422, 12798 ^ [_1027420, _1027422]), 12799 ^ [_1027420, _1027422]))]]], (12781 ^ _784416) ^ [_1027122, _1027124] : [c_Equiv__Relations_Oequivp(_1027122, _1027124), 12784 ^ _784416 : [(12785 ^ _784416) ^ [_1027216, _1027218] : [hBOOL(hAPP(hAPP(_1027124, _1027218), _1027216)), -(hAPP(_1027124, _1027218) = hAPP(_1027124, _1027216))], (12791 ^ _784416) ^ [_1027315, _1027317] : [hAPP(_1027124, _1027317) = hAPP(_1027124, _1027315), -(hBOOL(hAPP(hAPP(_1027124, _1027317), _1027315)))]]], (12813 ^ _784416) ^ [_1027749, _1027751, _1027753] : [c_Equiv__Relations_Oequivp(_1027749, _1027751), -(hBOOL(hAPP(hAPP(_1027751, _1027753), _1027753)))], (12819 ^ _784416) ^ [_1027838, _1027840, _1027842, _1027844] : [c_Equiv__Relations_Oequivp(_1027838, _1027840), hBOOL(hAPP(hAPP(_1027840, _1027842), _1027844)), -(hBOOL(hAPP(hAPP(_1027840, _1027844), _1027842)))], (12829 ^ _784416) ^ [_1027995, _1027997, _1027999, _1028001, _1028003] : [c_Equiv__Relations_Oequivp(_1027995, _1027997), hBOOL(hAPP(hAPP(_1027997, _1027999), _1028001)), hBOOL(hAPP(hAPP(_1027997, _1028001), _1028003)), -(hBOOL(hAPP(hAPP(_1027997, _1027999), _1028003)))], (12843 ^ _784416) ^ [_1028224] : [-(c_Relation_OId__on(_1028224, c_Orderings_Obot__class_Obot(tc_fun(_1028224, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1028224, _1028224), tc_HOL_Obool)))], (12845 ^ _784416) ^ [_1028263, _1028265, _1028267] : [-(hAPP(c_Relation_OImage(_1028263, _1028263, c_Relation_OId__on(_1028263, _1028265)), _1028267) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1028263, tc_HOL_Obool)), _1028265), _1028267))], (12847 ^ _784416) ^ [_1028311] : [-(hAPP(c_Relation_OField(_1028311), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1028311, _1028311), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1028311, tc_HOL_Obool)))], (12849 ^ _784416) ^ [_1028352, _1028354, _1028356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1028352, _1028352), tc_HOL_Obool)), _1028354), _1028356)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1028352, tc_HOL_Obool)), hAPP(c_Relation_OField(_1028352), _1028354)), hAPP(c_Relation_OField(_1028352), _1028356))))], (12855 ^ _784416) ^ [_1028497, _1028499, _1028501, _1028503, _1028505, _1028507, _1028509, _1028511, _1028513, _1028515, _1028517] : [hAPP(_1028497, hAPP(_1028499, _1028501)) = hAPP(_1028503, hAPP(_1028505, _1028507)), -(hAPP(hAPP(c_Fun_Ocomp(_1028509, _1028511, _1028513, _1028497), _1028499), _1028501) = hAPP(hAPP(c_Fun_Ocomp(_1028515, _1028511, _1028517, _1028503), _1028505), _1028507))], (12861 ^ _784416) ^ [_1028660, _1028662, _1028664] : [-(hAPP(c_Relation_OField(_1028660), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1028660, _1028660), tc_HOL_Obool)), _1028662), _1028664)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1028660, tc_HOL_Obool)), hAPP(c_Relation_OField(_1028660), _1028662)), hAPP(c_Relation_OField(_1028660), _1028664)))], (12863 ^ _784416) ^ [_1028748, _1028750, _1028752, _1028754] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1028748, _1028748)), hAPP(hAPP(c_Product__Type_OPair(_1028748, _1028748), _1028750), _1028752)), c_Relation_OId__on(_1028748, _1028754))), 12866 ^ _784416 : [(12867 ^ _784416) ^ [] : [-(_1028750 = _1028752)], (12869 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1028748), _1028750), _1028754)))]]], (12871 ^ _784416) ^ [_1028909, _1028911, _1028913, _1028915] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1028909, _1028909)), hAPP(hAPP(c_Product__Type_OPair(_1028909, _1028909), _1028911), _1028913)), c_Relation_OId__on(_1028909, _1028915)))), _1028911 = _1028913, hBOOL(hAPP(hAPP(c_member(_1028909), _1028911), _1028915))], (12881 ^ _784416) ^ [_1029106, _1029108, _1029110, _1029112] : [_1029106 = _1029108, hBOOL(hAPP(hAPP(c_member(_1029110), _1029106), _1029112)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1029110, _1029110)), hAPP(hAPP(c_Product__Type_OPair(_1029110, _1029110), _1029106), _1029108)), c_Relation_OId__on(_1029110, _1029112))))], (12891 ^ _784416) ^ [_1029319, _1029321, _1029323] : [hBOOL(hAPP(hAPP(c_member(_1029319), _1029321), c_Option_Oset(_1029319, _1029323))), -(_1029323 = hAPP(c_Option_Ooption_OSome(_1029319), _1029321))], (12897 ^ _784416) ^ [_1029424, _1029426, _1029428] : [_1029428 = hAPP(c_Option_Ooption_OSome(_1029424), _1029426), -(hBOOL(hAPP(hAPP(c_member(_1029424), _1029426), c_Option_Oset(_1029424, _1029428))))], (12903 ^ _784416) ^ [_1029559, _1029561, _1029563, _1029565, _1029567] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1029559, _1029561, _1029563), _1029565), _1029567)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1029559, _1029561)), hAPP(hAPP(c_Product__Type_OPair(_1029559, _1029561), _1029565), _1029567)), _1029563)))], (12909 ^ _784416) ^ [_1029694, _1029696, _1029698, _1029700, _1029702] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1029694, _1029696)), hAPP(hAPP(c_Product__Type_OPair(_1029694, _1029696), _1029700), _1029702)), _1029698)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1029694, _1029696, _1029698), _1029700), _1029702)))], (12915 ^ _784416) ^ [_1029835, _1029837, _1029839] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1029835, _1029835)), _1029837), c_Relation_OId__on(_1029835, _1029839))), 12919 ^ _784416 : [(12920 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1029835), 12918 ^ [_1029835, _1029837, _1029839]), _1029839)))], (12922 ^ _784416) ^ [] : [-(_1029837 = hAPP(hAPP(c_Product__Type_OPair(_1029835, _1029835), 12918 ^ [_1029835, _1029837, _1029839]), 12918 ^ [_1029835, _1029837, _1029839]))]]], (12924 ^ _784416) ^ [_1030034, _1030036, _1030038, _1030040, _1030042] : [-(c_Map_Orestrict__map(_1030034, _1030036, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1030034, tc_Option_Ooption(_1030036)), _1030038), _1030040), hAPP(c_Option_Ooption_OSome(_1030036), _1030042)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1030034, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1030034), _1030040), c_Orderings_Obot__class_Obot(tc_fun(_1030034, tc_HOL_Obool))))) = c_Map_Orestrict__map(_1030034, _1030036, _1030038, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1030034, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1030034), _1030040), c_Orderings_Obot__class_Obot(tc_fun(_1030034, tc_HOL_Obool))))))], (12926 ^ _784416) ^ [_1030136, _1030138, _1030140, _1030142] : [-(c_Map_Orestrict__map(_1030136, _1030138, _1030140, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1030136, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1030136), _1030142), c_Orderings_Obot__class_Obot(tc_fun(_1030136, tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1030136, tc_Option_Ooption(_1030138)), _1030140), _1030142), c_Option_Ooption_ONone(_1030138)))], (12928 ^ _784416) ^ [_1030207, _1030209, _1030211, _1030213, _1030215] : [class_Groups_Oab__semigroup__mult(_1030207), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1030207, _1030207, c_Groups_Otimes__class_Otimes(_1030207), _1030209, _1030211), _1030213)), hBOOL(hAPP(hAPP(c_member(_1030207), _1030215), _1030211)), -(hBOOL(hAPP(hAPP(c_member(_1030207), _1030209), _1030211))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1030207, _1030207, c_Groups_Otimes__class_Otimes(_1030207), _1030215, hAPP(hAPP(c_Set_Oinsert(_1030207), _1030209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1030207, tc_HOL_Obool)), _1030211), hAPP(hAPP(c_Set_Oinsert(_1030207), _1030215), c_Orderings_Obot__class_Obot(tc_fun(_1030207, tc_HOL_Obool)))))), _1030213)))], (12946 ^ _784416) ^ [_1030551, _1030553, _1030555, _1030557, _1030559] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1030551)), hAPP(c_Set_Oimage(_1030553, tc_Option_Ooption(_1030551), _1030555), c_Orderings_Otop__class_Otop(tc_fun(_1030553, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1030551)), hAPP(c_Set_Oimage(_1030553, tc_Option_Ooption(_1030551), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1030553, tc_Option_Ooption(_1030551)), _1030555), _1030557), hAPP(c_Option_Ooption_OSome(_1030551), _1030559))), c_Orderings_Otop__class_Otop(tc_fun(_1030553, tc_HOL_Obool))))))], (12952 ^ _784416) ^ [_1030752, _1030754, _1030756, _1030758, _1030760] : [-(hAPP(c_Option_Ooption_Ooption__case(_1030752, _1030754, _1030756, _1030758), hAPP(c_Option_Ooption_OSome(_1030754), _1030760)) = hAPP(_1030758, _1030760))], (12954 ^ _784416) ^ [_1030799, _1030801, _1030803, _1030805, _1030807] : [-(c_Option_Ooption_Ooption__rec(_1030799, _1030801, _1030803, _1030805, hAPP(c_Option_Ooption_OSome(_1030801), _1030807)) = hAPP(_1030805, _1030807))], (12956 ^ _784416) ^ [_1030844] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1030844), c_Orderings_Obot__class_Obot(tc_fun(_1030844, tc_HOL_Obool)))))], (12958 ^ _784416) ^ [_1030876, _1030878, _1030880] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1030876), _1030878)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1030876), hAPP(hAPP(c_Set_Oinsert(_1030876), _1030880), _1030878))))], (12964 ^ _784416) ^ [_1030987, _1030989, _1030991, _1030993] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1030987), _1030989)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1030991), hAPP(c_Set_Oimage(_1030987, _1030991, _1030993), _1030989))))], (12970 ^ _784416) ^ [_1031098, _1031100, _1031102] : [12971 ^ _784416 : [(12972 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1031098), _1031100))], (12974 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1031098), _1031102))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1031098), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1031098, tc_HOL_Obool)), _1031100), _1031102))))], (12978 ^ _784416) ^ [_1031261, _1031263, _1031265] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1031261), _1031263)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1031261), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1031261, tc_HOL_Obool)), _1031263), _1031265))))], (12984 ^ _784416) ^ [_1031378, _1031380] : [class_Groups_Oordered__ab__group__add(_1031378), -(c_Fun_Oinj__on(_1031378, _1031378, c_Groups_Ouminus__class_Ouminus(_1031378), _1031380))], (12990 ^ _784416) ^ [_1031457, _1031459, _1031461] : [-(hBOOL(hAPP(hAPP(c_member(_1031457), _1031459), _1031461))), -(hBOOL(hAPP(hAPP(c_member(_1031457), _1031459), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1031457, tc_HOL_Obool)), _1031461))))], (12996 ^ _784416) ^ [_1031517, _1031519, _1031521] : [12997 ^ _784416 : [(12998 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1031517), hAPP(c_Set_OCollect(_1031517), _1031519)))], (13000 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1031517), hAPP(c_Set_OCollect(_1031517), _1031521)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1031517), hAPP(c_Set_OCollect(_1031517), hAPP(hAPP(c_COMBS(_1031517, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1031517), c_fconj), _1031519)), _1031521)))))], (13004 ^ _784416) ^ [_1031728, _1031730] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1031728), _1031730)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1031728, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1031728, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1031728, tc_HOL_Obool), tc_fun(_1031728, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1031728, tc_HOL_Obool))), _1031730)))))], (13010 ^ _784416) ^ [_1031900, _1031902] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1031900, tc_HOL_Obool)), hAPP(c_Set_OPow(_1031900), _1031902))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1031900), _1031902)))], (13016 ^ _784416) ^ [_1032005, _1032007] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1032005), _1032007)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1032005, tc_HOL_Obool)), hAPP(c_Set_OPow(_1032005), _1032007))))], (13022 ^ _784416) ^ [_1032116, _1032118] : [class_Finite__Set_Ofinite(_1032116), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1032116), _1032118)))], (13028 ^ _784416) ^ [_1032199, _1032201] : [class_Finite__Set_Ofinite(_1032199), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1032199), _1032201)))], (13034 ^ _784416) ^ [_1032282, _1032284, _1032286, _1032288] : [class_Groups_Oab__semigroup__mult(_1032282), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032282), _1032284), _1032286)), _1032288) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032282), _1032284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032282), _1032286), _1032288)))], (13040 ^ _784416) ^ [_1032425, _1032427, _1032429] : [class_Groups_Ogroup__add(_1032425), 13043 ^ _784416 : [(13044 ^ _784416) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1032425), _1032427) = hAPP(c_Groups_Ouminus__class_Ouminus(_1032425), _1032429), -(_1032427 = _1032429)], (13050 ^ _784416) ^ [] : [_1032427 = _1032429, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1032425), _1032427) = hAPP(c_Groups_Ouminus__class_Ouminus(_1032425), _1032429))]]], (13056 ^ _784416) ^ [_1032666, _1032668, _1032670] : [class_Groups_Ogroup__add(_1032666), 13059 ^ _784416 : [(13060 ^ _784416) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1032666), _1032668) = _1032670, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1032666), _1032670) = _1032668)], (13066 ^ _784416) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1032666), _1032670) = _1032668, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1032666), _1032668) = _1032670)]]], (13072 ^ _784416) ^ [_1032907, _1032909, _1032911] : [class_Groups_Ogroup__add(_1032907), 13075 ^ _784416 : [(13076 ^ _784416) ^ [] : [_1032909 = hAPP(c_Groups_Ouminus__class_Ouminus(_1032907), _1032911), -(_1032911 = hAPP(c_Groups_Ouminus__class_Ouminus(_1032907), _1032909))], (13082 ^ _784416) ^ [] : [_1032911 = hAPP(c_Groups_Ouminus__class_Ouminus(_1032907), _1032909), -(_1032909 = hAPP(c_Groups_Ouminus__class_Ouminus(_1032907), _1032911))]]], (13088 ^ _784416) ^ [_1033148, _1033150] : [class_Groups_Ogroup__add(_1033148), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1033148), hAPP(c_Groups_Ouminus__class_Ouminus(_1033148), _1033150)) = _1033150)], (13094 ^ _784416) ^ [_1033243, _1033245, _1033247] : [class_Lattices_Oboolean__algebra(_1033243), 13097 ^ _784416 : [(13098 ^ _784416) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1033243), _1033245) = hAPP(c_Groups_Ouminus__class_Ouminus(_1033243), _1033247), -(_1033245 = _1033247)], (13104 ^ _784416) ^ [] : [_1033245 = _1033247, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1033243), _1033245) = hAPP(c_Groups_Ouminus__class_Ouminus(_1033243), _1033247))]]], (13110 ^ _784416) ^ [_1033484, _1033486, _1033488] : [class_Lattices_Oab__semigroup__idem__mult(_1033484), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033484), _1033486), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033484), _1033486), _1033488)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033484), _1033486), _1033488))], (13116 ^ _784416) ^ [_1033609, _1033611, _1033613, _1033615] : [class_Groups_Ouminus(_1033609), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1033611, _1033609)), _1033613), _1033615) = hAPP(c_Groups_Ouminus__class_Ouminus(_1033609), hAPP(_1033613, _1033615)))], (13122 ^ _784416) ^ [_1033726, _1033728] : [class_Lattices_Oab__semigroup__idem__mult(_1033726), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033726), _1033728), _1033728) = _1033728)], (13128 ^ _784416) ^ [_1033817, _1033819] : [class_Lattices_Oab__semigroup__idem__mult(_1033817), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033817), _1033819), _1033819) = _1033819)], (13134 ^ _784416) ^ [_1033908, _1033910] : [class_Lattices_Oboolean__algebra(_1033908), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1033908), hAPP(c_Groups_Ouminus__class_Ouminus(_1033908), _1033910)) = _1033910)], (13140 ^ _784416) ^ [_1034003, _1034005, _1034007, _1034009] : [class_Groups_Ouminus(_1034003), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1034005, _1034003)), _1034007), _1034009) = hAPP(c_Groups_Ouminus__class_Ouminus(_1034003), hAPP(_1034007, _1034009)))], (13146 ^ _784416) ^ [_1034138, _1034140, _1034142] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1034138, tc_HOL_Obool)), _1034140) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1034138, tc_HOL_Obool)), _1034142), -(_1034140 = _1034142)], (13152 ^ _784416) ^ [_1034245, _1034247, _1034249] : [_1034247 = _1034249, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1034245, tc_HOL_Obool)), _1034247) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1034245, tc_HOL_Obool)), _1034249))], (13158 ^ _784416) ^ [_1034358, _1034360] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1034358, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1034358, tc_HOL_Obool)), _1034360)) = _1034360)], (13160 ^ _784416) ^ [_1034399, _1034401, _1034403, _1034405] : [_1034399 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1034401, _1034403), 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)), _1034405))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1034401), _1034399)))], (13166 ^ _784416) ^ [_1034529, _1034531] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1034529, _1034531)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1034529, _1034531), tc_HOL_Obool)))), 13169 ^ _784416 : [(13170 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1034529), c_Orderings_Otop__class_Otop(tc_fun(_1034529, tc_HOL_Obool)))))], (13172 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1034531), c_Orderings_Otop__class_Otop(tc_fun(_1034531, tc_HOL_Obool)))))]]], (13174 ^ _784416) ^ [_1034694, _1034696] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1034694, _1034696)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1034694, _1034696), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034694), c_Orderings_Otop__class_Otop(tc_fun(_1034694, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034696), c_Orderings_Otop__class_Otop(tc_fun(_1034696, tc_HOL_Obool))))], (13184 ^ _784416) ^ [_1034891, _1034893] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1034891), c_Orderings_Otop__class_Otop(tc_fun(_1034891, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034893), c_Orderings_Otop__class_Otop(tc_fun(_1034893, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1034891, _1034893)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1034891, _1034893), tc_HOL_Obool)))))], (13194 ^ _784416) ^ [_1035086, _1035088] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1035086), _1035088)), 13197 ^ _784416 : [(13198 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1035086), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1035086, tc_HOL_Obool)), _1035088))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1035086), c_Orderings_Otop__class_Otop(tc_fun(_1035086, tc_HOL_Obool)))))], (13204 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1035086), c_Orderings_Otop__class_Otop(tc_fun(_1035086, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1035086), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1035086, tc_HOL_Obool)), _1035088))))]]], (13210 ^ _784416) ^ [_1035364, _1035366] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1035364, _1035364)), _1035366)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1035364), hAPP(c_Relation_OField(_1035364), _1035366))))], (13216 ^ _784416) ^ [_1035473, _1035475, _1035477] : [class_Lattices_Oboolean__algebra(_1035473), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035473), _1035475), _1035477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035473), hAPP(c_Groups_Ouminus__class_Ouminus(_1035473), _1035477)), hAPP(c_Groups_Ouminus__class_Ouminus(_1035473), _1035475))))], (13226 ^ _784416) ^ [_1035652, _1035654, _1035656] : [class_Lattices_Oboolean__algebra(_1035652), 13229 ^ _784416 : [(13230 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035652), hAPP(c_Groups_Ouminus__class_Ouminus(_1035652), _1035654)), hAPP(c_Groups_Ouminus__class_Ouminus(_1035652), _1035656))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035652), _1035656), _1035654)))], (13236 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035652), _1035656), _1035654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035652), hAPP(c_Groups_Ouminus__class_Ouminus(_1035652), _1035654)), hAPP(c_Groups_Ouminus__class_Ouminus(_1035652), _1035656))))]]], (13242 ^ _784416) ^ [_1035935, _1035937, _1035939] : [class_Groups_Oordered__ab__group__add(_1035935), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035935), _1035937), _1035939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035935), hAPP(c_Groups_Ouminus__class_Ouminus(_1035935), _1035939)), hAPP(c_Groups_Ouminus__class_Ouminus(_1035935), _1035937))))], (13252 ^ _784416) ^ [_1036114, _1036116, _1036118] : [class_Groups_Oordered__ab__group__add(_1036114), 13255 ^ _784416 : [(13256 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036114), hAPP(c_Groups_Ouminus__class_Ouminus(_1036114), _1036116)), hAPP(c_Groups_Ouminus__class_Ouminus(_1036114), _1036118))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036114), _1036118), _1036116)))], (13262 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036114), _1036118), _1036116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036114), hAPP(c_Groups_Ouminus__class_Ouminus(_1036114), _1036116)), hAPP(c_Groups_Ouminus__class_Ouminus(_1036114), _1036118))))]]], (13268 ^ _784416) ^ [_1036397, _1036399, _1036401] : [class_Groups_Oordered__ab__group__add(_1036397), 13271 ^ _784416 : [(13272 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036397), hAPP(c_Groups_Ouminus__class_Ouminus(_1036397), _1036399)), _1036401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036397), hAPP(c_Groups_Ouminus__class_Ouminus(_1036397), _1036401)), _1036399)))], (13278 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036397), hAPP(c_Groups_Ouminus__class_Ouminus(_1036397), _1036401)), _1036399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036397), hAPP(c_Groups_Ouminus__class_Ouminus(_1036397), _1036399)), _1036401)))]]], (13284 ^ _784416) ^ [_1036680, _1036682, _1036684] : [class_Groups_Oordered__ab__group__add(_1036680), 13287 ^ _784416 : [(13288 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036680), _1036682), hAPP(c_Groups_Ouminus__class_Ouminus(_1036680), _1036684))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036680), _1036684), hAPP(c_Groups_Ouminus__class_Ouminus(_1036680), _1036682))))], (13294 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036680), _1036684), hAPP(c_Groups_Ouminus__class_Ouminus(_1036680), _1036682))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036680), _1036682), hAPP(c_Groups_Ouminus__class_Ouminus(_1036680), _1036684))))]]], (13300 ^ _784416) ^ [_1036963, _1036965, _1036967] : [class_Groups_Oordered__ab__group__add(_1036963), 13303 ^ _784416 : [(13304 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036963), _1036965), hAPP(c_Groups_Ouminus__class_Ouminus(_1036963), _1036967))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036963), _1036967), hAPP(c_Groups_Ouminus__class_Ouminus(_1036963), _1036965))))], (13310 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036963), _1036967), hAPP(c_Groups_Ouminus__class_Ouminus(_1036963), _1036965))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036963), _1036965), hAPP(c_Groups_Ouminus__class_Ouminus(_1036963), _1036967))))]]], (13316 ^ _784416) ^ [_1037246, _1037248, _1037250] : [class_Groups_Oordered__ab__group__add(_1037246), 13319 ^ _784416 : [(13320 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037246), hAPP(c_Groups_Ouminus__class_Ouminus(_1037246), _1037248)), _1037250)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037246), hAPP(c_Groups_Ouminus__class_Ouminus(_1037246), _1037250)), _1037248)))], (13326 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037246), hAPP(c_Groups_Ouminus__class_Ouminus(_1037246), _1037250)), _1037248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037246), hAPP(c_Groups_Ouminus__class_Ouminus(_1037246), _1037248)), _1037250)))]]], (13332 ^ _784416) ^ [_1037529, _1037531, _1037533] : [class_Groups_Oordered__ab__group__add(_1037529), 13335 ^ _784416 : [(13336 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037529), hAPP(c_Groups_Ouminus__class_Ouminus(_1037529), _1037531)), hAPP(c_Groups_Ouminus__class_Ouminus(_1037529), _1037533))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037529), _1037533), _1037531)))], (13342 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037529), _1037533), _1037531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037529), hAPP(c_Groups_Ouminus__class_Ouminus(_1037529), _1037531)), hAPP(c_Groups_Ouminus__class_Ouminus(_1037529), _1037533))))]]], (13348 ^ _784416) ^ [_1037812, _1037814, _1037816] : [hBOOL(hAPP(hAPP(c_member(_1037812), _1037814), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1037812, tc_HOL_Obool)), _1037816))), hBOOL(hAPP(hAPP(c_member(_1037812), _1037814), _1037816))], (13354 ^ _784416) ^ [_1037936, _1037938, _1037940] : [hBOOL(hAPP(hAPP(c_member(_1037936), _1037938), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1037936, tc_HOL_Obool)), _1037940))), hBOOL(hAPP(hAPP(c_member(_1037936), _1037938), _1037940))], (13360 ^ _784416) ^ [_1038078, _1038080, _1038082] : [hBOOL(hAPP(hAPP(c_member(_1038078), _1038080), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038078, tc_HOL_Obool)), _1038082))), hBOOL(hAPP(hAPP(c_member(_1038078), _1038080), _1038082))], (13366 ^ _784416) ^ [_1038196, _1038198, _1038200] : [-(hBOOL(hAPP(hAPP(c_member(_1038196), _1038198), _1038200))), -(hBOOL(hAPP(hAPP(c_member(_1038196), _1038198), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038196, tc_HOL_Obool)), _1038200))))], (13372 ^ _784416) ^ [_1038258, _1038260, _1038262] : [class_Groups_Oab__group__add(_1038258), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1038258), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038258), _1038260), _1038262)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1038258), _1038262), _1038260))], (13378 ^ _784416) ^ [_1038377, _1038379, _1038381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1038377, tc_HOL_Obool)), _1038379), _1038381)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1038377, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038377, tc_HOL_Obool)), _1038381)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038377, tc_HOL_Obool)), _1038379))))], (13384 ^ _784416) ^ [_1038546, _1038548, _1038550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1038546, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038546, tc_HOL_Obool)), _1038548)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038546, tc_HOL_Obool)), _1038550))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1038546, tc_HOL_Obool)), _1038550), _1038548)))], (13390 ^ _784416) ^ [_1038693, _1038695, _1038697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1038693, tc_HOL_Obool)), _1038697), _1038695)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1038693, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038693, tc_HOL_Obool)), _1038695)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038693, tc_HOL_Obool)), _1038697))))], (13396 ^ _784416) ^ [_1038846] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1038846), c_Orderings_Obot__class_Obot(tc_fun(_1038846, tc_HOL_Obool)))))], (13398 ^ _784416) ^ [_1038878, _1038880, _1038882, _1038884] : [-(hAPP(c_Set_Ovimage(_1038878, _1038880, _1038882), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038880, tc_HOL_Obool)), _1038884)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038878, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1038878, _1038880, _1038882), _1038884)))], (13400 ^ _784416) ^ [_1038955, _1038957, _1038959] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1038955), hAPP(hAPP(c_Set_Oinsert(_1038955), _1038957), _1038959))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1038955), _1038959)))], (13406 ^ _784416) ^ [_1039062, _1039064, _1039066] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039062), _1039066)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039062), hAPP(hAPP(c_Set_Oinsert(_1039062), _1039064), _1039066))))], (13412 ^ _784416) ^ [_1039175, _1039177] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1039175, _1039177)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1039175, _1039177), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039177), c_Orderings_Otop__class_Otop(tc_fun(_1039177, tc_HOL_Obool)))))], (13418 ^ _784416) ^ [_1039300, _1039302, _1039304] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1039300, tc_HOL_Obool)), _1039302), _1039304)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039300), _1039304)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039300), _1039302)))], (13428 ^ _784416) ^ [_1039469, _1039471, _1039473] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039469), _1039471)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1039469, tc_HOL_Obool)), _1039473), _1039471)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039469), _1039473)))], (13438 ^ _784416) ^ [_1039638] : [class_Finite__Set_Ofinite(_1039638), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039638), c_Orderings_Otop__class_Otop(tc_fun(_1039638, tc_HOL_Obool)))))], (13444 ^ _784416) ^ [_1039747, _1039749, _1039751] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039747), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1039747, tc_HOL_Obool)), _1039749), _1039751))), 13447 ^ _784416 : [(13448 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039747), _1039749)))], (13450 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039747), _1039751)))]]], (13452 ^ _784416) ^ [_1039894, _1039896, _1039898] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039894), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1039894, tc_HOL_Obool)), _1039896), _1039898)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039894), _1039896)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039894), _1039898))], (13462 ^ _784416) ^ [_1040075, _1040077, _1040079] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040075), _1040077)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040075), _1040079)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1040075), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040075, tc_HOL_Obool)), _1040077), _1040079))))], (13472 ^ _784416) ^ [_1040254, _1040256, _1040258] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040254), _1040256)), 13475 ^ _784416 : [(13476 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040254), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1040254, tc_HOL_Obool)), _1040258), _1040256))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1040254), _1040258)))], (13482 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040254), _1040258)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1040254), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1040254, tc_HOL_Obool)), _1040258), _1040256))))]]], (13488 ^ _784416) ^ [_1040532, _1040534, _1040536, _1040538] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040532), _1040534)), 13491 ^ _784416 : [(13502 ^ _784416) ^ [] : [13504 ^ _784416 : [(13505 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1040532), 13503 ^ [_1040532, _1040534, _1040536, _1040538]), _1040534)))], (13507 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040536), hAPP(_1040538, 13503 ^ [_1040532, _1040534, _1040536, _1040538])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1040536), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1040532, tc_fun(_1040536, tc_HOL_Obool)), _1040534), _1040538))))], (13492 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040536), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1040532, tc_fun(_1040536, tc_HOL_Obool)), _1040534), _1040538))), 13495 ^ _784416 : [(13496 ^ _784416) ^ [_1040716] : [hBOOL(hAPP(hAPP(c_member(_1040532), _1040716), _1040534)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1040536), hAPP(_1040538, _1040716))))]]]]], (13511 ^ _784416) ^ [_1041007, _1041009, _1041011, _1041013, _1041015, _1041017] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1041007, _1041009, _1041011, _1041013, _1041015), _1041017)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1041007), _1041015)))], (13517 ^ _784416) ^ [_1041116] : [class_Lattices_Oab__semigroup__idem__mult(_1041116), -(c_Finite__Set_Ofun__left__comm__idem(_1041116, _1041116, c_Groups_Otimes__class_Otimes(_1041116)))], (13523 ^ _784416) ^ [_1041195, _1041197] : [-(hAPP(c_Set_OCollect(_1041195), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1041195), c_fNot), _1041197)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1041195, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1041195), _1041197)))], (13525 ^ _784416) ^ [_1041260] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1041260)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1041260), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1041260), c_Orderings_Otop__class_Otop(tc_fun(_1041260, tc_HOL_Obool)))))], (13531 ^ _784416) ^ [_1041375] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1041375), c_Orderings_Otop__class_Otop(tc_fun(_1041375, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1041375)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1041375), tc_HOL_Obool)))))], (13537 ^ _784416) ^ [_1041514, _1041516, _1041518] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1041514), hAPP(c_Set_OCollect(_1041514), hAPP(hAPP(c_COMBS(_1041514, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1041514), c_fdisj), _1041516)), _1041518)))), 13540 ^ _784416 : [(13541 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1041514), hAPP(c_Set_OCollect(_1041514), _1041516))))], (13543 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1041514), hAPP(c_Set_OCollect(_1041514), _1041518))))]]], (13545 ^ _784416) ^ [_1041709, _1041711, _1041713] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1041709), hAPP(c_Set_OCollect(_1041709), hAPP(hAPP(c_COMBS(_1041709, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1041709), c_fdisj), _1041711)), _1041713))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1041709), hAPP(c_Set_OCollect(_1041709), _1041711))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1041709), hAPP(c_Set_OCollect(_1041709), _1041713)))], (13555 ^ _784416) ^ [_1041938, _1041940] : [class_Lattices_Oboolean__algebra(_1041938), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1041938), hAPP(c_Groups_Ouminus__class_Ouminus(_1041938), _1041940)), _1041940) = c_Orderings_Obot__class_Obot(_1041938))], (13561 ^ _784416) ^ [_1042043, _1042045] : [class_Lattices_Oboolean__algebra(_1042043), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1042043), _1042045), hAPP(c_Groups_Ouminus__class_Ouminus(_1042043), _1042045)) = c_Orderings_Obot__class_Obot(_1042043))], (13567 ^ _784416) ^ [_1042148, _1042150, _1042152] : [class_Lattices_Oboolean__algebra(_1042148), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1042148), _1042150), _1042152) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1042148), _1042150), hAPP(c_Groups_Ouminus__class_Ouminus(_1042148), _1042152)))], (13573 ^ _784416) ^ [_1042267] : [class_Lattices_Oboolean__algebra(_1042267), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1042267), c_Orderings_Otop__class_Otop(_1042267)) = c_Orderings_Obot__class_Obot(_1042267))], (13579 ^ _784416) ^ [_1042358] : [class_Lattices_Oboolean__algebra(_1042358), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1042358), c_Orderings_Obot__class_Obot(_1042358)) = c_Orderings_Otop__class_Otop(_1042358))], (13585 ^ _784416) ^ [_1042449, _1042451, _1042453] : [class_Lattices_Oboolean__algebra(_1042449), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1042449), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1042449), _1042451), _1042453)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1042449), hAPP(c_Groups_Ouminus__class_Ouminus(_1042449), _1042451)), hAPP(c_Groups_Ouminus__class_Ouminus(_1042449), _1042453)))], (13591 ^ _784416) ^ [_1042588, _1042590, _1042592] : [class_Lattices_Oboolean__algebra(_1042588), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1042588), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1042588), _1042590), _1042592)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1042588), hAPP(c_Groups_Ouminus__class_Ouminus(_1042588), _1042590)), hAPP(c_Groups_Ouminus__class_Ouminus(_1042588), _1042592)))], (13597 ^ _784416) ^ [_1042727, _1042729] : [class_Lattices_Oboolean__algebra(_1042727), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1042727), hAPP(c_Groups_Ouminus__class_Ouminus(_1042727), _1042729)), _1042729) = c_Orderings_Otop__class_Otop(_1042727))], (13603 ^ _784416) ^ [_1042832, _1042834] : [class_Lattices_Oboolean__algebra(_1042832), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1042832), _1042834), hAPP(c_Groups_Ouminus__class_Ouminus(_1042832), _1042834)) = c_Orderings_Otop__class_Otop(_1042832))], (13609 ^ _784416) ^ [_1042952, _1042954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1042952, tc_HOL_Obool)), _1042954), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1042952, tc_HOL_Obool)), _1042954))), -(_1042954 = c_Orderings_Obot__class_Obot(tc_fun(_1042952, tc_HOL_Obool)))], (13615 ^ _784416) ^ [_1043071, _1043073] : [_1043073 = c_Orderings_Obot__class_Obot(tc_fun(_1043071, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1043071, tc_HOL_Obool)), _1043073), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043071, tc_HOL_Obool)), _1043073))))], (13621 ^ _784416) ^ [_1043196] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043196, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1043196, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1043196, tc_HOL_Obool)))], (13623 ^ _784416) ^ [_1043237] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043237, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1043237, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1043237, tc_HOL_Obool)))], (13625 ^ _784416) ^ [_1043278, _1043280] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1043278, tc_HOL_Obool)), _1043280), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043278, tc_HOL_Obool)), _1043280)) = c_Orderings_Obot__class_Obot(tc_fun(_1043278, tc_HOL_Obool)))], (13627 ^ _784416) ^ [_1043327, _1043329] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1043327, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043327, tc_HOL_Obool)), _1043329)), _1043329) = c_Orderings_Obot__class_Obot(tc_fun(_1043327, tc_HOL_Obool)))], (13629 ^ _784416) ^ [_1043376, _1043378] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1043376, tc_HOL_Obool)), _1043378), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043376, tc_HOL_Obool)), _1043378)) = c_Orderings_Otop__class_Otop(tc_fun(_1043376, tc_HOL_Obool)))], (13631 ^ _784416) ^ [_1043425, _1043427] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1043425, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043425, tc_HOL_Obool)), _1043427)), _1043427) = c_Orderings_Otop__class_Otop(tc_fun(_1043425, tc_HOL_Obool)))], (13633 ^ _784416) ^ [_1043474, _1043476, _1043478] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043474, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1043474, tc_HOL_Obool)), _1043476), _1043478)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1043474, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043474, tc_HOL_Obool)), _1043476)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043474, tc_HOL_Obool)), _1043478)))], (13635 ^ _784416) ^ [_1043547, _1043549, _1043551] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043547, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1043547, tc_HOL_Obool)), _1043549), _1043551)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1043547, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043547, tc_HOL_Obool)), _1043549)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043547, tc_HOL_Obool)), _1043551)))], (13637 ^ _784416) ^ [_1043620, _1043622] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043620, tc_HOL_Obool)), _1043622) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043620, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1043620, tc_HOL_Obool))), _1043622))], (13639 ^ _784416) ^ [_1043669, _1043671, _1043673] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043669, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043669, tc_HOL_Obool)), _1043671), _1043673)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1043669, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043669, tc_HOL_Obool)), _1043671)), _1043673))], (13641 ^ _784416) ^ [_1043734, _1043736, _1043738] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043734, tc_HOL_Obool)), _1043736), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043734, tc_HOL_Obool)), _1043738)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1043734, tc_HOL_Obool)), _1043736), _1043738))], (13643 ^ _784416) ^ [_1043791, _1043793, _1043795] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043791, tc_HOL_Obool)), _1043793), _1043795) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1043791, tc_HOL_Obool)), _1043793), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043791, tc_HOL_Obool)), _1043795)))], (13645 ^ _784416) ^ [_1043848, _1043850, _1043852, _1043854, _1043856] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1043848), _1043850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1043852, tc_HOL_Obool)), _1043854), hAPP(c_Set_Oimage(_1043848, _1043852, _1043856), _1043850))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1043852), _1043854)))], (13655 ^ _784416) ^ [_1044060, _1044062, _1044064, _1044066] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044060), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044060, tc_HOL_Obool)), _1044062), hAPP(hAPP(c_Set_Oinsert(_1044060), _1044064), _1044066)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1044060), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044060, tc_HOL_Obool)), _1044062), _1044066))))], (13661 ^ _784416) ^ [_1044213, _1044215, _1044217, _1044219] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044213), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044213, tc_HOL_Obool)), _1044215), _1044219))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1044213), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044213, tc_HOL_Obool)), _1044215), hAPP(hAPP(c_Set_Oinsert(_1044213), _1044217), _1044219)))))], (13667 ^ _784416) ^ [_1044372, _1044374, _1044376, _1044378] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044372), hAPP(c_Set_Oimage(_1044374, _1044372, _1044376), _1044378))), c_Fun_Oinj__on(_1044374, _1044372, _1044376, _1044378), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1044374), _1044378)))], (13677 ^ _784416) ^ [_1044543, _1044545] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1044543, tc_HOL_Obool)), _1044545) = hAPP(c_Set_OCollect(_1044543), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1044543), c_fNot), hAPP(hAPP(c_COMBC(_1044543, tc_fun(_1044543, tc_HOL_Obool), tc_HOL_Obool), c_member(_1044543)), _1044545))))], (13679 ^ _784416) ^ [_1044606, _1044608, _1044610] : [-(hAPP(c_Set_OCollect(_1044606), hAPP(hAPP(c_COMBS(_1044606, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1044606), c_fimplies), _1044608)), _1044610)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1044606, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1044606, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1044606), _1044608))), hAPP(c_Set_OCollect(_1044606), _1044610)))], (13681 ^ _784416) ^ [_1044687, _1044689] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044687), hAPP(c_Set_OCollect(_1044687), _1044689))), 13684 ^ _784416 : [(13685 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044687), hAPP(c_Set_OCollect(_1044687), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1044687), c_fNot), _1044689)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1044687), c_Orderings_Otop__class_Otop(tc_fun(_1044687, tc_HOL_Obool)))))], (13691 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044687), c_Orderings_Otop__class_Otop(tc_fun(_1044687, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1044687), hAPP(c_Set_OCollect(_1044687), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1044687), c_fNot), _1044689)))))]]], (13697 ^ _784416) ^ [_1044996, _1044998, _1045000, _1045002, _1045004] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044996), hAPP(c_Set_Oimage(_1044998, _1044996, _1045000), c_Orderings_Otop__class_Otop(tc_fun(_1044998, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045002), hAPP(c_Set_Oimage(_1044998, _1045002, hAPP(hAPP(c_COMBB(_1044996, _1045002, _1044998), _1045004), _1045000)), c_Orderings_Otop__class_Otop(tc_fun(_1044998, tc_HOL_Obool))))))], (13703 ^ _784416) ^ [_1045181, _1045183, _1045185] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1045181, tc_HOL_Obool)), _1045183), _1045185) = c_Orderings_Obot__class_Obot(tc_fun(_1045181, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1045181, tc_HOL_Obool)), _1045183), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1045181, tc_HOL_Obool)), _1045185))))], (13709 ^ _784416) ^ [_1045324, _1045326, _1045328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1045324, tc_HOL_Obool)), _1045326), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1045324, tc_HOL_Obool)), _1045328))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1045324, tc_HOL_Obool)), _1045326), _1045328) = c_Orderings_Obot__class_Obot(tc_fun(_1045324, tc_HOL_Obool)))], (13715 ^ _784416) ^ [_1045473, _1045475, _1045477, _1045479] : [hAPP(c_Set_Oimage(_1045473, _1045475, _1045477), c_Orderings_Otop__class_Otop(tc_fun(_1045473, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1045475, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1045475, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1045475, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1045473, _1045475, _1045477), _1045479))), hAPP(c_Set_Oimage(_1045473, _1045475, _1045477), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1045473, tc_HOL_Obool)), _1045479)))))], (13721 ^ _784416) ^ [_1045668, _1045670, _1045672, _1045674, _1045676] : [class_Groups_Oab__semigroup__mult(_1045668), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1045668, _1045668, c_Groups_Otimes__class_Otimes(_1045668), _1045670, _1045672), _1045674)), -(hBOOL(hAPP(hAPP(c_member(_1045668), _1045670), _1045672))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1045668, _1045668, c_Groups_Otimes__class_Otimes(_1045668), _1045676, hAPP(hAPP(c_Set_Oinsert(_1045668), _1045670), _1045672)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045668), _1045676), _1045674))))], (13735 ^ _784416) ^ [_1045908, _1045910, _1045912] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045908), _1045910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1045908, tc_HOL_Obool)), _1045910), hAPP(c_Set_Oimage(_1045908, _1045908, _1045912), _1045910))), -(c_Fun_Oinj__on(_1045908, _1045908, _1045912, _1045910))], (13745 ^ _784416) ^ [_1046087, _1046089, _1046091] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1046087), _1046089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1046087, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1046087, _1046087, _1046091), _1046089)), _1046089)), c_Fun_Oinj__on(_1046087, _1046087, _1046091, _1046089), -(hAPP(c_Set_Oimage(_1046087, _1046087, _1046091), _1046089) = _1046089)], (13759 ^ _784416) ^ [_1046334, _1046336] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1046334), c_Orderings_Otop__class_Otop(tc_fun(_1046334, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1046334, _1046334, _1046336), c_Orderings_Otop__class_Otop(tc_fun(_1046334, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1046334, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1046334, _1046334, _1046336, c_Orderings_Otop__class_Otop(tc_fun(_1046334, tc_HOL_Obool))))], (13769 ^ _784416) ^ [_1046529, _1046531] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1046529), c_Orderings_Otop__class_Otop(tc_fun(_1046529, tc_HOL_Obool)))), c_Fun_Oinj__on(_1046529, _1046529, _1046531, c_Orderings_Otop__class_Otop(tc_fun(_1046529, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1046529, _1046529, _1046531), c_Orderings_Otop__class_Otop(tc_fun(_1046529, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1046529, tc_HOL_Obool)))], (13779 ^ _784416) ^ [_1046724, _1046726, _1046728, _1046730] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1046724), hAPP(c_Set_Ovimage(_1046724, _1046726, _1046728), _1046730))), hAPP(c_Set_Oimage(_1046724, _1046726, _1046728), c_Orderings_Otop__class_Otop(tc_fun(_1046724, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1046726, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046726), _1046730)))], (13789 ^ _784416) ^ [_1046925, _1046927, _1046929, _1046931] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1046925), _1046927)), c_Fun_Oinj__on(_1046929, _1046925, _1046931, c_Orderings_Otop__class_Otop(tc_fun(_1046929, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046929), hAPP(c_Set_Ovimage(_1046929, _1046925, _1046931), _1046927))))], (13799 ^ _784416) ^ [_1047106, _1047108, _1047110] : [class_Lattices_Oboolean__algebra(_1047106), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1047106), _1047108), _1047110) = c_Orderings_Obot__class_Obot(_1047106), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1047106), _1047108), _1047110) = c_Orderings_Otop__class_Otop(_1047106), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1047106), _1047108) = _1047110)], (13813 ^ _784416) ^ [_1047341, _1047343, _1047345, _1047347] : [c_Fun_Oinj__on(_1047341, _1047343, _1047345, c_Orderings_Otop__class_Otop(tc_fun(_1047341, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1047343, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1047341, _1047343, _1047345), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1047341, tc_HOL_Obool)), _1047347))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1047343, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1047341, _1047343, _1047345), _1047347)))))], (13819 ^ _784416) ^ [_1047537, _1047539, _1047541, _1047543, _1047545, _1047547] : [hBOOL(hAPP(hAPP(c_member(_1047537), _1047539), _1047541)), 13822 ^ _784416 : [(13823 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1047537), _1047543), _1047541)), -(hAPP(c_Set_Ovimage(_1047545, _1047537, hAPP(hAPP(c_COMBC(_1047545, _1047537, _1047537), hAPP(hAPP(c_COMBC(_1047545, _1047537, tc_fun(_1047537, _1047537)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1047537, tc_fun(_1047537, _1047537)), _1047545), c_If(_1047537)), hAPP(hAPP(c_COMBC(_1047545, tc_fun(_1047545, tc_HOL_Obool), tc_HOL_Obool), c_member(_1047545)), _1047547))), _1047539)), _1047543)), _1047541) = c_Orderings_Otop__class_Otop(tc_fun(_1047545, tc_HOL_Obool)))], (13829 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1047537), _1047543), _1047541))), -(hAPP(c_Set_Ovimage(_1047545, _1047537, hAPP(hAPP(c_COMBC(_1047545, _1047537, _1047537), hAPP(hAPP(c_COMBC(_1047545, _1047537, tc_fun(_1047537, _1047537)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1047537, tc_fun(_1047537, _1047537)), _1047545), c_If(_1047537)), hAPP(hAPP(c_COMBC(_1047545, tc_fun(_1047545, tc_HOL_Obool), tc_HOL_Obool), c_member(_1047545)), _1047547))), _1047539)), _1047543)), _1047541) = _1047547)]]], (13835 ^ _784416) ^ [_1048028, _1048030, _1048032, _1048034, _1048036, _1048038] : [-(hBOOL(hAPP(hAPP(c_member(_1048028), _1048030), _1048032))), 13838 ^ _784416 : [(13839 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1048028), _1048034), _1048032)), -(hAPP(c_Set_Ovimage(_1048036, _1048028, hAPP(hAPP(c_COMBC(_1048036, _1048028, _1048028), hAPP(hAPP(c_COMBC(_1048036, _1048028, tc_fun(_1048028, _1048028)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1048028, tc_fun(_1048028, _1048028)), _1048036), c_If(_1048028)), hAPP(hAPP(c_COMBC(_1048036, tc_fun(_1048036, tc_HOL_Obool), tc_HOL_Obool), c_member(_1048036)), _1048038))), _1048030)), _1048034)), _1048032) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1048036, tc_HOL_Obool)), _1048038))], (13845 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1048028), _1048034), _1048032))), -(hAPP(c_Set_Ovimage(_1048036, _1048028, hAPP(hAPP(c_COMBC(_1048036, _1048028, _1048028), hAPP(hAPP(c_COMBC(_1048036, _1048028, tc_fun(_1048028, _1048028)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1048028, tc_fun(_1048028, _1048028)), _1048036), c_If(_1048028)), hAPP(hAPP(c_COMBC(_1048036, tc_fun(_1048036, tc_HOL_Obool), tc_HOL_Obool), c_member(_1048036)), _1048038))), _1048030)), _1048034)), _1048032) = c_Orderings_Obot__class_Obot(tc_fun(_1048036, tc_HOL_Obool)))]]], (13851 ^ _784416) ^ [_1048533, _1048535, _1048537, _1048539] : [-(c_Option_Ooption_Ooption__rec(_1048533, _1048535, _1048537, _1048539, c_Option_Ooption_ONone(_1048535)) = _1048537)], (13853 ^ _784416) ^ [_1048570, _1048572, _1048574, _1048576] : [-(hAPP(c_Option_Ooption_Ooption__case(_1048570, _1048572, _1048574, _1048576), c_Option_Ooption_ONone(_1048572)) = _1048574)], (13855 ^ _784416) ^ [_1048609, _1048611, _1048613, _1048615, _1048617, _1048619] : [c_Finite__Set_Ofolding(_1048609, _1048611, _1048613, _1048615), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048609), _1048617)), hBOOL(hAPP(hAPP(c_member(_1048609), _1048619), _1048617)), -(hAPP(_1048615, _1048617) = hAPP(c_Fun_Ocomp(_1048611, _1048611, _1048611, hAPP(_1048615, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1048609, tc_HOL_Obool)), _1048617), hAPP(hAPP(c_Set_Oinsert(_1048609), _1048619), c_Orderings_Obot__class_Obot(tc_fun(_1048609, tc_HOL_Obool)))))), hAPP(_1048613, _1048619)))], (13869 ^ _784416) ^ [_1048922, _1048924, _1048926, _1048928, _1048930, _1048932, _1048934, _1048936] : [c_Finite__Set_Ofolding__image__simple(_1048922, _1048924, _1048926, _1048928, _1048930, _1048932), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048924), _1048934)), hBOOL(hAPP(hAPP(c_member(_1048924), _1048936), _1048934)), -(hAPP(_1048932, _1048934) = hAPP(hAPP(_1048926, hAPP(_1048930, _1048936)), hAPP(_1048932, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1048924, tc_HOL_Obool)), _1048934), hAPP(hAPP(c_Set_Oinsert(_1048924), _1048936), c_Orderings_Obot__class_Obot(tc_fun(_1048924, tc_HOL_Obool)))))))], (13883 ^ _784416) ^ [_1049247, _1049249, _1049251, _1049253, _1049255] : [c_Finite__Set_Ofolding__one(_1049247, _1049249, _1049251), hBOOL(hAPP(c_Finite__Set_Ofinite(_1049247), _1049253)), hBOOL(hAPP(hAPP(c_member(_1049247), _1049255), _1049253)), 13894 ^ _784416 : [(13895 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049247, tc_HOL_Obool)), _1049253), hAPP(hAPP(c_Set_Oinsert(_1049247), _1049255), c_Orderings_Obot__class_Obot(tc_fun(_1049247, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1049247, tc_HOL_Obool)), -(hAPP(_1049251, _1049253) = _1049255)], (13901 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049247, tc_HOL_Obool)), _1049253), hAPP(hAPP(c_Set_Oinsert(_1049247), _1049255), c_Orderings_Obot__class_Obot(tc_fun(_1049247, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1049247, tc_HOL_Obool))), -(hAPP(_1049251, _1049253) = hAPP(hAPP(_1049249, _1049255), hAPP(_1049251, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049247, tc_HOL_Obool)), _1049253), hAPP(hAPP(c_Set_Oinsert(_1049247), _1049255), c_Orderings_Obot__class_Obot(tc_fun(_1049247, tc_HOL_Obool)))))))]]], (13907 ^ _784416) ^ [_1049769, _1049771, _1049773, _1049775, _1049777, _1049779, _1049781, _1049783] : [c_Finite__Set_Ofolding__image(_1049769, _1049771, _1049773, _1049775, _1049777), hBOOL(hAPP(c_Finite__Set_Ofinite(_1049771), _1049779)), c_Fun_Oinj__on(_1049771, _1049771, _1049781, _1049779), -(hAPP(hAPP(_1049777, _1049783), hAPP(c_Set_Oimage(_1049771, _1049771, _1049781), _1049779)) = hAPP(hAPP(_1049777, hAPP(c_Fun_Ocomp(_1049771, _1049769, _1049771, _1049783), _1049781)), _1049779))], (13921 ^ _784416) ^ [_1050058, _1050060, _1050062, _1050064, _1050066, _1050068] : [c_Finite__Set_Ofolding(_1050058, _1050060, _1050062, _1050064), hBOOL(hAPP(c_Finite__Set_Ofinite(_1050058), _1050066)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1050058), _1050068)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1050058, tc_HOL_Obool)), _1050066), _1050068) = c_Orderings_Obot__class_Obot(tc_fun(_1050058, tc_HOL_Obool)), -(hAPP(_1050064, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1050058, tc_HOL_Obool)), _1050066), _1050068)) = hAPP(c_Fun_Ocomp(_1050060, _1050060, _1050060, hAPP(_1050064, _1050066)), hAPP(_1050064, _1050068)))], (13939 ^ _784416) ^ [_1050431, _1050433, _1050435, _1050437, _1050439, _1050441] : [c_Finite__Set_Ofolding(_1050431, _1050433, _1050435, _1050437), hBOOL(hAPP(c_Finite__Set_Ofinite(_1050431), _1050439)), -(hAPP(_1050437, hAPP(hAPP(c_Set_Oinsert(_1050431), _1050441), _1050439)) = hAPP(c_Fun_Ocomp(_1050433, _1050433, _1050433, hAPP(_1050437, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050431, tc_HOL_Obool)), _1050439), hAPP(hAPP(c_Set_Oinsert(_1050431), _1050441), c_Orderings_Obot__class_Obot(tc_fun(_1050431, tc_HOL_Obool)))))), hAPP(_1050435, _1050441)))], (13949 ^ _784416) ^ [_1050686, _1050688, _1050690, _1050692, _1050694, _1050696, _1050698, _1050700] : [c_Finite__Set_Ofolding__image__simple(_1050686, _1050688, _1050690, _1050692, _1050694, _1050696), hBOOL(hAPP(c_Finite__Set_Ofinite(_1050688), _1050698)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1050688), _1050700)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1050688, tc_HOL_Obool)), _1050698), _1050700) = c_Orderings_Obot__class_Obot(tc_fun(_1050688, tc_HOL_Obool)), -(hAPP(_1050696, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1050688, tc_HOL_Obool)), _1050698), _1050700)) = hAPP(hAPP(_1050690, hAPP(_1050696, _1050698)), hAPP(_1050696, _1050700)))], (13967 ^ _784416) ^ [_1051075, _1051077, _1051079, _1051081, _1051083] : [c_Finite__Set_Ofolding__one(_1051075, _1051077, _1051079), hBOOL(hAPP(c_Finite__Set_Ofinite(_1051075), _1051081)), -(_1051081 = c_Orderings_Obot__class_Obot(tc_fun(_1051075, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1051075), _1051083)), -(_1051083 = c_Orderings_Obot__class_Obot(tc_fun(_1051075, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1051075, tc_HOL_Obool)), _1051081), _1051083) = c_Orderings_Obot__class_Obot(tc_fun(_1051075, tc_HOL_Obool)), -(hAPP(_1051079, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1051075, tc_HOL_Obool)), _1051081), _1051083)) = hAPP(hAPP(_1051077, hAPP(_1051079, _1051081)), hAPP(_1051079, _1051083)))], (13993 ^ _784416) ^ [_1051576] : [-(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)), _1051576)))))], (13995 ^ _784416) ^ [_1051607] : [-(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)), _1051607)))))], (13997 ^ _784416) ^ [_1051638, _1051640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051638), _1051640)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051638), _1051640)))], (14003 ^ _784416) ^ [_1051735, _1051737, _1051739, _1051741, _1051743, _1051745, _1051747, _1051749] : [c_Finite__Set_Ofolding(_1051735, _1051737, _1051739, _1051741), -(hAPP(c_Fun_Ocomp(_1051737, _1051737, _1051743, hAPP(_1051739, _1051745)), hAPP(c_Fun_Ocomp(_1051737, _1051737, _1051743, hAPP(_1051739, _1051747)), _1051749)) = hAPP(c_Fun_Ocomp(_1051737, _1051737, _1051743, hAPP(_1051739, _1051747)), hAPP(c_Fun_Ocomp(_1051737, _1051737, _1051743, hAPP(_1051739, _1051745)), _1051749)))], (14009 ^ _784416) ^ [_1051916, _1051918, _1051920, _1051922, _1051924, _1051926] : [c_Finite__Set_Ofolding(_1051916, _1051918, _1051920, _1051922), -(hAPP(c_Fun_Ocomp(_1051918, _1051918, _1051918, hAPP(_1051920, _1051924)), hAPP(_1051920, _1051926)) = hAPP(c_Fun_Ocomp(_1051918, _1051918, _1051918, hAPP(_1051920, _1051926)), hAPP(_1051920, _1051924)))], (14015 ^ _784416) ^ [_1052061, _1052063, _1052065, _1052067, _1052069, _1052071, _1052073, _1052075, _1052077, _1052079, _1052081] : [c_Finite__Set_Ofolding(_1052061, _1052063, _1052065, _1052067), -(hAPP(c_Fun_Ocomp(_1052069, _1052071, _1052073, _1052075), hAPP(c_Fun_Ocomp(_1052077, _1052069, _1052073, _1052079), _1052081)) = hAPP(c_Fun_Ocomp(_1052077, _1052071, _1052073, hAPP(c_Fun_Ocomp(_1052069, _1052071, _1052077, _1052075), _1052079)), _1052081))], (14021 ^ _784416) ^ [_1052224, _1052226, _1052228, _1052230, _1052232, _1052234] : [c_Finite__Set_Ofolding__image__simple(_1052224, _1052226, _1052228, _1052230, _1052232, _1052234), -(hAPP(_1052234, c_Orderings_Obot__class_Obot(tc_fun(_1052226, tc_HOL_Obool))) = _1052230)], (14027 ^ _784416) ^ [_1052333, _1052335, _1052337, _1052339, _1052341, _1052343, _1052345, _1052347] : [c_Finite__Set_Ofolding__image(_1052333, _1052335, _1052337, _1052339, _1052341), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052335), _1052343)), -(hAPP(hAPP(_1052341, hAPP(hAPP(c_COMBS(_1052335, _1052333, _1052333), hAPP(hAPP(c_COMBB(_1052333, tc_fun(_1052333, _1052333), _1052335), _1052337), _1052345)), _1052347)), _1052343) = hAPP(hAPP(_1052337, hAPP(hAPP(_1052341, _1052345), _1052343)), hAPP(hAPP(_1052341, _1052347), _1052343)))], (14037 ^ _784416) ^ [_1052594, _1052596, _1052598, _1052600, _1052602, _1052604, _1052606, _1052608] : [c_Finite__Set_Ofolding(_1052594, _1052596, _1052598, _1052600), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052594), _1052602)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052594), _1052604)), -(hAPP(c_Fun_Ocomp(_1052596, _1052596, _1052606, hAPP(_1052600, _1052604)), hAPP(c_Fun_Ocomp(_1052596, _1052596, _1052606, hAPP(_1052600, _1052602)), _1052608)) = hAPP(c_Fun_Ocomp(_1052596, _1052596, _1052606, hAPP(_1052600, _1052602)), hAPP(c_Fun_Ocomp(_1052596, _1052596, _1052606, hAPP(_1052600, _1052604)), _1052608)))], (14051 ^ _784416) ^ [_1052919, _1052921, _1052923, _1052925, _1052927, _1052929] : [c_Finite__Set_Ofolding(_1052919, _1052921, _1052923, _1052925), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052919), _1052927)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052919), _1052929)), -(hAPP(c_Fun_Ocomp(_1052921, _1052921, _1052921, hAPP(_1052925, _1052929)), hAPP(_1052925, _1052927)) = hAPP(c_Fun_Ocomp(_1052921, _1052921, _1052921, hAPP(_1052925, _1052927)), hAPP(_1052925, _1052929)))], (14065 ^ _784416) ^ [_1053200, _1053202, _1053204, _1053206, _1053208, _1053210, _1053212, _1053214] : [c_Finite__Set_Ofolding(_1053200, _1053202, _1053204, _1053206), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053200), _1053208)), -(hAPP(c_Fun_Ocomp(_1053202, _1053202, _1053210, hAPP(_1053204, _1053212)), hAPP(c_Fun_Ocomp(_1053202, _1053202, _1053210, hAPP(_1053206, _1053208)), _1053214)) = hAPP(c_Fun_Ocomp(_1053202, _1053202, _1053210, hAPP(_1053206, _1053208)), hAPP(c_Fun_Ocomp(_1053202, _1053202, _1053210, hAPP(_1053204, _1053212)), _1053214)))], (14075 ^ _784416) ^ [_1053453, _1053455, _1053457, _1053459, _1053461, _1053463] : [c_Finite__Set_Ofolding(_1053453, _1053455, _1053457, _1053459), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053453), _1053461)), -(hAPP(c_Fun_Ocomp(_1053455, _1053455, _1053455, hAPP(_1053457, _1053463)), hAPP(_1053459, _1053461)) = hAPP(c_Fun_Ocomp(_1053455, _1053455, _1053455, hAPP(_1053459, _1053461)), hAPP(_1053457, _1053463)))], (14085 ^ _784416) ^ [_1053666, _1053668, _1053670, _1053672] : [c_Finite__Set_Ofolding__one(_1053666, _1053668, _1053670), -(hAPP(_1053670, hAPP(hAPP(c_Set_Oinsert(_1053666), _1053672), c_Orderings_Obot__class_Obot(tc_fun(_1053666, tc_HOL_Obool)))) = _1053672)], (14091 ^ _784416) ^ [_1053781, _1053783, _1053785, _1053787, _1053789, _1053791, _1053793, _1053795] : [c_Finite__Set_Ofolding__image__simple(_1053781, _1053783, _1053785, _1053787, _1053789, _1053791), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053783), _1053793)), -(hBOOL(hAPP(hAPP(c_member(_1053783), _1053795), _1053793))), -(hAPP(_1053791, hAPP(hAPP(c_Set_Oinsert(_1053783), _1053795), _1053793)) = hAPP(hAPP(_1053785, hAPP(_1053789, _1053795)), hAPP(_1053791, _1053793)))], (14105 ^ _784416) ^ [_1054025, _1054027, _1054029, _1054031, _1054033, _1054035, _1054037, _1054039] : [c_Finite__Set_Ofolding__image__simple(_1054025, _1054027, _1054029, _1054031, _1054033, _1054035), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054027), _1054037)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054027), _1054039)), -(hAPP(hAPP(_1054029, hAPP(_1054035, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1054027, tc_HOL_Obool)), _1054037), _1054039))), hAPP(_1054035, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1054027, tc_HOL_Obool)), _1054037), _1054039))) = hAPP(hAPP(_1054029, hAPP(_1054035, _1054037)), hAPP(_1054035, _1054039)))], (14119 ^ _784416) ^ [_1054358, _1054360, _1054362, _1054364, _1054366, _1054368] : [c_Finite__Set_Ofolding(_1054358, _1054360, _1054362, _1054364), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054358), _1054366)), -(hBOOL(hAPP(hAPP(c_member(_1054358), _1054368), _1054366))), -(hAPP(_1054364, hAPP(hAPP(c_Set_Oinsert(_1054358), _1054368), _1054366)) = hAPP(c_Fun_Ocomp(_1054360, _1054360, _1054360, hAPP(_1054364, _1054366)), hAPP(_1054362, _1054368)))], (14133 ^ _784416) ^ [_1054594, _1054596, _1054598, _1054600, _1054602, _1054604] : [c_Finite__Set_Ofolding(_1054594, _1054596, _1054598, _1054600), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054594), _1054602)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054594), _1054604)), -(hAPP(c_Fun_Ocomp(_1054596, _1054596, _1054596, hAPP(_1054600, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1054594, tc_HOL_Obool)), _1054602), _1054604))), hAPP(_1054600, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1054594, tc_HOL_Obool)), _1054602), _1054604))) = hAPP(c_Fun_Ocomp(_1054596, _1054596, _1054596, hAPP(_1054600, _1054602)), hAPP(_1054600, _1054604)))], (14147 ^ _784416) ^ [_1054919, _1054921, _1054923, _1054925, _1054927] : [c_Finite__Set_Ofolding__one(_1054919, _1054921, _1054923), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054919), _1054925)), -(hBOOL(hAPP(hAPP(c_member(_1054919), _1054927), _1054925))), -(_1054925 = c_Orderings_Obot__class_Obot(tc_fun(_1054919, tc_HOL_Obool))), -(hAPP(_1054923, hAPP(hAPP(c_Set_Oinsert(_1054919), _1054927), _1054925)) = hAPP(hAPP(_1054921, _1054927), hAPP(_1054923, _1054925)))], (14165 ^ _784416) ^ [_1055164, _1055166, _1055168, _1055170, _1055172] : [c_Finite__Set_Ofolding__one(_1055164, _1055166, _1055168), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055164), _1055170)), 14172 ^ _784416 : [(14173 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055164, tc_HOL_Obool)), _1055170), hAPP(hAPP(c_Set_Oinsert(_1055164), _1055172), c_Orderings_Obot__class_Obot(tc_fun(_1055164, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1055164, tc_HOL_Obool)), -(hAPP(_1055168, hAPP(hAPP(c_Set_Oinsert(_1055164), _1055172), _1055170)) = _1055172)], (14179 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055164, tc_HOL_Obool)), _1055170), hAPP(hAPP(c_Set_Oinsert(_1055164), _1055172), c_Orderings_Obot__class_Obot(tc_fun(_1055164, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1055164, tc_HOL_Obool))), -(hAPP(_1055168, hAPP(hAPP(c_Set_Oinsert(_1055164), _1055172), _1055170)) = hAPP(hAPP(_1055166, _1055172), hAPP(_1055168, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055164, tc_HOL_Obool)), _1055170), hAPP(hAPP(c_Set_Oinsert(_1055164), _1055172), c_Orderings_Obot__class_Obot(tc_fun(_1055164, tc_HOL_Obool)))))))]]], (14185 ^ _784416) ^ [_1055646, _1055648, _1055650, _1055652, _1055654, _1055656, _1055658, _1055660] : [c_Finite__Set_Ofolding__image__simple(_1055646, _1055648, _1055650, _1055652, _1055654, _1055656), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055648), _1055658)), -(hAPP(_1055656, hAPP(hAPP(c_Set_Oinsert(_1055648), _1055660), _1055658)) = hAPP(hAPP(_1055650, hAPP(_1055654, _1055660)), hAPP(_1055656, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055648, tc_HOL_Obool)), _1055658), hAPP(hAPP(c_Set_Oinsert(_1055648), _1055660), c_Orderings_Obot__class_Obot(tc_fun(_1055648, tc_HOL_Obool)))))))], (14195 ^ _784416) ^ [_1055909, _1055911, _1055913, _1055915, _1055917] : [c_Finite__Set_Ofolding__one(_1055909, _1055911, _1055913), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055909), _1055915)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055909), _1055917)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1055909, tc_HOL_Obool)), _1055915), _1055917) = c_Orderings_Obot__class_Obot(tc_fun(_1055909, tc_HOL_Obool))), -(hAPP(hAPP(_1055911, hAPP(_1055913, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1055909, tc_HOL_Obool)), _1055915), _1055917))), hAPP(_1055913, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1055909, tc_HOL_Obool)), _1055915), _1055917))) = hAPP(hAPP(_1055911, hAPP(_1055913, _1055915)), hAPP(_1055913, _1055917)))], (14213 ^ _784416) ^ [_1056265, _1056267] : [-(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), _1056265)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1056267))))))], (14215 ^ _784416) ^ [_1056307, _1056309, _1056311] : [class_Rings_Oidom(_1056307), 14218 ^ _784416 : [(14229 ^ _784416) ^ [] : [14230 ^ _784416 : [(14231 ^ _784416) ^ [] : [_1056309 = _1056311], (14233 ^ _784416) ^ [] : [_1056309 = hAPP(c_Groups_Ouminus__class_Ouminus(_1056307), _1056311)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056307), _1056309), _1056309) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056307), _1056311), _1056311))], (14219 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056307), _1056309), _1056309) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056307), _1056311), _1056311), -(_1056309 = _1056311), -(_1056309 = hAPP(c_Groups_Ouminus__class_Ouminus(_1056307), _1056311))]]], (14237 ^ _784416) ^ [_1056626, _1056628, _1056630] : [class_Rings_Oring(_1056626), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056626), hAPP(c_Groups_Ouminus__class_Ouminus(_1056626), _1056628)), hAPP(c_Groups_Ouminus__class_Ouminus(_1056626), _1056630)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056626), _1056628), _1056630))], (14243 ^ _784416) ^ [_1056755, _1056757, _1056759] : [class_Rings_Oring(_1056755), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056755), hAPP(c_Groups_Ouminus__class_Ouminus(_1056755), _1056757)), _1056759) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056755), _1056757), hAPP(c_Groups_Ouminus__class_Ouminus(_1056755), _1056759)))], (14249 ^ _784416) ^ [_1056884, _1056886, _1056888] : [class_Rings_Oring(_1056884), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1056884), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056884), _1056886), _1056888)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056884), hAPP(c_Groups_Ouminus__class_Ouminus(_1056884), _1056886)), _1056888))], (14255 ^ _784416) ^ [_1057013, _1057015, _1057017] : [class_Rings_Oring(_1057013), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1057013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057013), _1057015), _1057017)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057013), _1057015), hAPP(c_Groups_Ouminus__class_Ouminus(_1057013), _1057017)))], (14261 ^ _784416) ^ [_1057142, _1057144, _1057146] : [class_Lattices_Olattice(_1057142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057142), _1057144)), hBOOL(hAPP(hAPP(c_member(_1057142), _1057146), _1057144)), 14272 ^ _784416 : [(14273 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1057142, tc_HOL_Obool)), _1057144), hAPP(hAPP(c_Set_Oinsert(_1057142), _1057146), c_Orderings_Obot__class_Obot(tc_fun(_1057142, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1057142, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1057142, _1057144) = _1057146)], (14279 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1057142, tc_HOL_Obool)), _1057144), hAPP(hAPP(c_Set_Oinsert(_1057142), _1057146), c_Orderings_Obot__class_Obot(tc_fun(_1057142, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1057142, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1057142, _1057144) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1057142), _1057146), c_Big__Operators_Olattice__class_OInf__fin(_1057142, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1057142, tc_HOL_Obool)), _1057144), hAPP(hAPP(c_Set_Oinsert(_1057142), _1057146), c_Orderings_Obot__class_Obot(tc_fun(_1057142, tc_HOL_Obool)))))))]]], (14285 ^ _784416) ^ [_1057648, _1057650, _1057652] : [class_Lattices_Olattice(_1057648), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057648), _1057650)), hBOOL(hAPP(hAPP(c_member(_1057648), _1057652), _1057650)), 14296 ^ _784416 : [(14297 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1057648, tc_HOL_Obool)), _1057650), hAPP(hAPP(c_Set_Oinsert(_1057648), _1057652), c_Orderings_Obot__class_Obot(tc_fun(_1057648, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1057648, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1057648, _1057650) = _1057652)], (14303 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1057648, tc_HOL_Obool)), _1057650), hAPP(hAPP(c_Set_Oinsert(_1057648), _1057652), c_Orderings_Obot__class_Obot(tc_fun(_1057648, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1057648, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1057648, _1057650) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1057648), _1057652), c_Big__Operators_Olattice__class_OSup__fin(_1057648, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1057648, tc_HOL_Obool)), _1057650), hAPP(hAPP(c_Set_Oinsert(_1057648), _1057652), c_Orderings_Obot__class_Obot(tc_fun(_1057648, tc_HOL_Obool)))))))]]], (14320 ^ _784416) ^ [_1058353] : [14322 ^ _784416 : [(14323 ^ _784416) ^ [_1058429] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 14321 ^ [_1058353, _1058429]), _1058353)))], (14325 ^ _784416) ^ [_1058463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 14321 ^ [_1058353, _1058463]), _1058463))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1058353)))], (14309 ^ _784416) ^ [_1058166] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1058166)), 14313 ^ _784416 : [(14314 ^ _784416) ^ [_1058246] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1058246), _1058166)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1058246), 14312 ^ [_1058166])))]]], (14329 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (14331 ^ _784416) ^ [_1058556, _1058558] : [class_Lattices_Olattice(_1058556), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058556), _1058558)), -(_1058558 = c_Orderings_Obot__class_Obot(tc_fun(_1058556, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058556), c_Big__Operators_Olattice__class_OInf__fin(_1058556, _1058558)), c_Big__Operators_Olattice__class_OSup__fin(_1058556, _1058558))))], (14345 ^ _784416) ^ [_1058742, _1058744] : [class_Lattices_Olattice(_1058742), -(c_Big__Operators_Olattice__class_OSup__fin(_1058742, hAPP(hAPP(c_Set_Oinsert(_1058742), _1058744), c_Orderings_Obot__class_Obot(tc_fun(_1058742, tc_HOL_Obool)))) = _1058744)], (14351 ^ _784416) ^ [_1058849, _1058851] : [class_Lattices_Olattice(_1058849), -(c_Big__Operators_Olattice__class_OInf__fin(_1058849, hAPP(hAPP(c_Set_Oinsert(_1058849), _1058851), c_Orderings_Obot__class_Obot(tc_fun(_1058849, tc_HOL_Obool)))) = _1058851)], (14357 ^ _784416) ^ [_1058956, _1058958, _1058960] : [class_Rings_Olinordered__idom(_1058956), -(_1058958 = _1058960), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058956), _1058958), _1058960))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058956), _1058960), _1058958)))], (14382 ^ _784416) ^ [_1059290] : [14384 ^ _784416 : [(14385 ^ _784416) ^ [_1059366] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 14383 ^ [_1059290, _1059366]), _1059290)))], (14387 ^ _784416) ^ [_1059400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14383 ^ [_1059290, _1059400]), _1059400))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1059290)))], (14371 ^ _784416) ^ [_1059103] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1059103)), 14375 ^ _784416 : [(14376 ^ _784416) ^ [_1059183] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1059183), _1059103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1059183), 14374 ^ [_1059103])))]]], (14391 ^ _784416) ^ [_1059469, _1059471, _1059473] : [class_Lattices_Olattice(_1059469), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059469), _1059471)), hBOOL(hAPP(hAPP(c_member(_1059469), _1059473), _1059471)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1059469), _1059473), c_Big__Operators_Olattice__class_OInf__fin(_1059469, _1059471)) = _1059473)], (14405 ^ _784416) ^ [_1059698, _1059700, _1059702] : [class_Lattices_Olattice(_1059698), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059698), _1059700)), hBOOL(hAPP(hAPP(c_member(_1059698), _1059702), _1059700)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1059698), _1059702), c_Big__Operators_Olattice__class_OSup__fin(_1059698, _1059700)) = c_Big__Operators_Olattice__class_OSup__fin(_1059698, _1059700))], (14419 ^ _784416) ^ [_1059933, _1059935, _1059937] : [class_Lattices_Olattice(_1059933), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059933), _1059935)), hBOOL(hAPP(hAPP(c_member(_1059933), _1059937), _1059935)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1059933), _1059937), c_Big__Operators_Olattice__class_OInf__fin(_1059933, _1059935)) = c_Big__Operators_Olattice__class_OInf__fin(_1059933, _1059935))], (14433 ^ _784416) ^ [_1060168, _1060170, _1060172] : [class_Lattices_Olattice(_1060168), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060168), _1060170)), hBOOL(hAPP(hAPP(c_member(_1060168), _1060172), _1060170)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1060168), _1060172), c_Big__Operators_Olattice__class_OSup__fin(_1060168, _1060170)) = _1060172)], (14447 ^ _784416) ^ [_1060397, _1060399, _1060401] : [class_Lattices_Olattice(_1060397), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060397), _1060399)), -(_1060399 = c_Orderings_Obot__class_Obot(tc_fun(_1060397, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1060397, hAPP(hAPP(c_Set_Oinsert(_1060397), _1060401), _1060399)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1060397), _1060401), c_Big__Operators_Olattice__class_OSup__fin(_1060397, _1060399)))], (14461 ^ _784416) ^ [_1060605, _1060607, _1060609] : [class_Lattices_Olattice(_1060605), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060605), _1060607)), -(_1060607 = c_Orderings_Obot__class_Obot(tc_fun(_1060605, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1060605, hAPP(hAPP(c_Set_Oinsert(_1060605), _1060609), _1060607)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1060605), _1060609), c_Big__Operators_Olattice__class_OInf__fin(_1060605, _1060607)))], (14475 ^ _784416) ^ [_1060813, _1060815, _1060817] : [class_Lattices_Olattice(_1060813), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060813), _1060815)), -(_1060817 = c_Orderings_Obot__class_Obot(tc_fun(_1060813, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1060813, tc_HOL_Obool)), _1060817), _1060815)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1060813), c_Big__Operators_Olattice__class_OSup__fin(_1060813, _1060817)), c_Big__Operators_Olattice__class_OSup__fin(_1060813, _1060815)) = c_Big__Operators_Olattice__class_OSup__fin(_1060813, _1060815))], (14493 ^ _784416) ^ [_1061127, _1061129, _1061131] : [class_Lattices_Olattice(_1061127), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061127), _1061129)), -(_1061131 = c_Orderings_Obot__class_Obot(tc_fun(_1061127, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1061127, tc_HOL_Obool)), _1061131), _1061129)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1061127), c_Big__Operators_Olattice__class_OInf__fin(_1061127, _1061131)), c_Big__Operators_Olattice__class_OInf__fin(_1061127, _1061129)) = c_Big__Operators_Olattice__class_OInf__fin(_1061127, _1061129))], (14511 ^ _784416) ^ [_1061441, _1061443, _1061445] : [class_Lattices_Olattice(_1061441), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061441), _1061443)), -(_1061443 = c_Orderings_Obot__class_Obot(tc_fun(_1061441, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061441), _1061445)), -(_1061445 = c_Orderings_Obot__class_Obot(tc_fun(_1061441, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1061441, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1061441, tc_HOL_Obool)), _1061443), _1061445)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1061441), c_Big__Operators_Olattice__class_OSup__fin(_1061441, _1061443)), c_Big__Operators_Olattice__class_OSup__fin(_1061441, _1061445)))], (14533 ^ _784416) ^ [_1061790, _1061792, _1061794] : [class_Lattices_Olattice(_1061790), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061790), _1061792)), -(_1061792 = c_Orderings_Obot__class_Obot(tc_fun(_1061790, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061790), _1061794)), -(_1061794 = c_Orderings_Obot__class_Obot(tc_fun(_1061790, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1061790, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1061790, tc_HOL_Obool)), _1061792), _1061794)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1061790), c_Big__Operators_Olattice__class_OInf__fin(_1061790, _1061792)), c_Big__Operators_Olattice__class_OInf__fin(_1061790, _1061794)))], (14555 ^ _784416) ^ [_1062139, _1062141, _1062143] : [class_Lattices_Olattice(_1062139), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062139), _1062141)), -(hBOOL(hAPP(hAPP(c_member(_1062139), _1062143), _1062141))), -(_1062141 = c_Orderings_Obot__class_Obot(tc_fun(_1062139, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1062139, hAPP(hAPP(c_Set_Oinsert(_1062139), _1062143), _1062141)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1062139), _1062143), c_Big__Operators_Olattice__class_OSup__fin(_1062139, _1062141)))], (14573 ^ _784416) ^ [_1062376, _1062378, _1062380] : [class_Lattices_Olattice(_1062376), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062376), _1062378)), -(hBOOL(hAPP(hAPP(c_member(_1062376), _1062380), _1062378))), -(_1062378 = c_Orderings_Obot__class_Obot(tc_fun(_1062376, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1062376, hAPP(hAPP(c_Set_Oinsert(_1062376), _1062380), _1062378)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062376), _1062380), c_Big__Operators_Olattice__class_OInf__fin(_1062376, _1062378)))], (14591 ^ _784416) ^ [_1062613, _1062615, _1062617] : [class_Lattices_Olattice(_1062613), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062613), _1062615)), 14598 ^ _784416 : [(14599 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1062613, tc_HOL_Obool)), _1062615), hAPP(hAPP(c_Set_Oinsert(_1062613), _1062617), c_Orderings_Obot__class_Obot(tc_fun(_1062613, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1062613, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1062613, hAPP(hAPP(c_Set_Oinsert(_1062613), _1062617), _1062615)) = _1062617)], (14605 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1062613, tc_HOL_Obool)), _1062615), hAPP(hAPP(c_Set_Oinsert(_1062613), _1062617), c_Orderings_Obot__class_Obot(tc_fun(_1062613, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1062613, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1062613, hAPP(hAPP(c_Set_Oinsert(_1062613), _1062617), _1062615)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1062613), _1062617), c_Big__Operators_Olattice__class_OSup__fin(_1062613, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1062613, tc_HOL_Obool)), _1062615), hAPP(hAPP(c_Set_Oinsert(_1062613), _1062617), c_Orderings_Obot__class_Obot(tc_fun(_1062613, tc_HOL_Obool)))))))]]], (14611 ^ _784416) ^ [_1063083, _1063085, _1063087] : [class_Lattices_Olattice(_1063083), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063083), _1063085)), 14618 ^ _784416 : [(14619 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1063083, tc_HOL_Obool)), _1063085), hAPP(hAPP(c_Set_Oinsert(_1063083), _1063087), c_Orderings_Obot__class_Obot(tc_fun(_1063083, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1063083, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1063083, hAPP(hAPP(c_Set_Oinsert(_1063083), _1063087), _1063085)) = _1063087)], (14625 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1063083, tc_HOL_Obool)), _1063085), hAPP(hAPP(c_Set_Oinsert(_1063083), _1063087), c_Orderings_Obot__class_Obot(tc_fun(_1063083, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1063083, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1063083, hAPP(hAPP(c_Set_Oinsert(_1063083), _1063087), _1063085)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1063083), _1063087), c_Big__Operators_Olattice__class_OInf__fin(_1063083, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1063083, tc_HOL_Obool)), _1063085), hAPP(hAPP(c_Set_Oinsert(_1063083), _1063087), c_Orderings_Obot__class_Obot(tc_fun(_1063083, tc_HOL_Obool)))))))]]], (14631 ^ _784416) ^ [_1063553, _1063555, _1063557] : [class_Lattices_Olattice(_1063553), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063553), _1063555)), -(_1063555 = c_Orderings_Obot__class_Obot(tc_fun(_1063553, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063553), _1063557)), -(_1063557 = c_Orderings_Obot__class_Obot(tc_fun(_1063553, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063553, tc_HOL_Obool)), _1063555), _1063557) = c_Orderings_Obot__class_Obot(tc_fun(_1063553, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1063553, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063553, tc_HOL_Obool)), _1063555), _1063557)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1063553), c_Big__Operators_Olattice__class_OSup__fin(_1063553, _1063555)), c_Big__Operators_Olattice__class_OSup__fin(_1063553, _1063557)))], (14657 ^ _784416) ^ [_1064030, _1064032, _1064034] : [class_Lattices_Olattice(_1064030), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064030), _1064032)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064030), _1064034)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1064030, tc_HOL_Obool)), _1064032), _1064034) = c_Orderings_Obot__class_Obot(tc_fun(_1064030, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064030), c_Big__Operators_Olattice__class_OSup__fin(_1064030, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1064030, tc_HOL_Obool)), _1064032), _1064034))), c_Big__Operators_Olattice__class_OSup__fin(_1064030, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1064030, tc_HOL_Obool)), _1064032), _1064034))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064030), c_Big__Operators_Olattice__class_OSup__fin(_1064030, _1064032)), c_Big__Operators_Olattice__class_OSup__fin(_1064030, _1064034)))], (14675 ^ _784416) ^ [_1064378, _1064380, _1064382] : [class_Lattices_Olattice(_1064378), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064378), _1064380)), -(_1064380 = c_Orderings_Obot__class_Obot(tc_fun(_1064378, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064378), _1064382)), -(_1064382 = c_Orderings_Obot__class_Obot(tc_fun(_1064378, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1064378, tc_HOL_Obool)), _1064380), _1064382) = c_Orderings_Obot__class_Obot(tc_fun(_1064378, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1064378, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1064378, tc_HOL_Obool)), _1064380), _1064382)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064378), c_Big__Operators_Olattice__class_OInf__fin(_1064378, _1064380)), c_Big__Operators_Olattice__class_OInf__fin(_1064378, _1064382)))], (14701 ^ _784416) ^ [_1064855, _1064857, _1064859] : [class_Lattices_Olattice(_1064855), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064855), _1064857)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064855), _1064859)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1064855, tc_HOL_Obool)), _1064857), _1064859) = c_Orderings_Obot__class_Obot(tc_fun(_1064855, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064855), c_Big__Operators_Olattice__class_OInf__fin(_1064855, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1064855, tc_HOL_Obool)), _1064857), _1064859))), c_Big__Operators_Olattice__class_OInf__fin(_1064855, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1064855, tc_HOL_Obool)), _1064857), _1064859))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064855), c_Big__Operators_Olattice__class_OInf__fin(_1064855, _1064857)), c_Big__Operators_Olattice__class_OInf__fin(_1064855, _1064859)))], (14719 ^ _784416) ^ [_1065203, _1065205] : [class_Lattices_Olattice(_1065203), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065203), _1065205)), -(_1065205 = c_Orderings_Obot__class_Obot(tc_fun(_1065203, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1065203), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065203), 14732 ^ [_1065203, _1065205]), 14733 ^ [_1065203, _1065205])), hAPP(hAPP(c_Set_Oinsert(_1065203), 14732 ^ [_1065203, _1065205]), hAPP(hAPP(c_Set_Oinsert(_1065203), 14733 ^ [_1065203, _1065205]), c_Orderings_Obot__class_Obot(tc_fun(_1065203, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1065203), c_Big__Operators_Olattice__class_OInf__fin(_1065203, _1065205)), _1065205)))], (14739 ^ _784416) ^ [_1065647, _1065649] : [class_Lattices_Olattice(_1065647), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065647), _1065649)), -(_1065649 = c_Orderings_Obot__class_Obot(tc_fun(_1065647, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1065647), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1065647), 14752 ^ [_1065647, _1065649]), 14753 ^ [_1065647, _1065649])), hAPP(hAPP(c_Set_Oinsert(_1065647), 14752 ^ [_1065647, _1065649]), hAPP(hAPP(c_Set_Oinsert(_1065647), 14753 ^ [_1065647, _1065649]), c_Orderings_Obot__class_Obot(tc_fun(_1065647, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1065647), c_Big__Operators_Olattice__class_OSup__fin(_1065647, _1065649)), _1065649)))], (14759 ^ _784416) ^ [_1066112, _1066114, _1066116, _1066118] : [hBOOL(hAPP(hAPP(c_member(_1066112), _1066114), c_SetInterval_Oord_OatMost(_1066112, _1066116, _1066118))), -(hBOOL(hAPP(hAPP(_1066116, _1066114), _1066118)))], (14765 ^ _784416) ^ [_1066221, _1066223, _1066225, _1066227] : [hBOOL(hAPP(hAPP(_1066225, _1066223), _1066227)), -(hBOOL(hAPP(hAPP(c_member(_1066221), _1066223), c_SetInterval_Oord_OatMost(_1066221, _1066225, _1066227))))], (14771 ^ _784416) ^ [_1066357, _1066359, _1066361, _1066363] : [hBOOL(hAPP(hAPP(c_member(_1066357), _1066359), c_SetInterval_Oord_OatLeast(_1066357, _1066361, _1066363))), -(hBOOL(hAPP(hAPP(_1066361, _1066363), _1066359)))], (14777 ^ _784416) ^ [_1066466, _1066468, _1066470, _1066472] : [hBOOL(hAPP(hAPP(_1066470, _1066472), _1066468)), -(hBOOL(hAPP(hAPP(c_member(_1066466), _1066468), c_SetInterval_Oord_OatLeast(_1066466, _1066470, _1066472))))], (14783 ^ _784416) ^ [_1066602, _1066604, _1066606, _1066608] : [hBOOL(hAPP(hAPP(c_member(_1066602), _1066604), c_SetInterval_Oord_OlessThan(_1066602, _1066606, _1066608))), -(hBOOL(hAPP(hAPP(_1066606, _1066604), _1066608)))], (14789 ^ _784416) ^ [_1066711, _1066713, _1066715, _1066717] : [hBOOL(hAPP(hAPP(_1066715, _1066713), _1066717)), -(hBOOL(hAPP(hAPP(c_member(_1066711), _1066713), c_SetInterval_Oord_OlessThan(_1066711, _1066715, _1066717))))], (14795 ^ _784416) ^ [_1066847, _1066849, _1066851, _1066853] : [hBOOL(hAPP(hAPP(c_member(_1066847), _1066849), c_SetInterval_Oord_OgreaterThan(_1066847, _1066851, _1066853))), -(hBOOL(hAPP(hAPP(_1066851, _1066853), _1066849)))], (14801 ^ _784416) ^ [_1066956, _1066958, _1066960, _1066962] : [hBOOL(hAPP(hAPP(_1066960, _1066962), _1066958)), -(hBOOL(hAPP(hAPP(c_member(_1066956), _1066958), c_SetInterval_Oord_OgreaterThan(_1066956, _1066960, _1066962))))], (14807 ^ _784416) ^ [_1067095, _1067097, _1067099, _1067101, _1067103] : [hBOOL(hAPP(hAPP(c_member(_1067095), _1067097), c_SetInterval_Oord_OatLeastAtMost(_1067095, _1067099, _1067101, _1067103))), 14810 ^ _784416 : [(14811 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1067099, _1067101), _1067097)))], (14813 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1067099, _1067097), _1067103)))]]], (14815 ^ _784416) ^ [_1067244, _1067246, _1067248, _1067250, _1067252] : [-(hBOOL(hAPP(hAPP(c_member(_1067244), _1067246), c_SetInterval_Oord_OatLeastAtMost(_1067244, _1067248, _1067250, _1067252)))), hBOOL(hAPP(hAPP(_1067248, _1067250), _1067246)), hBOOL(hAPP(hAPP(_1067248, _1067246), _1067252))], (14825 ^ _784416) ^ [_1067455, _1067457, _1067459, _1067461, _1067463] : [hBOOL(hAPP(hAPP(c_member(_1067455), _1067457), c_SetInterval_Oord_OgreaterThanLessThan(_1067455, _1067459, _1067461, _1067463))), 14828 ^ _784416 : [(14829 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1067459, _1067461), _1067457)))], (14831 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1067459, _1067457), _1067463)))]]], (14833 ^ _784416) ^ [_1067604, _1067606, _1067608, _1067610, _1067612] : [-(hBOOL(hAPP(hAPP(c_member(_1067604), _1067606), c_SetInterval_Oord_OgreaterThanLessThan(_1067604, _1067608, _1067610, _1067612)))), hBOOL(hAPP(hAPP(_1067608, _1067610), _1067606)), hBOOL(hAPP(hAPP(_1067608, _1067606), _1067612))], (14843 ^ _784416) ^ [_1067818, _1067820, _1067822, _1067824, _1067826, _1067828] : [hBOOL(hAPP(hAPP(c_member(_1067818), _1067820), c_SetInterval_Oord_OgreaterThanAtMost(_1067818, _1067822, _1067824, _1067826, _1067828))), 14846 ^ _784416 : [(14847 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1067824, _1067826), _1067820)))], (14849 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1067822, _1067820), _1067828)))]]], (14851 ^ _784416) ^ [_1067971, _1067973, _1067975, _1067977, _1067979, _1067981] : [-(hBOOL(hAPP(hAPP(c_member(_1067971), _1067973), c_SetInterval_Oord_OgreaterThanAtMost(_1067971, _1067975, _1067977, _1067979, _1067981)))), hBOOL(hAPP(hAPP(_1067977, _1067979), _1067973)), hBOOL(hAPP(hAPP(_1067975, _1067973), _1067981))], (14861 ^ _784416) ^ [_1068191, _1068193, _1068195, _1068197, _1068199, _1068201] : [hBOOL(hAPP(hAPP(c_member(_1068191), _1068193), c_SetInterval_Oord_OatLeastLessThan(_1068191, _1068195, _1068197, _1068199, _1068201))), 14864 ^ _784416 : [(14865 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1068195, _1068199), _1068193)))], (14867 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1068197, _1068193), _1068201)))]]], (14869 ^ _784416) ^ [_1068344, _1068346, _1068348, _1068350, _1068352, _1068354] : [-(hBOOL(hAPP(hAPP(c_member(_1068344), _1068346), c_SetInterval_Oord_OatLeastLessThan(_1068344, _1068348, _1068350, _1068352, _1068354)))), hBOOL(hAPP(hAPP(_1068348, _1068352), _1068346)), hBOOL(hAPP(hAPP(_1068350, _1068346), _1068354))], (14879 ^ _784416) ^ [_1068552, _1068554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068552), _1068554)), 14882 ^ _784416 : [(14883 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068552), _1068554)))], (14885 ^ _784416) ^ [] : [_1068552 = _1068554]]], (14887 ^ _784416) ^ [_1068679, _1068681] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068679), _1068681))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068679), _1068681)), -(_1068679 = _1068681)], (14907 ^ _784416) ^ [_1068954, _1068956] : [14908 ^ _784416 : [(14909 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068954), _1068956))], (14911 ^ _784416) ^ [] : [_1068954 = _1068956]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068954), _1068956)))], (14897 ^ _784416) ^ [_1068848, _1068850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1068848), _1068850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068848), _1068850))), -(_1068848 = _1068850)], (14915 ^ _784416) ^ [_1069091, _1069093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069091), _1069093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069091), _1069093)))], (14921 ^ _784416) ^ [_1069188, _1069190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069188), _1069190)), -(_1069188 = _1069190), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069188), _1069190)))], (14931 ^ _784416) ^ [_1069300, _1069302] : [14932 ^ _784416 : [(14933 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069300), _1069302))], (14935 ^ _784416) ^ [] : [_1069300 = _1069302]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069300), _1069302)))], (14939 ^ _784416) ^ [_1069435, _1069437, _1069439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069435), _1069437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1069439), _1069435)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1069435), _1069439)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1069437), _1069439))))], (14949 ^ _784416) ^ [_1069622, _1069624, _1069626] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1069622), _1069624)), _1069626) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1069622), _1069626)), _1069624))], (14951 ^ _784416) ^ [_1069673, _1069675, _1069677] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069673), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1069675), _1069677)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069673), _1069675)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069673), _1069677)))], (14953 ^ _784416) ^ [_1069730, _1069732, _1069734] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1069730), _1069732)), _1069734) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069730), _1069734)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069732), _1069734)))], (14955 ^ _784416) ^ [_1069787, _1069789, _1069791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069787), _1069789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1069787), _1069791)), _1069789)))], (14961 ^ _784416) ^ [_1069898, _1069900, _1069902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069898), _1069900)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069898), _1069902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1069902), _1069900)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1069902), _1069898))))], (14971 ^ _784416) ^ [_1070094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070094), _1070094))], (14983 ^ _784416) ^ [_1070180, _1070182] : [14984 ^ _784416 : [(14985 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070180), _1070182))], (14987 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070182), _1070180))]], _1070180 = _1070182], (14973 ^ _784416) ^ [_1070131, _1070133] : [-(_1070131 = _1070133), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070131), _1070133))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070133), _1070131)))], (14991 ^ _784416) ^ [_1070314, _1070316] : [-(_1070314 = _1070316), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070314), _1070316))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070316), _1070314)))], (15001 ^ _784416) ^ [_1070376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070376), _1070376))], (15003 ^ _784416) ^ [_1070404, _1070406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070404), _1070406)), _1070406 = _1070404], (15009 ^ _784416) ^ [_1070492, _1070494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070492), _1070494)), _1070492 = _1070494], (15015 ^ _784416) ^ [_1070580, _1070582, _1070584] : [15016 ^ _784416 : [(15017 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070580), _1070582)))], (15019 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1070584, _1070582), _1070580))]], 15022 ^ _784416 : [(15023 ^ _784416) ^ [] : [-(_1070580 = _1070582)], (15025 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1070584, _1070582), _1070580))]], 15028 ^ _784416 : [(15029 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070582), _1070580)))], (15031 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1070584, _1070582), _1070580))]], -(hBOOL(hAPP(hAPP(_1070584, _1070582), _1070580)))], (15035 ^ _784416) ^ [_1070926, _1070928] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1070926), _1070928)), _1070926)))], (15037 ^ _784416) ^ [_1070962, _1070964, _1070966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1070962), _1070964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1070966), _1070964)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1070966), _1070962))))], (15043 ^ _784416) ^ [_1071085, _1071087, _1071089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071085), _1071087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071085), _1071089)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071087), _1071089))))], (15049 ^ _784416) ^ [_1071208, _1071210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071208), _1071210)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071210), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071210), _1071208)) = _1071208)], (15055 ^ _784416) ^ [_1071319, _1071321, _1071323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071319), _1071321)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071319), _1071323)), 15062 ^ _784416 : [(15063 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071321), _1071319) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071323), _1071319), -(_1071321 = _1071323)], (15069 ^ _784416) ^ [] : [_1071321 = _1071323, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071321), _1071319) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071323), _1071319))]]], (15075 ^ _784416) ^ [_1071642, _1071644, _1071646] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071642), _1071644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071642), _1071646)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071644), _1071642)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071646), _1071642)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071644), _1071646))], (15085 ^ _784416) ^ [_1071843, _1071845, _1071847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071843), _1071845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071843), _1071847)), 15092 ^ _784416 : [(15093 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071845), _1071843)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071847), _1071843))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071845), _1071847)))], (15099 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071845), _1071847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071845), _1071843)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1071847), _1071843))))]]], (15105 ^ _784416) ^ [_1072196, _1072198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072196), _1072198)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072198), _1072196)), -(_1072196 = _1072198)], (15115 ^ _784416) ^ [_1072345, _1072347, _1072349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072345), _1072347)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072347), _1072349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072345), _1072349)))], (15125 ^ _784416) ^ [_1072508, _1072510] : [_1072508 = _1072510, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072508), _1072510)))], (15131 ^ _784416) ^ [_1072591, _1072593] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072591), _1072593))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072593), _1072591)))], (15137 ^ _784416) ^ [_1072637] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072637), _1072637)))], (15139 ^ _784416) ^ [_1072665] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072665), _1072665))))], (15141 ^ _784416) ^ [_1072699] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072699), _1072699)))))], (15143 ^ _784416) ^ [_1072739, _1072741, _1072743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072739), _1072741)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072739), _1072743)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072741), _1072743))))], (15149 ^ _784416) ^ [_1072862, _1072864, _1072866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072862), _1072864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072866), _1072862)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072866), _1072864))))], (15155 ^ _784416) ^ [_1072985, _1072987, _1072989, _1072991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072985), _1072987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072989), _1072991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072985), _1072989)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072987), _1072991))))], (15165 ^ _784416) ^ [_1073176, _1073178, _1073180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1073176), _1073178)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1073176), _1073180)), 15172 ^ _784416 : [(15173 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073178), _1073176)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073180), _1073176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1073178), _1073180)))], (15179 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1073178), _1073180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073178), _1073176)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073180), _1073176))))]]], (15185 ^ _784416) ^ [_1073529, _1073531, _1073533, _1073535, _1073537, _1073539] : [c_Finite__Set_Ofolding__idem(_1073529, _1073531, _1073533, _1073535), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073529), _1073537)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073529), _1073539)), -(hAPP(_1073535, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073529, tc_HOL_Obool)), _1073537), _1073539)) = hAPP(c_Fun_Ocomp(_1073531, _1073531, _1073531, hAPP(_1073535, _1073537)), hAPP(_1073535, _1073539)))], (15199 ^ _784416) ^ [_1073810, _1073812, _1073814, _1073816, _1073818, _1073820] : [c_Finite__Set_Ofolding__idem(_1073810, _1073812, _1073814, _1073816), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073810), _1073818)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073810, tc_HOL_Obool)), _1073820), _1073818)), -(hAPP(c_Fun_Ocomp(_1073812, _1073812, _1073812, hAPP(_1073816, _1073818)), hAPP(_1073816, _1073820)) = hAPP(_1073816, _1073818))], (15213 ^ _784416) ^ [_1074081, _1074083, _1074085, _1074087, _1074089, _1074091] : [c_Finite__Set_Ofolding__idem(_1074081, _1074083, _1074085, _1074087), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074081), _1074089)), -(hAPP(_1074087, hAPP(hAPP(c_Set_Oinsert(_1074081), _1074091), _1074089)) = hAPP(c_Fun_Ocomp(_1074083, _1074083, _1074083, hAPP(_1074087, _1074089)), hAPP(_1074085, _1074091)))], (15223 ^ _784416) ^ [_1074288, _1074290, _1074292, _1074294] : [c_Finite__Set_Ofolding__one(_1074288, _1074290, _1074292), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074288), _1074294)), -(_1074294 = c_Orderings_Obot__class_Obot(tc_fun(_1074288, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1074288), hAPP(hAPP(_1074290, 15236 ^ [_1074288, _1074290, _1074292, _1074294]), 15237 ^ [_1074288, _1074290, _1074292, _1074294])), hAPP(hAPP(c_Set_Oinsert(_1074288), 15236 ^ [_1074288, _1074290, _1074292, _1074294]), hAPP(hAPP(c_Set_Oinsert(_1074288), 15237 ^ [_1074288, _1074290, _1074292, _1074294]), c_Orderings_Obot__class_Obot(tc_fun(_1074288, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1074288), hAPP(_1074292, _1074294)), _1074294)))], (15243 ^ _784416) ^ [_1074774, _1074776, _1074778] : [class_Lattices_Odistrib__lattice(_1074774), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074774), _1074776)), -(_1074776 = c_Orderings_Obot__class_Obot(tc_fun(_1074774, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1074774), _1074778), c_Big__Operators_Olattice__class_OSup__fin(_1074774, _1074776)) = c_Big__Operators_Olattice__class_OSup__fin(_1074774, hAPP(c_Set_OCollect(_1074774), hAPP(hAPP(c_COMBB(tc_fun(_1074774, tc_HOL_Obool), tc_HOL_Obool, _1074774), c_HOL_OEx(_1074774)), hAPP(hAPP(c_COMBC(_1074774, tc_fun(_1074774, tc_HOL_Obool), tc_fun(_1074774, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1074774, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1074774, tc_HOL_Obool), tc_fun(_1074774, tc_HOL_Obool)), _1074774), c_COMBS(_1074774, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1074774, tc_HOL_Obool), tc_fun(_1074774, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1074774), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1074774), c_fconj)), hAPP(hAPP(c_COMBC(_1074774, tc_fun(_1074774, _1074774), tc_fun(_1074774, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1074774, tc_HOL_Obool), tc_fun(tc_fun(_1074774, _1074774), tc_fun(_1074774, tc_HOL_Obool)), _1074774), c_COMBB(_1074774, tc_HOL_Obool, _1074774)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1074774), _1074778))))), hAPP(hAPP(c_COMBC(_1074774, tc_fun(_1074774, tc_HOL_Obool), tc_HOL_Obool), c_member(_1074774)), _1074776))))))], (15257 ^ _784416) ^ [_1075260, _1075262, _1075264] : [class_Lattices_Odistrib__lattice(_1075260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075260), _1075262)), -(_1075262 = c_Orderings_Obot__class_Obot(tc_fun(_1075260, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075260), _1075264)), -(_1075264 = c_Orderings_Obot__class_Obot(tc_fun(_1075260, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1075260), c_Big__Operators_Olattice__class_OSup__fin(_1075260, _1075262)), c_Big__Operators_Olattice__class_OSup__fin(_1075260, _1075264)) = c_Big__Operators_Olattice__class_OSup__fin(_1075260, hAPP(c_Set_OCollect(_1075260), hAPP(hAPP(c_COMBB(tc_fun(_1075260, tc_HOL_Obool), tc_HOL_Obool, _1075260), c_HOL_OEx(_1075260)), hAPP(hAPP(c_COMBB(tc_fun(_1075260, tc_fun(_1075260, tc_HOL_Obool)), tc_fun(_1075260, tc_HOL_Obool), _1075260), hAPP(c_COMBB(tc_fun(_1075260, tc_HOL_Obool), tc_HOL_Obool, _1075260), c_HOL_OEx(_1075260))), hAPP(hAPP(c_COMBC(_1075260, tc_fun(_1075260, tc_fun(_1075260, tc_HOL_Obool)), tc_fun(_1075260, tc_fun(_1075260, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1075260, tc_fun(tc_fun(_1075260, tc_HOL_Obool), tc_fun(_1075260, tc_HOL_Obool))), tc_fun(tc_fun(_1075260, tc_fun(_1075260, tc_HOL_Obool)), tc_fun(_1075260, tc_fun(_1075260, tc_HOL_Obool))), _1075260), c_COMBS(_1075260, tc_fun(_1075260, tc_HOL_Obool), tc_fun(_1075260, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1075260, tc_fun(_1075260, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1075260, tc_fun(tc_fun(_1075260, tc_HOL_Obool), tc_fun(_1075260, tc_HOL_Obool))), _1075260), hAPP(c_COMBB(tc_fun(_1075260, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1075260, tc_HOL_Obool), tc_fun(_1075260, tc_HOL_Obool)), _1075260), c_COMBS(_1075260, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1075260, tc_fun(_1075260, tc_HOL_Obool)), tc_fun(_1075260, tc_fun(_1075260, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1075260), hAPP(c_COMBB(tc_fun(_1075260, tc_HOL_Obool), tc_fun(_1075260, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1075260), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1075260), c_fconj))), hAPP(hAPP(c_COMBC(_1075260, tc_fun(_1075260, tc_fun(_1075260, _1075260)), tc_fun(_1075260, tc_fun(_1075260, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1075260, _1075260), tc_fun(_1075260, tc_HOL_Obool)), tc_fun(tc_fun(_1075260, tc_fun(_1075260, _1075260)), tc_fun(_1075260, tc_fun(_1075260, tc_HOL_Obool))), _1075260), c_COMBB(tc_fun(_1075260, _1075260), tc_fun(_1075260, tc_HOL_Obool), _1075260)), hAPP(hAPP(c_COMBB(tc_fun(_1075260, tc_HOL_Obool), tc_fun(tc_fun(_1075260, _1075260), tc_fun(_1075260, tc_HOL_Obool)), _1075260), c_COMBB(_1075260, tc_HOL_Obool, _1075260)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1075260)))))), hAPP(hAPP(c_COMBC(_1075260, tc_fun(_1075260, tc_HOL_Obool), tc_fun(_1075260, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1075260, tc_HOL_Obool), tc_fun(_1075260, tc_HOL_Obool)), _1075260), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1075260)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1075260), c_fconj), hAPP(hAPP(c_COMBC(_1075260, tc_fun(_1075260, tc_HOL_Obool), tc_HOL_Obool), c_member(_1075260)), _1075262)))), hAPP(hAPP(c_COMBC(_1075260, tc_fun(_1075260, tc_HOL_Obool), tc_HOL_Obool), c_member(_1075260)), _1075264))))))))], (15279 ^ _784416) ^ [_1076359, _1076361, _1076363] : [class_Lattices_Odistrib__lattice(_1076359), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076359), _1076361)), -(_1076361 = c_Orderings_Obot__class_Obot(tc_fun(_1076359, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076359), _1076363), c_Big__Operators_Olattice__class_OInf__fin(_1076359, _1076361)) = c_Big__Operators_Olattice__class_OInf__fin(_1076359, hAPP(c_Set_OCollect(_1076359), hAPP(hAPP(c_COMBB(tc_fun(_1076359, tc_HOL_Obool), tc_HOL_Obool, _1076359), c_HOL_OEx(_1076359)), hAPP(hAPP(c_COMBC(_1076359, tc_fun(_1076359, tc_HOL_Obool), tc_fun(_1076359, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1076359, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1076359, tc_HOL_Obool), tc_fun(_1076359, tc_HOL_Obool)), _1076359), c_COMBS(_1076359, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1076359, tc_HOL_Obool), tc_fun(_1076359, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1076359), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1076359), c_fconj)), hAPP(hAPP(c_COMBC(_1076359, tc_fun(_1076359, _1076359), tc_fun(_1076359, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1076359, tc_HOL_Obool), tc_fun(tc_fun(_1076359, _1076359), tc_fun(_1076359, tc_HOL_Obool)), _1076359), c_COMBB(_1076359, tc_HOL_Obool, _1076359)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076359), _1076363))))), hAPP(hAPP(c_COMBC(_1076359, tc_fun(_1076359, tc_HOL_Obool), tc_HOL_Obool), c_member(_1076359)), _1076361))))))], (15293 ^ _784416) ^ [_1076845, _1076847, _1076849] : [class_Lattices_Odistrib__lattice(_1076845), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076845), _1076847)), -(_1076847 = c_Orderings_Obot__class_Obot(tc_fun(_1076845, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076845), _1076849)), -(_1076849 = c_Orderings_Obot__class_Obot(tc_fun(_1076845, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076845), c_Big__Operators_Olattice__class_OInf__fin(_1076845, _1076847)), c_Big__Operators_Olattice__class_OInf__fin(_1076845, _1076849)) = c_Big__Operators_Olattice__class_OInf__fin(_1076845, hAPP(c_Set_OCollect(_1076845), hAPP(hAPP(c_COMBB(tc_fun(_1076845, tc_HOL_Obool), tc_HOL_Obool, _1076845), c_HOL_OEx(_1076845)), hAPP(hAPP(c_COMBB(tc_fun(_1076845, tc_fun(_1076845, tc_HOL_Obool)), tc_fun(_1076845, tc_HOL_Obool), _1076845), hAPP(c_COMBB(tc_fun(_1076845, tc_HOL_Obool), tc_HOL_Obool, _1076845), c_HOL_OEx(_1076845))), hAPP(hAPP(c_COMBC(_1076845, tc_fun(_1076845, tc_fun(_1076845, tc_HOL_Obool)), tc_fun(_1076845, tc_fun(_1076845, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1076845, tc_fun(tc_fun(_1076845, tc_HOL_Obool), tc_fun(_1076845, tc_HOL_Obool))), tc_fun(tc_fun(_1076845, tc_fun(_1076845, tc_HOL_Obool)), tc_fun(_1076845, tc_fun(_1076845, tc_HOL_Obool))), _1076845), c_COMBS(_1076845, tc_fun(_1076845, tc_HOL_Obool), tc_fun(_1076845, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1076845, tc_fun(_1076845, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1076845, tc_fun(tc_fun(_1076845, tc_HOL_Obool), tc_fun(_1076845, tc_HOL_Obool))), _1076845), hAPP(c_COMBB(tc_fun(_1076845, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1076845, tc_HOL_Obool), tc_fun(_1076845, tc_HOL_Obool)), _1076845), c_COMBS(_1076845, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1076845, tc_fun(_1076845, tc_HOL_Obool)), tc_fun(_1076845, tc_fun(_1076845, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1076845), hAPP(c_COMBB(tc_fun(_1076845, tc_HOL_Obool), tc_fun(_1076845, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1076845), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1076845), c_fconj))), hAPP(hAPP(c_COMBC(_1076845, tc_fun(_1076845, tc_fun(_1076845, _1076845)), tc_fun(_1076845, tc_fun(_1076845, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1076845, _1076845), tc_fun(_1076845, tc_HOL_Obool)), tc_fun(tc_fun(_1076845, tc_fun(_1076845, _1076845)), tc_fun(_1076845, tc_fun(_1076845, tc_HOL_Obool))), _1076845), c_COMBB(tc_fun(_1076845, _1076845), tc_fun(_1076845, tc_HOL_Obool), _1076845)), hAPP(hAPP(c_COMBB(tc_fun(_1076845, tc_HOL_Obool), tc_fun(tc_fun(_1076845, _1076845), tc_fun(_1076845, tc_HOL_Obool)), _1076845), c_COMBB(_1076845, tc_HOL_Obool, _1076845)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1076845)))))), hAPP(hAPP(c_COMBC(_1076845, tc_fun(_1076845, tc_HOL_Obool), tc_fun(_1076845, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1076845, tc_HOL_Obool), tc_fun(_1076845, tc_HOL_Obool)), _1076845), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1076845)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1076845), c_fconj), hAPP(hAPP(c_COMBC(_1076845, tc_fun(_1076845, tc_HOL_Obool), tc_HOL_Obool), c_member(_1076845)), _1076847)))), hAPP(hAPP(c_COMBC(_1076845, tc_fun(_1076845, tc_HOL_Obool), tc_HOL_Obool), c_member(_1076845)), _1076849))))))))], (15315 ^ _784416) ^ [_1077944, _1077946, _1077948] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1077944), _1077946)), _1077948) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1077944), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1077946), _1077948)))], (15317 ^ _784416) ^ [_1077995, _1077997] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1077995), _1077997) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1077997), _1077995))], (15319 ^ _784416) ^ [_1078032, _1078034, _1078036, _1078038] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1078032), hAPP(c_Set_OCollect(_1078032), _1078034))), 15322 ^ _784416 : [(15333 ^ _784416) ^ [] : [15335 ^ _784416 : [(15336 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1078034, 15334 ^ [_1078032, _1078034, _1078036, _1078038])))], (15338 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1078036), hAPP(c_Set_OCollect(_1078036), hAPP(hAPP(c_COMBC(_1078036, _1078032, tc_HOL_Obool), _1078038), 15334 ^ [_1078032, _1078034, _1078036, _1078038]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1078036), hAPP(c_Set_OCollect(_1078036), hAPP(hAPP(c_COMBB(tc_fun(_1078032, tc_HOL_Obool), tc_HOL_Obool, _1078036), c_HOL_OEx(_1078032)), hAPP(hAPP(c_COMBB(tc_fun(_1078032, tc_HOL_Obool), tc_fun(_1078032, tc_HOL_Obool), _1078036), hAPP(c_COMBS(_1078032, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1078032), c_fconj), _1078034))), _1078038))))))], (15323 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1078036), hAPP(c_Set_OCollect(_1078036), hAPP(hAPP(c_COMBB(tc_fun(_1078032, tc_HOL_Obool), tc_HOL_Obool, _1078036), c_HOL_OEx(_1078032)), hAPP(hAPP(c_COMBB(tc_fun(_1078032, tc_HOL_Obool), tc_fun(_1078032, tc_HOL_Obool), _1078036), hAPP(c_COMBS(_1078032, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1078032), c_fconj), _1078034))), _1078038))))), 15326 ^ _784416 : [(15327 ^ _784416) ^ [_1078315] : [hBOOL(hAPP(_1078034, _1078315)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1078036), hAPP(c_Set_OCollect(_1078036), hAPP(hAPP(c_COMBC(_1078036, _1078032, tc_HOL_Obool), _1078038), _1078315)))))]]]]], (15342 ^ _784416) ^ [_1078680, _1078682, _1078684, _1078686] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1078680), hAPP(c_Set_OCollect(_1078680), _1078682))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1078684), hAPP(c_Set_OCollect(_1078684), hAPP(hAPP(c_COMBB(tc_fun(_1078680, tc_HOL_Obool), tc_HOL_Obool, _1078684), c_HOL_OEx(_1078680)), hAPP(hAPP(c_COMBC(_1078684, tc_fun(_1078680, tc_HOL_Obool), tc_fun(_1078680, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1078680, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1078680, tc_HOL_Obool), tc_fun(_1078680, tc_HOL_Obool)), _1078684), c_COMBS(_1078680, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1078680, tc_HOL_Obool), tc_fun(_1078680, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1078684), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1078680), c_fconj)), hAPP(hAPP(c_COMBC(_1078684, tc_fun(_1078680, _1078684), tc_fun(_1078680, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1078684, tc_HOL_Obool), tc_fun(tc_fun(_1078680, _1078684), tc_fun(_1078680, tc_HOL_Obool)), _1078684), c_COMBB(_1078684, tc_HOL_Obool, _1078680)), c_fequal)), _1078686)))), _1078682))))))], (15348 ^ _784416) ^ [_1079041, _1079043, _1079045, _1079047, _1079049, _1079051, _1079053] : [c_Finite__Set_Ofolding__idem(_1079041, _1079043, _1079045, _1079047), -(hAPP(c_Fun_Ocomp(_1079043, _1079043, _1079049, hAPP(_1079045, _1079051)), hAPP(c_Fun_Ocomp(_1079043, _1079043, _1079049, hAPP(_1079045, _1079051)), _1079053)) = hAPP(c_Fun_Ocomp(_1079043, _1079043, _1079049, hAPP(_1079045, _1079051)), _1079053))], (15354 ^ _784416) ^ [_1079198, _1079200, _1079202, _1079204, _1079206] : [c_Finite__Set_Ofolding__idem(_1079198, _1079200, _1079202, _1079204), -(hAPP(c_Fun_Ocomp(_1079200, _1079200, _1079200, hAPP(_1079202, _1079206)), hAPP(_1079202, _1079206)) = hAPP(_1079202, _1079206))], (15360 ^ _784416) ^ [_1079319, _1079321, _1079323] : [-(c_Map_Oran(_1079319, _1079321, _1079323) = hAPP(c_Set_OCollect(_1079321), hAPP(hAPP(c_COMBB(tc_fun(_1079319, tc_HOL_Obool), tc_HOL_Obool, _1079321), c_HOL_OEx(_1079319)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1079321), tc_fun(_1079319, tc_HOL_Obool), _1079321), hAPP(c_COMBC(_1079319, tc_Option_Ooption(_1079321), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1079321), tc_fun(tc_Option_Ooption(_1079321), tc_HOL_Obool), _1079319), c_fequal), _1079323))), c_Option_Ooption_OSome(_1079321)))))], (15362 ^ _784416) ^ [_1079413, _1079415] : [-(hAPP(c_Set_OPow(_1079413), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079413, tc_HOL_Obool)), _1079415)) = hAPP(c_Set_OCollect(tc_fun(_1079413, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1079413, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1079413, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1079413, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1079413, tc_HOL_Obool), tc_fun(tc_fun(_1079413, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1079413, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1079413, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1079413, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1079413, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1079413, tc_HOL_Obool)), c_COMBS(tc_fun(_1079413, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1079413, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1079413, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1079413, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1079413, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1079413, tc_HOL_Obool), tc_fun(tc_fun(_1079413, tc_HOL_Obool), tc_fun(_1079413, tc_HOL_Obool)), tc_fun(tc_fun(_1079413, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1079413, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1079413, tc_HOL_Obool), tc_fun(_1079413, tc_HOL_Obool)), tc_fun(tc_fun(_1079413, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1079413, tc_HOL_Obool)), c_COMBB(tc_fun(_1079413, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1079413, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1079413, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1079413, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1079413, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1079413, tc_HOL_Obool)), _1079415)), c_Set_OPow(_1079413))))))], (15364 ^ _784416) ^ [_1079693, _1079695, _1079697, _1079699, _1079701, _1079703] : [c_Finite__Set_Ofolding__idem(_1079693, _1079695, _1079697, _1079699), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079693), _1079701)), hBOOL(hAPP(hAPP(c_member(_1079693), _1079703), _1079701)), -(hAPP(c_Fun_Ocomp(_1079695, _1079695, _1079695, hAPP(_1079699, _1079701)), hAPP(_1079697, _1079703)) = hAPP(_1079699, _1079701))], (15378 ^ _784416) ^ [_1079958, _1079960, _1079962] : [class_Lattices_Olattice(_1079958), hAPP(_1079960, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1079958), 15383 ^ [_1079958, _1079960, _1079962]), 15384 ^ [_1079958, _1079960, _1079962])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1079958), hAPP(_1079960, 15383 ^ [_1079958, _1079960, _1079962])), hAPP(_1079960, 15384 ^ [_1079958, _1079960, _1079962])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079958), _1079962)), -(_1079962 = c_Orderings_Obot__class_Obot(tc_fun(_1079958, tc_HOL_Obool))), -(hAPP(_1079960, c_Big__Operators_Olattice__class_OInf__fin(_1079958, _1079962)) = c_Big__Operators_Olattice__class_OInf__fin(_1079958, hAPP(c_Set_Oimage(_1079958, _1079958, _1079960), _1079962)))], (15398 ^ _784416) ^ [_1080361, _1080363, _1080365] : [class_Lattices_Olattice(_1080361), hAPP(_1080363, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1080361), 15403 ^ [_1080361, _1080363, _1080365]), 15404 ^ [_1080361, _1080363, _1080365])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1080361), hAPP(_1080363, 15403 ^ [_1080361, _1080363, _1080365])), hAPP(_1080363, 15404 ^ [_1080361, _1080363, _1080365])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080361), _1080365)), -(_1080365 = c_Orderings_Obot__class_Obot(tc_fun(_1080361, tc_HOL_Obool))), -(hAPP(_1080363, c_Big__Operators_Olattice__class_OSup__fin(_1080361, _1080365)) = c_Big__Operators_Olattice__class_OSup__fin(_1080361, hAPP(c_Set_Oimage(_1080361, _1080361, _1080363), _1080365)))], (15418 ^ _784416) ^ [_1080764, _1080766, _1080768] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1080764), _1080766)), hBOOL(hAPP(_1080768, _1080766)), 15429 ^ _784416 : [(15430 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1080764), 15428 ^ [_1080764, _1080766, _1080768])))], (15432 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1080764), 15427 ^ [_1080764, _1080766, _1080768]), 15428 ^ [_1080764, _1080766, _1080768])))], (15434 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1080768, 15428 ^ [_1080764, _1080766, _1080768])))], (15436 ^ _784416) ^ [] : [hBOOL(hAPP(_1080768, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1080764, tc_HOL_Obool)), 15428 ^ [_1080764, _1080766, _1080768]), hAPP(hAPP(c_Set_Oinsert(_1080764), 15427 ^ [_1080764, _1080766, _1080768]), c_Orderings_Obot__class_Obot(tc_fun(_1080764, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1080768, c_Orderings_Obot__class_Obot(tc_fun(_1080764, tc_HOL_Obool)))))], (15440 ^ _784416) ^ [_1081289, _1081291, _1081293, _1081295, _1081297] : [c_Finite__Set_Ofolding__one__idem(_1081289, _1081291, _1081293), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081289), _1081295)), -(_1081295 = c_Orderings_Obot__class_Obot(tc_fun(_1081289, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081289), _1081297)), -(_1081297 = c_Orderings_Obot__class_Obot(tc_fun(_1081289, tc_HOL_Obool))), -(hAPP(_1081293, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1081289, tc_HOL_Obool)), _1081295), _1081297)) = hAPP(hAPP(_1081291, hAPP(_1081293, _1081295)), hAPP(_1081293, _1081297)))], (15462 ^ _784416) ^ [_1081654, _1081656, _1081658, _1081660] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1081654), _1081656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1081654, tc_HOL_Obool)), _1081656), _1081658)), hBOOL(hAPP(_1081660, c_Orderings_Obot__class_Obot(tc_fun(_1081654, tc_HOL_Obool)))), 15477 ^ _784416 : [(15478 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1081654), 15476 ^ [_1081654, _1081656, _1081658, _1081660])))], (15480 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1081654), 15475 ^ [_1081654, _1081656, _1081658, _1081660]), _1081658)))], (15482 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1081654), 15475 ^ [_1081654, _1081656, _1081658, _1081660]), 15476 ^ [_1081654, _1081656, _1081658, _1081660]))], (15484 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1081660, 15476 ^ [_1081654, _1081656, _1081658, _1081660])))], (15486 ^ _784416) ^ [] : [hBOOL(hAPP(_1081660, hAPP(hAPP(c_Set_Oinsert(_1081654), 15475 ^ [_1081654, _1081656, _1081658, _1081660]), 15476 ^ [_1081654, _1081656, _1081658, _1081660])))]], -(hBOOL(hAPP(_1081660, _1081656)))], (15490 ^ _784416) ^ [_1082319, _1082321, _1082323, _1082325, _1082327] : [c_Finite__Set_Ofolding__one__idem(_1082319, _1082321, _1082323), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082319), _1082325)), -(_1082327 = c_Orderings_Obot__class_Obot(tc_fun(_1082319, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1082319, tc_HOL_Obool)), _1082327), _1082325)), -(hAPP(hAPP(_1082321, hAPP(_1082323, _1082327)), hAPP(_1082323, _1082325)) = hAPP(_1082323, _1082325))], (15508 ^ _784416) ^ [_1082649, _1082651, _1082653, _1082655, _1082657] : [c_Finite__Set_Ofolding__one__idem(_1082649, _1082651, _1082653), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082649), _1082655)), -(_1082655 = c_Orderings_Obot__class_Obot(tc_fun(_1082649, tc_HOL_Obool))), -(hAPP(_1082653, hAPP(hAPP(c_Set_Oinsert(_1082649), _1082657), _1082655)) = hAPP(hAPP(_1082651, _1082657), hAPP(_1082653, _1082655)))], (15522 ^ _784416) ^ [_1082880, _1082882] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1082880), _1082882)), -(_1082882 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1082880, 15526 ^ [_1082880, _1082882]), 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)), 15525 ^ [_1082880, _1082882]))))], (15530 ^ _784416) ^ [_1083011, _1083013] : [15531 ^ _784416 : [(15532 ^ _784416) ^ [_1083075, _1083077] : [_1083013 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1083011, _1083075), 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)), _1083077)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1083011), _1083013)))], (15536 ^ _784416) ^ [_1083147, _1083149, _1083151, _1083153] : [c_Finite__Set_Ofolding__one__idem(_1083147, _1083149, _1083151), -(hAPP(hAPP(_1083149, _1083153), _1083153) = _1083153)], (15542 ^ _784416) ^ [_1083242, _1083244, _1083246, _1083248, _1083250] : [c_Finite__Set_Ofolding__one__idem(_1083242, _1083244, _1083246), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083242), _1083248)), hBOOL(hAPP(hAPP(c_member(_1083242), _1083250), _1083248)), -(hAPP(hAPP(_1083244, _1083250), hAPP(_1083246, _1083248)) = hAPP(_1083246, _1083248))], (15556 ^ _784416) ^ [_1083489, _1083491, _1083493, _1083495] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1083489), _1083491)), -(hAPP(c_Set_Oimage(_1083489, _1083493, _1083495), _1083491) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1083493, tc_HOL_Obool), _1083489, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1083493, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1083489, tc_fun(_1083493, tc_HOL_Obool), tc_fun(_1083493, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1083493, tc_fun(tc_fun(_1083493, tc_HOL_Obool), tc_fun(_1083493, tc_HOL_Obool)), _1083489), c_Set_Oinsert(_1083493)), _1083495)), c_Orderings_Obot__class_Obot(tc_fun(_1083493, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1083493, tc_HOL_Obool))), _1083491))], (15562 ^ _784416) ^ [_1083728, _1083730, _1083732] : [class_Groups_Oab__semigroup__mult(_1083728), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083728), _1083730)), -(_1083730 = c_Orderings_Obot__class_Obot(tc_fun(_1083728, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083728), _1083732)), -(_1083732 = c_Orderings_Obot__class_Obot(tc_fun(_1083728, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1083728, tc_HOL_Obool)), _1083730), _1083732) = c_Orderings_Obot__class_Obot(tc_fun(_1083728, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1083728, c_Groups_Otimes__class_Otimes(_1083728)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1083728, tc_HOL_Obool)), _1083730), _1083732)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083728), hAPP(c_Finite__Set_Ofold1(_1083728, c_Groups_Otimes__class_Otimes(_1083728)), _1083730)), hAPP(c_Finite__Set_Ofold1(_1083728, c_Groups_Otimes__class_Otimes(_1083728)), _1083732)))], (15588 ^ _784416) ^ [_1084235, _1084237, _1084239, _1084241] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1084235), _1084237)), hBOOL(hAPP(hAPP(c_member(_1084235), _1084239), _1084237)), hBOOL(hAPP(hAPP(c_member(_1084235), _1084241), _1084237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1084235), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1084235, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1084235, tc_HOL_Obool)), _1084237), hAPP(hAPP(c_Set_Oinsert(_1084235), _1084239), c_Orderings_Obot__class_Obot(tc_fun(_1084235, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1084235), _1084241), c_Orderings_Obot__class_Obot(tc_fun(_1084235, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1084235), _1084237))))], (15602 ^ _784416) ^ [_1084590, _1084592, _1084594] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1084590), _1084592)), hBOOL(hAPP(hAPP(c_member(_1084590), _1084594), _1084592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1084590), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1084590, tc_HOL_Obool)), _1084592), hAPP(hAPP(c_Set_Oinsert(_1084590), _1084594), c_Orderings_Obot__class_Obot(tc_fun(_1084590, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1084590), _1084592))))], (15612 ^ _784416) ^ [_1084823, _1084825, _1084827, _1084829, _1084831] : [c_Finite__Set_Ofolding__one__idem(_1084823, _1084825, _1084827), hAPP(_1084829, hAPP(hAPP(_1084825, 15617 ^ [_1084823, _1084825, _1084827, _1084829, _1084831]), 15618 ^ [_1084823, _1084825, _1084827, _1084829, _1084831])) = hAPP(hAPP(_1084825, hAPP(_1084829, 15617 ^ [_1084823, _1084825, _1084827, _1084829, _1084831])), hAPP(_1084829, 15618 ^ [_1084823, _1084825, _1084827, _1084829, _1084831])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084823), _1084831)), -(_1084831 = c_Orderings_Obot__class_Obot(tc_fun(_1084823, tc_HOL_Obool))), -(hAPP(_1084829, hAPP(_1084827, _1084831)) = hAPP(_1084827, hAPP(c_Set_Oimage(_1084823, _1084823, _1084829), _1084831)))], (15632 ^ _784416) ^ [_1085258, _1085260, _1085262, _1085264, _1085266, _1085268, _1085270, _1085272] : [c_Finite__Set_Ofolding__image__simple(_1085258, _1085260, _1085262, _1085264, _1085266, _1085268), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085260), _1085270)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085260), _1085272)), 15646 ^ _784416 : [(15647 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1085260), 15645 ^ [_1085258, _1085260, _1085262, _1085264, _1085266, _1085268, _1085270, _1085272]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1085260, tc_HOL_Obool)), _1085270), _1085272))))], (15649 ^ _784416) ^ [] : [hAPP(_1085266, 15645 ^ [_1085258, _1085260, _1085262, _1085264, _1085266, _1085268, _1085270, _1085272]) = _1085264]], -(hAPP(_1085268, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1085260, tc_HOL_Obool)), _1085270), _1085272)) = hAPP(hAPP(_1085262, hAPP(_1085268, _1085270)), hAPP(_1085268, _1085272)))], (15653 ^ _784416) ^ [_1085759, _1085761, _1085763] : [class_Groups_Oab__semigroup__mult(_1085759), -(_1085761 = c_Orderings_Obot__class_Obot(tc_fun(_1085759, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085759), _1085761)), -(hBOOL(hAPP(hAPP(c_member(_1085759), _1085763), _1085761))), -(hAPP(c_Finite__Set_Ofold1(_1085759, c_Groups_Otimes__class_Otimes(_1085759)), hAPP(hAPP(c_Set_Oinsert(_1085759), _1085763), _1085761)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085759), _1085763), hAPP(c_Finite__Set_Ofold1(_1085759, c_Groups_Otimes__class_Otimes(_1085759)), _1085761)))], (15671 ^ _784416) ^ [_1086058, _1086060, _1086062, _1086064, _1086066] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086058, _1086060, _1086062), _1086064), _1086066), c_Orderings_Obot__class_Obot(tc_fun(_1086060, tc_HOL_Obool))) = _1086066)], (15673 ^ _784416) ^ [_1086107, _1086109] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1086107), c_Orderings_Otop__class_Otop(tc_fun(_1086107, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1086107), _1086109) = hAPP(c_Finite__Set_Ocard(_1086107), c_Orderings_Otop__class_Otop(tc_fun(_1086107, tc_HOL_Obool))), -(_1086109 = c_Orderings_Otop__class_Otop(tc_fun(_1086107, tc_HOL_Obool)))], (15683 ^ _784416) ^ [_1086294, _1086296, _1086298, _1086300] : [c_Fun_Oinj__on(_1086294, _1086296, _1086298, _1086300), -(hAPP(c_Finite__Set_Ocard(_1086296), hAPP(c_Set_Oimage(_1086294, _1086296, _1086298), _1086300)) = hAPP(c_Finite__Set_Ocard(_1086294), _1086300))], (15689 ^ _784416) ^ [_1086413, _1086415, _1086417] : [-(hAPP(c_Finite__Set_Ofold1(_1086413, _1086415), hAPP(hAPP(c_Set_Oinsert(_1086413), _1086417), c_Orderings_Obot__class_Obot(tc_fun(_1086413, tc_HOL_Obool)))) = _1086417)], (15691 ^ _784416) ^ [_1086459, _1086461, _1086463, _1086465] : [_1086459 = c_Finite__Set_Ofold1(_1086461, _1086463), -(hAPP(_1086459, hAPP(hAPP(c_Set_Oinsert(_1086461), _1086465), c_Orderings_Obot__class_Obot(tc_fun(_1086461, tc_HOL_Obool)))) = _1086465)], (15697 ^ _784416) ^ [_1086578, _1086580, _1086582, _1086584, _1086586, _1086588, _1086590] : [c_Finite__Set_Ofolding__image__simple(_1086578, _1086580, _1086582, _1086584, _1086586, _1086588), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086580), _1086590)), -(hAPP(_1086588, _1086590) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086578, _1086580, _1086582), _1086586), _1086584), _1086590))], (15707 ^ _784416) ^ [_1086775, _1086777, _1086779, _1086781, _1086783, _1086785, _1086787] : [c_Finite__Set_Ofolding__image(_1086775, _1086777, _1086779, _1086781, _1086783), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086777), _1086785)), -(hAPP(hAPP(_1086783, _1086787), _1086785) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086775, _1086777, _1086779), _1086787), _1086781), _1086785))], (15717 ^ _784416) ^ [_1086976, _1086978, _1086980, _1086982] : [c_Finite__Set_Ofolding__one(_1086976, _1086978, _1086980), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086976), _1086982)), -(hAPP(_1086980, _1086982) = hAPP(c_Finite__Set_Ofold1(_1086976, _1086978), _1086982))], (15727 ^ _784416) ^ [_1087141, _1087143, _1087145] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1087141), _1087143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1087141), _1087143)), hAPP(c_Finite__Set_Ocard(_1087141), hAPP(hAPP(c_Set_Oinsert(_1087141), _1087145), _1087143)))))], (15733 ^ _784416) ^ [_1087274, _1087276, _1087278] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1087274), _1087276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1087274, tc_HOL_Obool)), _1087278), _1087276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1087274), _1087276)), hAPP(c_Finite__Set_Ocard(_1087274), _1087278))), -(_1087278 = _1087276)], (15747 ^ _784416) ^ [_1087519, _1087521, _1087523] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1087519), _1087521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1087519, tc_HOL_Obool)), _1087523), _1087521)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1087519), _1087523)), hAPP(c_Finite__Set_Ocard(_1087519), _1087521))))], (15757 ^ _784416) ^ [_1087710, _1087712, _1087714, _1087716] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1087710), _1087712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1087714), hAPP(c_Set_Oimage(_1087710, _1087714, _1087716), _1087712))), hAPP(c_Finite__Set_Ocard(_1087710), _1087712))))], (15763 ^ _784416) ^ [_1087843, _1087845, _1087847, _1087849] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1087843), _1087845)), 15766 ^ _784416 : [(15767 ^ _784416) ^ [] : [c_Fun_Oinj__on(_1087843, _1087847, _1087849, _1087845), -(hAPP(c_Finite__Set_Ocard(_1087847), hAPP(c_Set_Oimage(_1087843, _1087847, _1087849), _1087845)) = hAPP(c_Finite__Set_Ocard(_1087843), _1087845))], (15773 ^ _784416) ^ [] : [hAPP(c_Finite__Set_Ocard(_1087847), hAPP(c_Set_Oimage(_1087843, _1087847, _1087849), _1087845)) = hAPP(c_Finite__Set_Ocard(_1087843), _1087845), -(c_Fun_Oinj__on(_1087843, _1087847, _1087849, _1087845))]]], (15779 ^ _784416) ^ [_1088127, _1088129, _1088131, _1088133] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1088127), _1088129)), hAPP(c_Finite__Set_Ocard(_1088131), hAPP(c_Set_Oimage(_1088127, _1088131, _1088133), _1088129)) = hAPP(c_Finite__Set_Ocard(_1088127), _1088129), -(c_Fun_Oinj__on(_1088127, _1088131, _1088133, _1088129))], (15789 ^ _784416) ^ [_1088310, _1088312, _1088314, _1088316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1088310), hAPP(c_Set_Oimage(_1088312, _1088310, _1088314), _1088316))), hAPP(c_Finite__Set_Ocard(_1088312), _1088316))), c_Fun_Oinj__on(_1088312, _1088310, _1088314, _1088316)], (15795 ^ _784416) ^ [_1088440, _1088442, _1088444] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1088440), _1088442)), c_Fun_Oinj__on(_1088440, tc_fun(tc_fun(_1088440, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1088440, tc_fun(tc_prod(_1088440, _1088440), tc_HOL_Obool), tc_fun(tc_fun(_1088440, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1088440, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1088440, _1088440), tc_HOL_Obool), tc_fun(tc_fun(_1088440, tc_HOL_Obool), tc_HOL_Obool)), _1088440), c_Equiv__Relations_Oquotient(_1088440)), hAPP(hAPP(c_COMBC(_1088440, tc_fun(_1088440, tc_HOL_Obool), tc_fun(_1088440, tc_HOL_Obool)), c_Set_Oinsert(_1088440)), c_Orderings_Obot__class_Obot(tc_fun(_1088440, tc_HOL_Obool))))), _1088444), _1088442), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1088440, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1088440), _1088442), _1088444)) = hAPP(c_Finite__Set_Ocard(_1088440), _1088442))], (15805 ^ _784416) ^ [_1088789, _1088791, _1088793] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1088789), _1088791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1088789, tc_HOL_Obool)), _1088793), _1088791)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1088789), _1088793)), hAPP(c_Finite__Set_Ocard(_1088789), _1088791))))], (15815 ^ _784416) ^ [_1088980, _1088982, _1088984] : [-(hAPP(c_Finite__Set_Ofold1(_1088980, _1088982), _1088984) = c_HOL_OThe(_1088980, c_Finite__Set_Ofold1Set(_1088980, _1088982, _1088984)))], (15817 ^ _784416) ^ [_1089020, _1089022] : [class_Lattices_Olattice(_1089020), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089020), _1089022)), -(c_Big__Operators_Olattice__class_OSup__fin(_1089020, _1089022) = hAPP(c_Finite__Set_Ofold1(_1089020, c_Lattices_Osemilattice__sup__class_Osup(_1089020)), _1089022))], (15827 ^ _784416) ^ [_1089177, _1089179] : [class_Lattices_Olattice(_1089177), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089177), _1089179)), -(c_Big__Operators_Olattice__class_OInf__fin(_1089177, _1089179) = hAPP(c_Finite__Set_Ofold1(_1089177, c_Lattices_Osemilattice__inf__class_Oinf(_1089177)), _1089179))], (15837 ^ _784416) ^ [_1089334, _1089336, _1089338, _1089340, _1089342, _1089344] : [c_Fun_Oinj__on(_1089334, _1089336, _1089338, _1089340), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1089336, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1089334, _1089336, _1089338), _1089340)), _1089342)), c_Fun_Oinj__on(_1089336, _1089334, _1089344, _1089342), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1089334, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1089336, _1089334, _1089344), _1089342)), _1089340)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089334), _1089340)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089336), _1089342)), -(hAPP(c_Finite__Set_Ocard(_1089334), _1089340) = hAPP(c_Finite__Set_Ocard(_1089336), _1089342))], (15863 ^ _784416) ^ [_1089831, _1089833, _1089835] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1089831), _1089833)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1089831, tc_HOL_Obool)), _1089833), _1089835)), -(hAPP(c_Finite__Set_Ocard(_1089831), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1089831, tc_HOL_Obool)), _1089835), _1089833)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1089831), _1089835)), hAPP(c_Finite__Set_Ocard(_1089831), _1089833)))], (15873 ^ _784416) ^ [_1090056, _1090058, _1090060] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1090056), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090056, tc_HOL_Obool)), _1090058), _1090060))), -(hAPP(c_Finite__Set_Ocard(_1090056), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090056, tc_HOL_Obool)), _1090058), _1090060)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1090056), _1090058)), hAPP(c_Finite__Set_Ocard(_1090056), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090056, tc_HOL_Obool)), _1090058), _1090060))))], (15879 ^ _784416) ^ [_1090251, _1090253, _1090255] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1090251), _1090253)), -(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(_1090251), _1090255)), hAPP(c_Finite__Set_Ocard(_1090251), _1090253))), hAPP(c_Finite__Set_Ocard(_1090251), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090251, tc_HOL_Obool)), _1090255), _1090253)))))], (15885 ^ _784416) ^ [_1090412, _1090414, _1090416] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1090412), _1090414)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1090412, tc_HOL_Obool)), _1090416), _1090414)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1090412), _1090416)), hAPP(c_Finite__Set_Ocard(_1090412), _1090414))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1090412, tc_HOL_Obool)), _1090416), _1090414)))], (15899 ^ _784416) ^ [_1090677, _1090679, _1090681, _1090683, _1090685, _1090687] : [class_Groups_Oab__semigroup__mult(_1090677), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090679), _1090681)), -(hBOOL(hAPP(hAPP(c_member(_1090679), _1090683), _1090681))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1090677, _1090679, c_Groups_Otimes__class_Otimes(_1090677)), _1090685), _1090687), hAPP(hAPP(c_Set_Oinsert(_1090679), _1090683), _1090681)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090677), hAPP(_1090685, _1090683)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1090677, _1090679, c_Groups_Otimes__class_Otimes(_1090677)), _1090685), _1090687), _1090681)))], (15913 ^ _784416) ^ [_1090955, _1090957, _1090959] : [class_Lattices_Osemilattice__inf(_1090955), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090955), _1090957)), hBOOL(hAPP(hAPP(c_member(_1090955), _1090959), _1090957)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090955), hAPP(c_Finite__Set_Ofold1(_1090955, c_Lattices_Osemilattice__inf__class_Oinf(_1090955)), _1090957)), _1090959)))], (15927 ^ _784416) ^ [_1091192, _1091194, _1091196] : [class_Lattices_Osemilattice__inf(_1091192), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091192), _1091194)), -(_1091194 = c_Orderings_Obot__class_Obot(tc_fun(_1091192, tc_HOL_Obool))), 15938 ^ _784416 : [(15949 ^ _784416) ^ [] : [15951 ^ _784416 : [(15952 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1091192), 15950 ^ [_1091192, _1091194, _1091196]), _1091194)))], (15954 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091192), _1091196), 15950 ^ [_1091192, _1091194, _1091196]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091192), _1091196), hAPP(c_Finite__Set_Ofold1(_1091192, c_Lattices_Osemilattice__inf__class_Oinf(_1091192)), _1091194))))], (15939 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091192), _1091196), hAPP(c_Finite__Set_Ofold1(_1091192, c_Lattices_Osemilattice__inf__class_Oinf(_1091192)), _1091194))), 15942 ^ _784416 : [(15943 ^ _784416) ^ [_1091485] : [hBOOL(hAPP(hAPP(c_member(_1091192), _1091485), _1091194)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091192), _1091196), _1091485)))]]]]], (15958 ^ _784416) ^ [_1091770, _1091772, _1091774] : [class_Lattices_Oab__semigroup__idem__mult(_1091770), -(_1091772 = c_Orderings_Obot__class_Obot(tc_fun(_1091770, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091770), _1091772)), -(hAPP(c_Finite__Set_Ofold1(_1091770, c_Groups_Otimes__class_Otimes(_1091770)), hAPP(hAPP(c_Set_Oinsert(_1091770), _1091774), _1091772)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091770), _1091774), hAPP(c_Finite__Set_Ofold1(_1091770, c_Groups_Otimes__class_Otimes(_1091770)), _1091772)))], (15972 ^ _784416) ^ [_1092040, _1092042, _1092044] : [class_Lattices_Oab__semigroup__idem__mult(_1092040), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092040), _1092042)), -(_1092042 = c_Orderings_Obot__class_Obot(tc_fun(_1092040, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092040), _1092044)), -(_1092044 = c_Orderings_Obot__class_Obot(tc_fun(_1092040, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1092040, c_Groups_Otimes__class_Otimes(_1092040)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1092040, tc_HOL_Obool)), _1092042), _1092044)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1092040), hAPP(c_Finite__Set_Ofold1(_1092040, c_Groups_Otimes__class_Otimes(_1092040)), _1092042)), hAPP(c_Finite__Set_Ofold1(_1092040, c_Groups_Otimes__class_Otimes(_1092040)), _1092044)))], (15994 ^ _784416) ^ [_1092419, _1092421, _1092423] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1092419), _1092421)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1092419), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1092419, tc_HOL_Obool)), _1092421), hAPP(hAPP(c_Set_Oinsert(_1092419), _1092423), c_Orderings_Obot__class_Obot(tc_fun(_1092419, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1092419), _1092421))))], (16000 ^ _784416) ^ [_1092584, _1092586, _1092588, _1092590, _1092592] : [c_Fun_Oinj__on(_1092584, _1092586, _1092588, _1092590), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1092586, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1092584, _1092586, _1092588), _1092590)), _1092592)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092586), _1092592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1092584), _1092590)), hAPP(c_Finite__Set_Ocard(_1092586), _1092592))))], (16014 ^ _784416) ^ [_1092859, _1092861, _1092863, _1092865] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1092859), _1092861)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092863), _1092865)), 16021 ^ _784416 : [(16032 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1092859), _1092861)), hAPP(c_Finite__Set_Ocard(_1092863), _1092865))), 16036 ^ _784416 : [(16037 ^ _784416) ^ [] : [-(c_Fun_Oinj__on(_1092859, _1092863, 16035 ^ [_1092859, _1092861, _1092863, _1092865], _1092861))], (16039 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1092863, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1092859, _1092863, 16035 ^ [_1092859, _1092861, _1092863, _1092865]), _1092861)), _1092865)))]]], (16022 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1092859), _1092861)), hAPP(c_Finite__Set_Ocard(_1092863), _1092865)))), 16023 ^ _784416 : [(16024 ^ _784416) ^ [_1093070] : [c_Fun_Oinj__on(_1092859, _1092863, _1093070, _1092861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1092863, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1092859, _1092863, _1093070), _1092861)), _1092865))]]]]], (16041 ^ _784416) ^ [_1093386, _1093388, _1093390, _1093392, _1093394, _1093396, _1093398] : [class_Groups_Oab__semigroup__mult(_1093386), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093388), _1093390)), c_Fun_Oinj__on(_1093388, _1093392, _1093394, _1093390), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1093386, _1093392, c_Groups_Otimes__class_Otimes(_1093386)), _1093396), _1093398), hAPP(c_Set_Oimage(_1093388, _1093392, _1093394), _1093390)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1093386, _1093388, c_Groups_Otimes__class_Otimes(_1093386)), hAPP(c_Fun_Ocomp(_1093392, _1093386, _1093388, _1093396), _1093394)), _1093398), _1093390))], (16055 ^ _784416) ^ [_1093697, _1093699, _1093701, _1093703] : [c_Big__Operators_Osemilattice__big(_1093697, _1093699, _1093701), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093697), _1093703)), -(hAPP(_1093701, _1093703) = hAPP(c_Finite__Set_Ofold1(_1093697, _1093699), _1093703))], (16065 ^ _784416) ^ [_1093862, _1093864, _1093866, _1093868, _1093870, _1093872, _1093874] : [c_Big__Operators_Ocomm__monoid__big(_1093862, _1093864, _1093866, _1093868, _1093870), 16068 ^ _784416 : [(16069 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1093864), _1093872)), -(hAPP(hAPP(_1093870, _1093874), _1093872) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1093862, _1093864, _1093866), _1093874), _1093868), _1093872))], (16075 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1093864), _1093872))), -(hAPP(hAPP(_1093870, _1093874), _1093872) = _1093868)]]], (16081 ^ _784416) ^ [_1094130, _1094132] : [class_Groups_Oab__semigroup__mult(_1094130), hBOOL(hAPP(c_Finite__Set_Ofinite(_1094130), _1094132)), -(_1094132 = c_Orderings_Obot__class_Obot(tc_fun(_1094130, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1094130), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094130), 16094 ^ [_1094130, _1094132]), 16095 ^ [_1094130, _1094132])), hAPP(hAPP(c_Set_Oinsert(_1094130), 16094 ^ [_1094130, _1094132]), hAPP(hAPP(c_Set_Oinsert(_1094130), 16095 ^ [_1094130, _1094132]), c_Orderings_Obot__class_Obot(tc_fun(_1094130, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1094130), hAPP(c_Finite__Set_Ofold1(_1094130, c_Groups_Otimes__class_Otimes(_1094130)), _1094132)), _1094132)))], (16101 ^ _784416) ^ [_1094584, _1094586, _1094588] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1094584), _1094586)), hBOOL(hAPP(hAPP(c_member(_1094584), _1094588), _1094586)), -(hAPP(c_Finite__Set_Ocard(_1094584), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1094584, tc_HOL_Obool)), _1094586), hAPP(hAPP(c_Set_Oinsert(_1094584), _1094588), c_Orderings_Obot__class_Obot(tc_fun(_1094584, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1094584), _1094586)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (16111 ^ _784416) ^ [_1094819, _1094821, _1094823] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1094819), _1094821)), 16114 ^ _784416 : [(16115 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1094819), _1094823), _1094821)), -(hAPP(c_Finite__Set_Ocard(_1094819), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1094819, tc_HOL_Obool)), _1094821), hAPP(hAPP(c_Set_Oinsert(_1094819), _1094823), c_Orderings_Obot__class_Obot(tc_fun(_1094819, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1094819), _1094821)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (16121 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1094819), _1094823), _1094821))), -(hAPP(c_Finite__Set_Ocard(_1094819), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1094819, tc_HOL_Obool)), _1094821), hAPP(hAPP(c_Set_Oinsert(_1094819), _1094823), c_Orderings_Obot__class_Obot(tc_fun(_1094819, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1094819), _1094821))]]], (16127 ^ _784416) ^ [_1095183, _1095185, _1095187] : [class_Lattices_Oab__semigroup__idem__mult(_1095183), hAPP(_1095185, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095183), 16132 ^ [_1095183, _1095185, _1095187]), 16133 ^ [_1095183, _1095185, _1095187])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095183), hAPP(_1095185, 16132 ^ [_1095183, _1095185, _1095187])), hAPP(_1095185, 16133 ^ [_1095183, _1095185, _1095187])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095183), _1095187)), -(_1095187 = c_Orderings_Obot__class_Obot(tc_fun(_1095183, tc_HOL_Obool))), -(hAPP(_1095185, hAPP(c_Finite__Set_Ofold1(_1095183, c_Groups_Otimes__class_Otimes(_1095183)), _1095187)) = hAPP(c_Finite__Set_Ofold1(_1095183, c_Groups_Otimes__class_Otimes(_1095183)), hAPP(c_Set_Oimage(_1095183, _1095183, _1095185), _1095187)))], (16147 ^ _784416) ^ [_1095606, _1095608, _1095610, _1095612] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1095606), _1095608)), hBOOL(hAPP(hAPP(c_member(_1095606), _1095610), _1095608)), -(hBOOL(hAPP(hAPP(c_member(_1095606), _1095610), _1095612))), -(hAPP(c_Finite__Set_Ocard(_1095606), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1095606, tc_HOL_Obool)), _1095608), hAPP(hAPP(c_Set_Oinsert(_1095606), _1095610), _1095612))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1095606), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1095606, tc_HOL_Obool)), _1095608), _1095612))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (16161 ^ _784416) ^ [] : [-(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))], (16163 ^ _784416) ^ [_1095904, _1095906] : [class_Groups_Oone(_1095904), 16166 ^ _784416 : [(16167 ^ _784416) ^ [] : [c_Groups_Oone__class_Oone(_1095904) = _1095906, -(_1095906 = c_Groups_Oone__class_Oone(_1095904))], (16173 ^ _784416) ^ [] : [_1095906 = c_Groups_Oone__class_Oone(_1095904), -(c_Groups_Oone__class_Oone(_1095904) = _1095906)]]], (16179 ^ _784416) ^ [_1096121, _1096123] : [class_Groups_Ocomm__monoid__mult(_1096121), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096121), _1096123), c_Groups_Oone__class_Oone(_1096121)) = _1096123)], (16185 ^ _784416) ^ [_1096216, _1096218] : [class_Groups_Omonoid__mult(_1096216), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096216), _1096218), c_Groups_Oone__class_Oone(_1096216)) = _1096218)], (16191 ^ _784416) ^ [_1096311, _1096313] : [class_Groups_Ocomm__monoid__mult(_1096311), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096311), c_Groups_Oone__class_Oone(_1096311)), _1096313) = _1096313)], (16197 ^ _784416) ^ [_1096406, _1096408] : [class_Groups_Omonoid__mult(_1096406), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1096406), c_Groups_Oone__class_Oone(_1096406)), _1096408) = _1096408)], (16203 ^ _784416) ^ [_1096501] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1096501) = _1096501)], (16205 ^ _784416) ^ [_1096542, _1096544] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1096542), _1096544), 16208 ^ _784416 : [(16209 ^ _784416) ^ [] : [-(_1096542 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (16211 ^ _784416) ^ [] : [-(_1096544 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (16213 ^ _784416) ^ [_1096653, _1096655] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1096653), _1096655)), _1096653 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1096655 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (16223 ^ _784416) ^ [_1096796] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1096796), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1096796)], (16225 ^ _784416) ^ [_1096840, _1096842] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1096840), _1096842) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 16228 ^ _784416 : [(16229 ^ _784416) ^ [] : [-(_1096840 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (16231 ^ _784416) ^ [] : [-(_1096842 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (16233 ^ _784416) ^ [_1096951, _1096953] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1096951), _1096953) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1096951 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1096953 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (16243 ^ _784416) ^ [_1097094, _1097096, _1097098] : [class_Rings_Olinordered__semidom(_1097094), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097094), c_Groups_Oone__class_Oone(_1097094)), _1097096)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097094), c_Groups_Oone__class_Oone(_1097094)), _1097098)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097094), c_Groups_Oone__class_Oone(_1097094)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097094), _1097096), _1097098))))], (16257 ^ _784416) ^ [_1097349, _1097351] : [class_Rings_Oring__1__no__zero__divisors(_1097349), 16260 ^ _784416 : [(16271 ^ _784416) ^ [] : [16272 ^ _784416 : [(16273 ^ _784416) ^ [] : [_1097351 = c_Groups_Oone__class_Oone(_1097349)], (16275 ^ _784416) ^ [] : [_1097351 = hAPP(c_Groups_Ouminus__class_Ouminus(_1097349), c_Groups_Oone__class_Oone(_1097349))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097349), _1097351), _1097351) = c_Groups_Oone__class_Oone(_1097349))], (16261 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097349), _1097351), _1097351) = c_Groups_Oone__class_Oone(_1097349), -(_1097351 = c_Groups_Oone__class_Oone(_1097349)), -(_1097351 = hAPP(c_Groups_Ouminus__class_Ouminus(_1097349), c_Groups_Oone__class_Oone(_1097349)))]]], (16279 ^ _784416) ^ [_1097656, _1097658, _1097660, _1097662, _1097664] : [class_Groups_Ocomm__monoid__mult(_1097656), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097658), _1097660)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1097656, _1097658, c_Groups_Otimes__class_Otimes(_1097656)), hAPP(hAPP(c_COMBS(_1097658, _1097656, _1097656), hAPP(hAPP(c_COMBB(_1097656, tc_fun(_1097656, _1097656), _1097658), c_Groups_Otimes__class_Otimes(_1097656)), _1097662)), _1097664)), c_Groups_Oone__class_Oone(_1097656)), _1097660) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097656), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1097656, _1097658, c_Groups_Otimes__class_Otimes(_1097656)), _1097662), c_Groups_Oone__class_Oone(_1097656)), _1097660)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1097656, _1097658, c_Groups_Otimes__class_Otimes(_1097656)), _1097664), c_Groups_Oone__class_Oone(_1097656)), _1097660)))], (16289 ^ _784416) ^ [_1097971, _1097973, _1097975, _1097977, _1097979, _1097981, _1097983] : [c_Big__Operators_Ocomm__monoid__big(_1097971, _1097973, _1097975, _1097977, _1097979), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1097973), _1097981))), -(hAPP(hAPP(_1097979, _1097983), _1097981) = _1097977)], (16299 ^ _784416) ^ [_1098099, _1098101, _1098103, _1098105, _1098107] : [class_Groups_Ocomm__monoid__mult(_1098099), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098101), _1098103)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098101), _1098105)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098099), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1098099, _1098101, c_Groups_Otimes__class_Otimes(_1098099)), _1098107), c_Groups_Oone__class_Oone(_1098099)), _1098103)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1098099, _1098101, c_Groups_Otimes__class_Otimes(_1098099)), _1098107), c_Groups_Oone__class_Oone(_1098099)), _1098105)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098099), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1098099, _1098101, c_Groups_Otimes__class_Otimes(_1098099)), _1098107), c_Groups_Oone__class_Oone(_1098099)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1098101, tc_HOL_Obool)), _1098103), _1098105))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1098099, _1098101, c_Groups_Otimes__class_Otimes(_1098099)), _1098107), c_Groups_Oone__class_Oone(_1098099)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1098101, tc_HOL_Obool)), _1098103), _1098105))))], (16313 ^ _784416) ^ [_1098524, _1098526, _1098528, _1098530, _1098532] : [class_Groups_Ocomm__monoid__mult(_1098524), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098526), _1098528)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098526), _1098530)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1098526, tc_HOL_Obool)), _1098528), _1098530) = c_Orderings_Obot__class_Obot(tc_fun(_1098526, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1098524, _1098526, c_Groups_Otimes__class_Otimes(_1098524)), _1098532), c_Groups_Oone__class_Oone(_1098524)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1098526, tc_HOL_Obool)), _1098528), _1098530)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098524), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1098524, _1098526, c_Groups_Otimes__class_Otimes(_1098524)), _1098532), c_Groups_Oone__class_Oone(_1098524)), _1098528)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1098524, _1098526, c_Groups_Otimes__class_Otimes(_1098524)), _1098532), c_Groups_Oone__class_Oone(_1098524)), _1098530)))], (16331 ^ _784416) ^ [_1098967, _1098969] : [class_Rings_Ocomm__ring__1(_1098967), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1098967), _1098969) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098967), hAPP(c_Groups_Ouminus__class_Ouminus(_1098967), c_Groups_Oone__class_Oone(_1098967))), _1098969))], (16337 ^ _784416) ^ [_1099082, _1099084, _1099086, _1099088, _1099090] : [class_Groups_Ocomm__monoid__mult(_1099082), hBOOL(hAPP(c_Finite__Set_Ofinite(_1099084), _1099086)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1099084), _1099088)), 16351 ^ _784416 : [(16352 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1099084), 16350 ^ [_1099082, _1099084, _1099086, _1099088, _1099090]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1099084, tc_HOL_Obool)), _1099086), _1099088))))], (16354 ^ _784416) ^ [] : [hAPP(_1099090, 16350 ^ [_1099082, _1099084, _1099086, _1099088, _1099090]) = c_Groups_Oone__class_Oone(_1099082)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1099082, _1099084, c_Groups_Otimes__class_Otimes(_1099082)), _1099090), c_Groups_Oone__class_Oone(_1099082)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1099084, tc_HOL_Obool)), _1099086), _1099088)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099082), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1099082, _1099084, c_Groups_Otimes__class_Otimes(_1099082)), _1099090), c_Groups_Oone__class_Oone(_1099082)), _1099086)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1099082, _1099084, c_Groups_Otimes__class_Otimes(_1099082)), _1099090), c_Groups_Oone__class_Oone(_1099082)), _1099088)))], (16358 ^ _784416) ^ [_1099625, _1099627, _1099629] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1099625), _1099627)), hBOOL(hAPP(hAPP(c_member(_1099625), _1099629), _1099627)), -(hAPP(c_Finite__Set_Ocard(_1099625), _1099627) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1099625), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1099625, tc_HOL_Obool)), _1099627), hAPP(hAPP(c_Set_Oinsert(_1099625), _1099629), c_Orderings_Obot__class_Obot(tc_fun(_1099625, tc_HOL_Obool)))))))], (16368 ^ _784416) ^ [_1099854, _1099856] : [class_Rings_Ocomm__semiring__1(_1099854), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099854), c_Groups_Oone__class_Oone(_1099854)), _1099856) = _1099856)], (16374 ^ _784416) ^ [_1099949, _1099951] : [class_Rings_Ocomm__semiring__1(_1099949), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099949), _1099951), c_Groups_Oone__class_Oone(_1099949)) = _1099951)], (16380 ^ _784416) ^ [_1100044, _1100046, _1100048] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1100044), _1100046)), -(hAPP(c_Finite__Set_Ocard(_1100044), hAPP(hAPP(c_Set_Oinsert(_1100044), _1100048), _1100046)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1100044), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100044, tc_HOL_Obool)), _1100046), hAPP(hAPP(c_Set_Oinsert(_1100044), _1100048), c_Orderings_Obot__class_Obot(tc_fun(_1100044, tc_HOL_Obool)))))))], (16386 ^ _784416) ^ [_1100221, _1100223, _1100225] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1100221), _1100223)), hBOOL(hAPP(hAPP(c_member(_1100221), _1100225), _1100223)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1100221), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100221, tc_HOL_Obool)), _1100223), hAPP(hAPP(c_Set_Oinsert(_1100221), _1100225), c_Orderings_Obot__class_Obot(tc_fun(_1100221, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1100221), _1100223))], (16396 ^ _784416) ^ [_1100450] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100450), hAPP(c_Nat_OSuc, _1100450))))], (16398 ^ _784416) ^ [_1100481, _1100483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100481), _1100483)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1100481)), hAPP(c_Nat_OSuc, _1100483))))], (16404 ^ _784416) ^ [_1100605, _1100607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100605), _1100607)), -(_1100607 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1100605), 16407 ^ [_1100605, _1100607])))], (16411 ^ _784416) ^ [_1100718, _1100720] : [16412 ^ _784416 : [(16413 ^ _784416) ^ [_1100771] : [_1100720 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1100718), _1100771))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100718), _1100720)))], (16417 ^ _784416) ^ [_1100838, _1100840] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100838), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1100840), _1100838)))))], (16419 ^ _784416) ^ [_1100877, _1100879] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1100877), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1100877), _1100879)))))], (16421 ^ _784416) ^ [_1100916, _1100918] : [-(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)), _1100916), _1100918))], (16423 ^ _784416) ^ [_1100946] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1100946))], (16425 ^ _784416) ^ [_1100980] : [_1100980 = hAPP(c_Nat_OSuc, _1100980)], (16427 ^ _784416) ^ [_1101015] : [hAPP(c_Nat_OSuc, _1101015) = _1101015], (16429 ^ _784416) ^ [_1101041, _1101043] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101041), _1101043) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101043), _1101041))], (16431 ^ _784416) ^ [_1101078, _1101080] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101078), hAPP(c_Nat_OSuc, _1101080)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101078), _1101080)))], (16433 ^ _784416) ^ [_1101121, _1101123, _1101125] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101121), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101123), _1101125)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101123), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101121), _1101125)))], (16435 ^ _784416) ^ [_1101172, _1101174] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1101172)), _1101174) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101172), _1101174)))], (16437 ^ _784416) ^ [_1101215, _1101217] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1101215)), _1101217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101215), hAPP(c_Nat_OSuc, _1101217)))], (16439 ^ _784416) ^ [_1101273, _1101275] : [hAPP(c_Nat_OSuc, _1101273) = hAPP(c_Nat_OSuc, _1101275), -(_1101273 = _1101275)], (16445 ^ _784416) ^ [_1101358, _1101360] : [_1101358 = _1101360, -(hAPP(c_Nat_OSuc, _1101358) = hAPP(c_Nat_OSuc, _1101360))], (16451 ^ _784416) ^ [_1101449, _1101451, _1101453] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101449), _1101451)), _1101453) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101449), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101451), _1101453)))], (16453 ^ _784416) ^ [_1101518, _1101520, _1101522] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101518), _1101520) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101518), _1101522), -(_1101520 = _1101522)], (16459 ^ _784416) ^ [_1101617, _1101619, _1101621] : [_1101619 = _1101621, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101617), _1101619) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101617), _1101621))], (16465 ^ _784416) ^ [_1101740, _1101742, _1101744] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101740), _1101742) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101744), _1101742), -(_1101740 = _1101744)], (16471 ^ _784416) ^ [_1101839, _1101841, _1101843] : [_1101839 = _1101843, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101839), _1101841) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1101843), _1101841))], (16477 ^ _784416) ^ [_1101944, _1101946] : [hAPP(c_Nat_OSuc, _1101944) = hAPP(c_Nat_OSuc, _1101946), -(_1101944 = _1101946)], (16483 ^ _784416) ^ [] : [-(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc))], (16485 ^ _784416) ^ [_1102051, _1102053, _1102055, _1102057, _1102059] : [class_Rings_Ocomm__semiring__1(_1102051), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102051), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102051), _1102053), _1102055)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102051), _1102057), _1102059)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102051), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102051), _1102053), _1102057)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102051), _1102055), _1102059)))], (16491 ^ _784416) ^ [_1102228, _1102230, _1102232, _1102234] : [class_Rings_Ocomm__semiring__1(_1102228), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102228), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102228), _1102230), _1102232)), _1102234) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102228), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102228), _1102230), _1102234)), _1102232))], (16497 ^ _784416) ^ [_1102371, _1102373, _1102375, _1102377] : [class_Rings_Ocomm__semiring__1(_1102371), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102371), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102371), _1102373), _1102375)), _1102377) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102371), _1102373), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102371), _1102375), _1102377)))], (16503 ^ _784416) ^ [_1102514, _1102516, _1102518, _1102520] : [class_Rings_Ocomm__semiring__1(_1102514), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102514), _1102516), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102514), _1102518), _1102520)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102514), _1102516), _1102518)), _1102520))], (16509 ^ _784416) ^ [_1102657, _1102659, _1102661, _1102663] : [class_Rings_Ocomm__semiring__1(_1102657), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102657), _1102659), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102657), _1102661), _1102663)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102657), _1102661), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102657), _1102659), _1102663)))], (16515 ^ _784416) ^ [_1102800, _1102802, _1102804] : [class_Rings_Ocomm__semiring__1(_1102800), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102800), _1102802), _1102804) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102800), _1102804), _1102802))], (16521 ^ _784416) ^ [_1102909, _1102911, _1102913, _1102915] : [class_Groups_Oab__semigroup__add(_1102909), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102909), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102909), _1102911), _1102913)), _1102915) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102909), _1102911), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102909), _1102913), _1102915)))], (16527 ^ _784416) ^ [_1103052, _1103054, _1103056, _1103058] : [class_Groups_Ocancel__semigroup__add(_1103052), 16530 ^ _784416 : [(16531 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103052), _1103054), _1103056) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103052), _1103054), _1103058), -(_1103056 = _1103058)], (16537 ^ _784416) ^ [] : [_1103056 = _1103058, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103052), _1103054), _1103056) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103052), _1103054), _1103058))]]], (16543 ^ _784416) ^ [_1103317, _1103319, _1103321, _1103323] : [class_Groups_Ocancel__semigroup__add(_1103317), 16546 ^ _784416 : [(16547 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103317), _1103319), _1103321) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103317), _1103323), _1103321), -(_1103319 = _1103323)], (16553 ^ _784416) ^ [] : [_1103319 = _1103323, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103317), _1103319), _1103321) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103317), _1103323), _1103321))]]], (16559 ^ _784416) ^ [_1103582, _1103584, _1103586, _1103588] : [class_Groups_Ocancel__semigroup__add(_1103582), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103582), _1103584), _1103586) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103582), _1103584), _1103588), -(_1103586 = _1103588)], (16569 ^ _784416) ^ [_1103749, _1103751, _1103753, _1103755] : [class_Groups_Ocancel__ab__semigroup__add(_1103749), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103749), _1103751), _1103753) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103749), _1103751), _1103755), -(_1103753 = _1103755)], (16579 ^ _784416) ^ [_1103916, _1103918, _1103920, _1103922] : [class_Groups_Ocancel__semigroup__add(_1103916), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103916), _1103918), _1103920) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103916), _1103922), _1103920), -(_1103918 = _1103922)], (16589 ^ _784416) ^ [_1104083, _1104085, _1104087, _1104089, _1104091] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1104083), 16592 ^ _784416 : [(16603 ^ _784416) ^ [] : [16604 ^ _784416 : [(16605 ^ _784416) ^ [] : [_1104085 = _1104089], (16607 ^ _784416) ^ [] : [_1104087 = _1104091]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104083), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104083), _1104085), _1104087)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104083), _1104089), _1104091)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104083), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104083), _1104085), _1104091)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104083), _1104089), _1104087)))], (16593 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104083), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104083), _1104085), _1104087)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104083), _1104089), _1104091)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104083), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104083), _1104085), _1104091)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104083), _1104089), _1104087)), -(_1104085 = _1104089), -(_1104087 = _1104091)]]], (16611 ^ _784416) ^ [_1104495, _1104497, _1104499, _1104501] : [class_Rings_Ocomm__semiring__1(_1104495), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104495), _1104497), _1104499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104495), _1104501), _1104499)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104495), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104495), _1104497), _1104501)), _1104499))], (16617 ^ _784416) ^ [_1104654, _1104656, _1104658, _1104660] : [class_Rings_Ocomm__semiring__1(_1104654), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104654), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104654), _1104656), _1104658)), _1104660) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104654), _1104656), _1104660)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104654), _1104658), _1104660)))], (16623 ^ _784416) ^ [_1104813, _1104815, _1104817, _1104819, _1104821] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1104813), 16626 ^ _784416 : [(16637 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104813), _1104815), _1104819)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104813), _1104817), _1104821)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104813), _1104815), _1104821)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104813), _1104817), _1104819))), 16640 ^ _784416 : [(16641 ^ _784416) ^ [] : [_1104815 = _1104817], (16643 ^ _784416) ^ [] : [_1104819 = _1104821]]], (16627 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104813), _1104815), _1104819)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104813), _1104817), _1104821)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104813), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104813), _1104815), _1104821)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104813), _1104817), _1104819)), -(_1104815 = _1104817), -(_1104819 = _1104821)]]], (16645 ^ _784416) ^ [_1105231, _1105233, _1105235, _1105237] : [class_Rings_Ocomm__semiring__1(_1105231), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105231), _1105233), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105231), _1105235), _1105237)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105231), _1105233), _1105235)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105231), _1105233), _1105237)))], (16651 ^ _784416) ^ [_1105390, _1105392] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1105390), hAPP(c_Nat_OSuc, _1105392)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1105390), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1105390), _1105392)))], (16653 ^ _784416) ^ [_1105436, _1105438] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1105436)), _1105438) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1105438), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1105436), _1105438)))], (16655 ^ _784416) ^ [_1105482, _1105484, _1105486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1105482), _1105484)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1105486), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1105484), _1105482))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1105486), _1105482)), hAPP(c_Nat_OSuc, _1105484)))], (16661 ^ _784416) ^ [_1105631, _1105633, _1105635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1105631), _1105633)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1105633), _1105631))), _1105635) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1105633)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1105631), _1105635)))], (16667 ^ _784416) ^ [_1105780, _1105782, _1105784, _1105786] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1105780), 16670 ^ _784416 : [(16671 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105780), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105780), _1105782), _1105784)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105780), _1105786), _1105784))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105780), _1105782), _1105786)))], (16677 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105780), _1105782), _1105786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105780), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105780), _1105782), _1105784)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105780), _1105786), _1105784))))]]], (16683 ^ _784416) ^ [_1106087, _1106089, _1106091, _1106093] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1106087), 16686 ^ _784416 : [(16687 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106087), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106087), _1106089), _1106091)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106087), _1106089), _1106093))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106087), _1106091), _1106093)))], (16693 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106087), _1106091), _1106093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106087), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106087), _1106089), _1106091)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106087), _1106089), _1106093))))]]], (16699 ^ _784416) ^ [_1106394, _1106396, _1106398, _1106400] : [class_Groups_Oordered__ab__semigroup__add(_1106394), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106394), _1106396), _1106398)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106394), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106394), _1106396), _1106400)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106394), _1106398), _1106400))))], (16709 ^ _784416) ^ [_1106589, _1106591, _1106593, _1106595] : [class_Groups_Oordered__ab__semigroup__add(_1106589), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106589), _1106591), _1106593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106589), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106589), _1106595), _1106591)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106589), _1106595), _1106593))))], (16719 ^ _784416) ^ [_1106784, _1106786, _1106788, _1106790, _1106792] : [class_Groups_Oordered__ab__semigroup__add(_1106784), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106784), _1106786), _1106788)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106784), _1106790), _1106792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1106784), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106784), _1106786), _1106790)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1106784), _1106788), _1106792))))], (16733 ^ _784416) ^ [_1107055, _1107057, _1107059, _1107061] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1107055), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107055), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107055), _1107057), _1107059)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107055), _1107061), _1107059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107055), _1107057), _1107061)))], (16743 ^ _784416) ^ [_1107250, _1107252, _1107254, _1107256] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1107250), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107250), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107250), _1107252), _1107254)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107250), _1107252), _1107256))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107250), _1107254), _1107256)))], (16753 ^ _784416) ^ [_1107445, _1107447, _1107449, _1107451] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1107445), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107445), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107445), _1107447), _1107449)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107445), _1107447), _1107451))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107445), _1107449), _1107451)))], (16763 ^ _784416) ^ [_1107640, _1107642, _1107644, _1107646] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1107640), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107640), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107640), _1107642), _1107644)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107640), _1107646), _1107644))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107640), _1107642), _1107646)))], (16773 ^ _784416) ^ [_1107835, _1107837, _1107839, _1107841, _1107843] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1107835), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107835), _1107837), _1107839)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107835), _1107841), _1107843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107835), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107835), _1107837), _1107841)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1107835), _1107839), _1107843))))], (16787 ^ _784416) ^ [_1108106, _1108108, _1108110, _1108112] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1108106), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108106), _1108108), _1108110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108106), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108106), _1108112), _1108108)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108106), _1108112), _1108110))))], (16797 ^ _784416) ^ [_1108301, _1108303, _1108305, _1108307] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1108301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108301), _1108303), _1108305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108301), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108301), _1108303), _1108307)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108301), _1108305), _1108307))))], (16807 ^ _784416) ^ [_1108496, _1108498, _1108500, _1108502] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1108496), 16810 ^ _784416 : [(16811 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108496), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108496), _1108498), _1108500)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108496), _1108498), _1108502))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108496), _1108500), _1108502)))], (16817 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108496), _1108500), _1108502)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108496), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108496), _1108498), _1108500)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108496), _1108498), _1108502))))]]], (16823 ^ _784416) ^ [_1108803, _1108805, _1108807, _1108809] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1108803), 16826 ^ _784416 : [(16827 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108803), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108803), _1108805), _1108807)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108803), _1108809), _1108807))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108803), _1108805), _1108809)))], (16833 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108803), _1108805), _1108809)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108803), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108803), _1108805), _1108807)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1108803), _1108809), _1108807))))]]], (16839 ^ _784416) ^ [_1109110, _1109112] : [class_Orderings_Oorder(_1109110), 16842 ^ _784416 : [(16843 ^ _784416) ^ [] : [c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _1109110, _1109112), 16846 ^ _784416 : [(16847 ^ _784416) ^ [_1109244] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109110), hAPP(_1109112, _1109244)), hAPP(_1109112, hAPP(c_Nat_OSuc, _1109244)))))]]], (16849 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109110), hAPP(_1109112, 16850 ^ [_1109110, _1109112])), hAPP(_1109112, hAPP(c_Nat_OSuc, 16850 ^ [_1109110, _1109112])))), -(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _1109110, _1109112))]]], (16856 ^ _784416) ^ [_1109417, _1109419, _1109421, _1109423] : [class_Rings_Ocomm__semiring(_1109417), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109417), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109417), _1109419), _1109421)), _1109423) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109417), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109417), _1109419), _1109423)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109417), _1109421), _1109423)))], (16862 ^ _784416) ^ [_1109576, _1109578, _1109580, _1109582, _1109584] : [class_Rings_Osemiring(_1109576), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109576), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109576), _1109578), _1109580)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109576), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109576), _1109582), _1109580)), _1109584)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109576), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109576), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109576), _1109578), _1109582)), _1109580)), _1109584))], (16868 ^ _784416) ^ [_1109769, _1109771, _1109773] : [class_Groups_Ogroup__add(_1109769), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1109769), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109769), _1109771), _1109773)), _1109773) = _1109771)], (16874 ^ _784416) ^ [_1109878, _1109880, _1109882] : [class_Groups_Ogroup__add(_1109878), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109878), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1109878), _1109880), _1109882)), _1109882) = _1109880)], (16880 ^ _784416) ^ [_1109987, _1109989, _1109991] : [class_Groups_Oab__group__add(_1109987), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1109987), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109987), _1109989), _1109991)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1109987), hAPP(c_Groups_Ouminus__class_Ouminus(_1109987), _1109989)), hAPP(c_Groups_Ouminus__class_Ouminus(_1109987), _1109991)))], (16886 ^ _784416) ^ [_1110126, _1110128, _1110130] : [class_Groups_Ogroup__add(_1110126), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1110126), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110126), _1110128), _1110130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110126), hAPP(c_Groups_Ouminus__class_Ouminus(_1110126), _1110130)), hAPP(c_Groups_Ouminus__class_Ouminus(_1110126), _1110128)))], (16892 ^ _784416) ^ [_1110265, _1110267, _1110269] : [class_Groups_Ogroup__add(_1110265), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110265), _1110267), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110265), hAPP(c_Groups_Ouminus__class_Ouminus(_1110265), _1110267)), _1110269)) = _1110269)], (16898 ^ _784416) ^ [_1110384, _1110386, _1110388] : [class_Groups_Ogroup__add(_1110384), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110384), hAPP(c_Groups_Ouminus__class_Ouminus(_1110384), _1110386)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110384), _1110386), _1110388)) = _1110388)], (16904 ^ _784416) ^ [_1110512, _1110514] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110512), _1110514))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110514), hAPP(c_Nat_OSuc, _1110512))))], (16910 ^ _784416) ^ [_1110557, _1110559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110559), hAPP(c_Nat_OSuc, _1110557))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110557), _1110559))], (16926 ^ _784416) ^ [_1110790, _1110792] : [16927 ^ _784416 : [(16928 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110790), _1110792))], (16930 ^ _784416) ^ [] : [_1110790 = _1110792]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110790), hAPP(c_Nat_OSuc, _1110792))))], (16916 ^ _784416) ^ [_1110678, _1110680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110678), hAPP(c_Nat_OSuc, _1110680))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110678), _1110680))), -(_1110678 = _1110680)], (16934 ^ _784416) ^ [_1110948, _1110950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1110948)), hAPP(c_Nat_OSuc, _1110950))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110948), _1110950)))], (16940 ^ _784416) ^ [_1111053, _1111055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111053), _1111055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1111053)), hAPP(c_Nat_OSuc, _1111055))))], (16946 ^ _784416) ^ [_1111163, _1111165] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111163), _1111165))), 16949 ^ _784416 : [(16950 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111163), hAPP(c_Nat_OSuc, _1111165))), -(_1111163 = _1111165)], (16956 ^ _784416) ^ [] : [_1111163 = _1111165, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111163), hAPP(c_Nat_OSuc, _1111165))))]]], (16962 ^ _784416) ^ [_1111396, _1111398] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111396), _1111398))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111396), hAPP(c_Nat_OSuc, _1111398))), -(_1111398 = _1111396)], (16972 ^ _784416) ^ [_1111544, _1111546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111544), _1111546)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111544), hAPP(c_Nat_OSuc, _1111546))))], (16978 ^ _784416) ^ [_1111647, _1111649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111647), _1111649)), -(hAPP(c_Nat_OSuc, _1111647) = _1111649), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1111647)), _1111649)))], (16988 ^ _784416) ^ [_1111771, _1111773, _1111775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111771), _1111773)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111773), _1111775)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1111771)), _1111775)))], (16998 ^ _784416) ^ [_1111940, _1111942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111940), hAPP(c_Nat_OSuc, _1111942))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111940), _1111942))), -(_1111940 = _1111942)], (17008 ^ _784416) ^ [_1112058, _1112060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1112058)), _1112060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112058), _1112060)))], (17014 ^ _784416) ^ [_1112161, _1112163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1112161)), hAPP(c_Nat_OSuc, _1112163))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112161), _1112163)))], (17020 ^ _784416) ^ [_1112270, _1112272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1112270)), _1112272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112270), _1112272)))], (17026 ^ _784416) ^ [_1112373, _1112375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112373), hAPP(c_Nat_OSuc, _1112375))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112373), _1112375))), -(_1112373 = hAPP(c_Nat_OSuc, _1112375))], (17036 ^ _784416) ^ [_1112497, _1112499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112497), _1112499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112497), hAPP(c_Nat_OSuc, _1112499))))], (17042 ^ _784416) ^ [_1112615, _1112617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1112615)), hAPP(c_Nat_OSuc, _1112617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112615), _1112617)))], (17048 ^ _784416) ^ [_1112720, _1112722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112720), _1112722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1112720)), hAPP(c_Nat_OSuc, _1112722))))], (17064 ^ _784416) ^ [_1112964, _1112966] : [17065 ^ _784416 : [(17066 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112964), _1112966))], (17068 ^ _784416) ^ [] : [_1112964 = hAPP(c_Nat_OSuc, _1112966)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112964), hAPP(c_Nat_OSuc, _1112966))))], (17054 ^ _784416) ^ [_1112846, _1112848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112846), hAPP(c_Nat_OSuc, _1112848))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112846), _1112848))), -(_1112846 = hAPP(c_Nat_OSuc, _1112848))], (17072 ^ _784416) ^ [_1113122, _1113124] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1113122), _1113124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1113124)), _1113122)))], (17078 ^ _784416) ^ [_1113167, _1113169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1113169)), _1113167)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1113167), _1113169))], (17084 ^ _784416) ^ [_1113282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1113282)), _1113282))], (17086 ^ _784416) ^ [_1113313, _1113315, _1113317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113313), _1113315)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113313), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113315), _1113317))))], (17092 ^ _784416) ^ [_1113424, _1113426, _1113428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113424), _1113426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113424), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113428), _1113426))))], (17098 ^ _784416) ^ [_1113547, _1113549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113547), _1113549)), _1113547))], (17100 ^ _784416) ^ [_1113595, _1113597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113595), _1113597)), _1113597))], (17102 ^ _784416) ^ [_1113649, _1113651, _1113653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113649), _1113651)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113649), _1113653))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113651), _1113653)))], (17108 ^ _784416) ^ [_1113768, _1113770, _1113772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113770), _1113772)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113768), _1113770)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113768), _1113772))))], (17114 ^ _784416) ^ [_1113893, _1113895, _1113897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113893), _1113895)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113893), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113895), _1113897))))], (17120 ^ _784416) ^ [_1114004, _1114006, _1114008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114004), _1114006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114004), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114008), _1114006))))], (17126 ^ _784416) ^ [_1114115, _1114117, _1114119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114115), _1114117)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114115), _1114119)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114117), _1114119))))], (17132 ^ _784416) ^ [_1114238, _1114240, _1114242, _1114244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114238), _1114240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114242), _1114244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114238), _1114242)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114240), _1114244))))], (17142 ^ _784416) ^ [_1114429, _1114431, _1114433, _1114435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114429), _1114431)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114433), _1114431) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114429), _1114435), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114433), _1114435)))], (17152 ^ _784416) ^ [_1114610, _1114612, _1114614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114610), _1114612)), _1114614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114610), _1114614)))], (17158 ^ _784416) ^ [_1114721, _1114723] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114721)), hAPP(c_Nat_OSuc, _1114723)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1114721), _1114723))], (17160 ^ _784416) ^ [_1114764, _1114766, _1114768] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114764)), _1114766)), hAPP(c_Nat_OSuc, _1114768)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1114764), _1114766)), _1114768))], (17162 ^ _784416) ^ [_1114839, _1114841, _1114843] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114839)), _1114841) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114839)), _1114843), -(_1114841 = _1114843)], (17168 ^ _784416) ^ [_1114950, _1114952, _1114954] : [_1114952 = _1114954, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114950)), _1114952) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114950)), _1114954))], (17174 ^ _784416) ^ [_1115067, _1115069, _1115071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115067), _1115069)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115067), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115071), _1115069))))], (17180 ^ _784416) ^ [_1115178, _1115180, _1115182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115178), _1115180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115178), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115180), _1115182))))], (17186 ^ _784416) ^ [_1115289, _1115291, _1115293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115289), _1115291)), _1115293)), 17189 ^ _784416 : [(17190 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115289), _1115293)))], (17192 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115291), _1115293)))]]], (17194 ^ _784416) ^ [_1115440, _1115442, _1115444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115440), _1115442)), _1115444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115440), _1115444)))], (17200 ^ _784416) ^ [_1115551, _1115553, _1115555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115551), _1115553)), _1115555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115553), _1115555)))], (17206 ^ _784416) ^ [_1115662, _1115664, _1115666, _1115668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115662), _1115664)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115666), _1115668)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115662), _1115666)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115664), _1115668))))], (17216 ^ _784416) ^ [_1115853, _1115855, _1115857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115853), _1115855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115853), _1115857)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115855), _1115857))))], (17222 ^ _784416) ^ [_1115976, _1115978, _1115980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115976), _1115978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115976), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115980), _1115978))))], (17228 ^ _784416) ^ [_1116087, _1116089, _1116091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116087), _1116089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116087), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116089), _1116091))))], (17234 ^ _784416) ^ [_1116216, _1116218, _1116220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116216), _1116218)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116216), _1116220))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116218), _1116220)))], (17240 ^ _784416) ^ [_1116335, _1116337, _1116339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116337), _1116339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116335), _1116337)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116335), _1116339))))], (17246 ^ _784416) ^ [_1116475, _1116477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116475), _1116477)), -(_1116477 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116475), 17249 ^ [_1116475, _1116477]))], (17253 ^ _784416) ^ [_1116582, _1116584] : [17254 ^ _784416 : [(17255 ^ _784416) ^ [_1116632] : [_1116584 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116582), _1116632)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116582), _1116584)))], (17259 ^ _784416) ^ [_1116696, _1116698] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116696), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116696), _1116698))))], (17261 ^ _784416) ^ [_1116732, _1116734] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116732), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116734), _1116732))))], (17263 ^ _784416) ^ [_1116768, _1116770] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116768), _1116770)), _1116770) = _1116768)], (17265 ^ _784416) ^ [_1116805, _1116807] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116805), _1116807)), _1116805) = _1116807)], (17267 ^ _784416) ^ [_1116842, _1116844, _1116846] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116842), _1116844)), _1116846) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116842), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116844), _1116846)))], (17269 ^ _784416) ^ [_1116893, _1116895, _1116897] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116893), _1116895)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116893), _1116897)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116895), _1116897))], (17271 ^ _784416) ^ [_1116944, _1116946, _1116948] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116944), _1116946)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116948), _1116946)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116944), _1116948))], (17273 ^ _784416) ^ [_1116995, _1116997, _1116999] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116995), _1116997)), _1116999) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116995), _1116999)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1116997), _1116999)))], (17275 ^ _784416) ^ [_1117052, _1117054, _1117056] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117052), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117054), _1117056)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117052), _1117054)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117052), _1117056)))], (17277 ^ _784416) ^ [_1117109, _1117111, _1117113] : [class_Rings_Ocomm__semiring__1(_1117109), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117109), _1117111), _1117113)), _1117113) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117109), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117109), _1117111), c_Groups_Oone__class_Oone(_1117109))), _1117113))], (17283 ^ _784416) ^ [_1117254, _1117256, _1117258] : [class_Rings_Ocomm__semiring__1(_1117254), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117254), _1117256), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117254), _1117258), _1117256)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117254), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117254), _1117258), c_Groups_Oone__class_Oone(_1117254))), _1117256))], (17289 ^ _784416) ^ [_1117399, _1117401] : [class_Rings_Ocomm__semiring__1(_1117399), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117399), _1117401), _1117401) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1117399), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117399), c_Groups_Oone__class_Oone(_1117399)), c_Groups_Oone__class_Oone(_1117399))), _1117401))], (17295 ^ _784416) ^ [_1117530, _1117532, _1117534] : [class_Rings_Ocomm__ring__1(_1117530), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1117530), _1117532), _1117534) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117530), _1117532), hAPP(c_Groups_Ouminus__class_Ouminus(_1117530), _1117534)))], (17301 ^ _784416) ^ [_1117649, _1117651, _1117653, _1117655, _1117657] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1117649), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117649), _1117651), _1117653)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117649), _1117655), _1117657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117649), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117649), _1117651), _1117655)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117649), _1117653), _1117657))))], (17315 ^ _784416) ^ [_1117920, _1117922, _1117924, _1117926, _1117928] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1117920), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117920), _1117922), _1117924)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117920), _1117926), _1117928)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1117920), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117920), _1117922), _1117926)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1117920), _1117924), _1117928))))], (17329 ^ _784416) ^ [_1118191, _1118193] : [class_Rings_Olinordered__semidom(_1118191), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118191), _1118193), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118191), _1118193), c_Groups_Oone__class_Oone(_1118191)))))], (17335 ^ _784416) ^ [_1118300, _1118302, _1118304, _1118306, _1118308, _1118310] : [class_Rings_Oring(_1118300), 17338 ^ _784416 : [(17339 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118300), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118300), _1118302), _1118304)), _1118306) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118300), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118300), _1118308), _1118304)), _1118310), -(_1118306 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118300), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118300), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118300), _1118308), _1118302)), _1118304)), _1118310))], (17345 ^ _784416) ^ [] : [_1118306 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118300), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118300), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118300), _1118308), _1118302)), _1118304)), _1118310), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118300), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118300), _1118302), _1118304)), _1118306) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118300), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118300), _1118308), _1118304)), _1118310))]]], (17351 ^ _784416) ^ [_1118697, _1118699, _1118701, _1118703, _1118705, _1118707] : [class_Rings_Oring(_1118697), 17354 ^ _784416 : [(17355 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118697), _1118699), _1118701)), _1118703) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118697), _1118705), _1118701)), _1118707), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118697), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118697), _1118699), _1118705)), _1118701)), _1118703) = _1118707)], (17361 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118697), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1118697), _1118699), _1118705)), _1118701)), _1118703) = _1118707, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118697), _1118699), _1118701)), _1118703) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118697), _1118705), _1118701)), _1118707))]]], (17367 ^ _784416) ^ [_1119094, _1119096, _1119098] : [class_Groups_Ogroup__add(_1119094), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1119094), _1119096), _1119098) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119094), _1119096), hAPP(c_Groups_Ouminus__class_Ouminus(_1119094), _1119098)))], (17373 ^ _784416) ^ [_1119213, _1119215, _1119217] : [class_Groups_Oab__group__add(_1119213), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1119213), _1119215), _1119217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119213), _1119215), hAPP(c_Groups_Ouminus__class_Ouminus(_1119213), _1119217)))], (17379 ^ _784416) ^ [_1119332, _1119334, _1119336] : [class_Groups_Ogroup__add(_1119332), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1119332), _1119334), hAPP(c_Groups_Ouminus__class_Ouminus(_1119332), _1119336)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1119332), _1119334), _1119336))], (17385 ^ _784416) ^ [_1119451, _1119453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1119451)), _1119453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119451), _1119453)))], (17391 ^ _784416) ^ [_1119554, _1119556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119554), _1119556)), 17394 ^ _784416 : [(17395 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119556), hAPP(c_Nat_OSuc, _1119554))), -(_1119556 = _1119554)], (17401 ^ _784416) ^ [] : [_1119556 = _1119554, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119556), hAPP(c_Nat_OSuc, _1119554))))]]], (17407 ^ _784416) ^ [_1119795, _1119797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119795), _1119797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1119795)), _1119797)))], (17413 ^ _784416) ^ [_1119898, _1119900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119898), _1119900)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119898), hAPP(c_Nat_OSuc, _1119900))))], (17419 ^ _784416) ^ [_1120016, _1120018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1120016)), _1120018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120016), _1120018)))], (17425 ^ _784416) ^ [_1120115, _1120117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120115), _1120117)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1120115)), _1120117)))], (17431 ^ _784416) ^ [_1120235, _1120237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120235), hAPP(c_Nat_OSuc, _1120237))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120235), _1120237)))], (17437 ^ _784416) ^ [_1120334, _1120336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120334), _1120336)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120334), hAPP(c_Nat_OSuc, _1120336))))], (17443 ^ _784416) ^ [_1120454, _1120456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120454), _1120456)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1120454)), _1120456)))], (17449 ^ _784416) ^ [_1120553, _1120555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1120553)), _1120555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120553), _1120555)))], (17455 ^ _784416) ^ [_1120658, _1120660] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120658), _1120660)), hAPP(c_Nat_OSuc, _1120658))))], (17457 ^ _784416) ^ [_1120715, _1120717, _1120719] : [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, _1120715)), _1120717)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1120715)), _1120719))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120717), _1120719)))], (17463 ^ _784416) ^ [_1120846, _1120848, _1120850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120848), _1120850)), -(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, _1120846)), _1120848)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1120846)), _1120850))))], (17469 ^ _784416) ^ [_1120983, _1120985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120983), _1120985)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1120985)), _1120983) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120985), _1120983)))], (17475 ^ _784416) ^ [_1121124, _1121126, _1121128] : [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, _1121124)), _1121126)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1121124)), _1121128))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121126), _1121128)))], (17481 ^ _784416) ^ [_1121255, _1121257, _1121259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121257), _1121259)), -(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, _1121255)), _1121257)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1121255)), _1121259))))], (17487 ^ _784416) ^ [_1121410, _1121412, _1121414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1121410), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121412), _1121414))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121410), _1121414)), _1121412)))], (17493 ^ _784416) ^ [_1121529, _1121531, _1121533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121529), _1121533)), _1121531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1121529), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121531), _1121533))))], (17499 ^ _784416) ^ [_1121650, _1121652] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1121650), _1121652))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121652), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121650), _1121652)) = _1121650)], (17505 ^ _784416) ^ [_1121703, _1121705, _1121707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121703), _1121705)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121707), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121705), _1121703)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121707), _1121703)), _1121705))], (17511 ^ _784416) ^ [_1121858, _1121860, _1121862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121858), _1121860)), _1121862)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121858), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121862), _1121860))))], (17517 ^ _784416) ^ [_1121977, _1121979, _1121981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121977), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121981), _1121979))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121977), _1121979)), _1121981)))], (17523 ^ _784416) ^ [_1122102, _1122104, _1122106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122102), _1122104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122106), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122104), _1122106)), _1122102))))], (17529 ^ _784416) ^ [_1122225, _1122227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122225), _1122227)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122225), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122227), _1122225)) = _1122227)], (17535 ^ _784416) ^ [_1122336, _1122338, _1122340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122336), _1122338)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122340), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122338), _1122336)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122340), _1122338)), _1122336))], (17541 ^ _784416) ^ [_1122473, _1122475, _1122477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122473), _1122475)), 17544 ^ _784416 : [(17545 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122477), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122475), _1122473))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122477), _1122473)), _1122475)))], (17551 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122477), _1122473)), _1122475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122477), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122475), _1122473))))]]], (17557 ^ _784416) ^ [_1122762, _1122764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122762), _1122764)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122764), _1122762)), _1122762) = _1122764)], (17563 ^ _784416) ^ [_1122873, _1122875, _1122877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122873), _1122875)), 17566 ^ _784416 : [(17567 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122875), _1122873) = _1122877, -(_1122875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122877), _1122873))], (17573 ^ _784416) ^ [] : [_1122875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122877), _1122873), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1122875), _1122873) = _1122877)]]], (17579 ^ _784416) ^ [_1123132, _1123134, _1123136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123132), _1123134)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1123136), _1123134)), _1123132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1123136), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1123134), _1123132)))], (17585 ^ _784416) ^ [_1123269, _1123271, _1123273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123269), _1123271)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1123271), _1123269)), _1123273) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1123271), _1123273)), _1123269))], (17591 ^ _784416) ^ [_1123406, _1123408, _1123410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123406), _1123408)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1123408), _1123410)), _1123406) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1123408), _1123406)), _1123410))], (17597 ^ _784416) ^ [_1123543] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1123543)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1123543)], (17599 ^ _784416) ^ [_1123575] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123575) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1123575)))], (17601 ^ _784416) ^ [_1123607, _1123609, _1123611, _1123613, _1123615, _1123617] : [class_Rings_Oordered__ring(_1123607), 17604 ^ _784416 : [(17605 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123607), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123607), _1123609), _1123611)), _1123613)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123607), _1123615), _1123611)), _1123617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123607), _1123613), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123607), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1123607), _1123615), _1123609)), _1123611)), _1123617))))], (17611 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123607), _1123613), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123607), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1123607), _1123615), _1123609)), _1123611)), _1123617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123607), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123607), _1123609), _1123611)), _1123613)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1123607), _1123615), _1123611)), _1123617))))]]], (17617 ^ _784416) ^ [_1124046, _1124048, _1124050, _1124052, _1124054, _1124056] : [class_Rings_Oordered__ring(_1124046), 17620 ^ _784416 : [(17621 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124046), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124046), _1124048), _1124050)), _1124052)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124046), _1124054), _1124050)), _1124056))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124046), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124046), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1124046), _1124048), _1124054)), _1124050)), _1124052)), _1124056)))], (17627 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124046), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124046), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1124046), _1124048), _1124054)), _1124050)), _1124052)), _1124056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1124046), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124046), _1124048), _1124050)), _1124052)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124046), _1124054), _1124050)), _1124056))))]]], (17633 ^ _784416) ^ [_1124485, _1124487, _1124489, _1124491, _1124493, _1124495] : [class_Rings_Oordered__ring(_1124485), 17636 ^ _784416 : [(17637 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124485), _1124487), _1124489)), _1124491)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124485), _1124493), _1124489)), _1124495))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124485), _1124491), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124485), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1124485), _1124493), _1124487)), _1124489)), _1124495))))], (17643 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124485), _1124491), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124485), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1124485), _1124493), _1124487)), _1124489)), _1124495))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124485), _1124487), _1124489)), _1124491)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124485), _1124493), _1124489)), _1124495))))]]], (17649 ^ _784416) ^ [_1124924, _1124926, _1124928, _1124930, _1124932, _1124934] : [class_Rings_Oordered__ring(_1124924), 17652 ^ _784416 : [(17653 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124924), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124924), _1124926), _1124928)), _1124930)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124924), _1124932), _1124928)), _1124934))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124924), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124924), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1124924), _1124926), _1124932)), _1124928)), _1124930)), _1124934)))], (17659 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124924), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124924), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1124924), _1124926), _1124932)), _1124928)), _1124930)), _1124934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124924), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124924), _1124926), _1124928)), _1124930)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124924), _1124932), _1124928)), _1124934))))]]], (17665 ^ _784416) ^ [_1125363, _1125365, _1125367, _1125369, _1125371] : [class_Rings_Ocomm__semiring__1(_1125363), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125363), _1125365), _1125367)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125363), _1125369), _1125371)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125363), _1125365), _1125369)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125363), _1125367), _1125371)))], (17671 ^ _784416) ^ [_1125540, _1125542, _1125544, _1125546, _1125548] : [class_Rings_Ocomm__semiring__1(_1125540), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125540), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125540), _1125542), _1125544)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125540), _1125546), _1125548)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125540), _1125546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125540), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125540), _1125542), _1125544)), _1125548)))], (17677 ^ _784416) ^ [_1125717, _1125719, _1125721, _1125723, _1125725] : [class_Rings_Ocomm__semiring__1(_1125717), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125717), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125717), _1125719), _1125721)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125717), _1125723), _1125725)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125717), _1125719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125717), _1125721), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125717), _1125723), _1125725))))], (17683 ^ _784416) ^ [_1125894, _1125896, _1125898, _1125900] : [class_Rings_Ocomm__semiring__1(_1125894), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125894), _1125896), _1125898)), _1125900) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125894), _1125896), _1125900)), _1125898))], (17689 ^ _784416) ^ [_1126037, _1126039, _1126041, _1126043] : [class_Rings_Ocomm__semiring__1(_1126037), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126037), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126037), _1126039), _1126041)), _1126043) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126037), _1126039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126037), _1126041), _1126043)))], (17695 ^ _784416) ^ [_1126180, _1126182, _1126184, _1126186] : [class_Rings_Ocomm__semiring__1(_1126180), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126180), _1126182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126180), _1126184), _1126186)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126180), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126180), _1126182), _1126184)), _1126186))], (17701 ^ _784416) ^ [_1126323, _1126325, _1126327, _1126329] : [class_Rings_Ocomm__semiring__1(_1126323), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126323), _1126325), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126323), _1126327), _1126329)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126323), _1126327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126323), _1126325), _1126329)))], (17707 ^ _784416) ^ [_1126466, _1126468, _1126470] : [class_Rings_Ocomm__semiring__1(_1126466), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126466), _1126468), _1126470) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1126466), _1126470), _1126468))], (17713 ^ _784416) ^ [_1126575, _1126577, _1126579] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1126575), _1126577)), -(hBOOL(hAPP(hAPP(c_member(_1126575), _1126579), _1126577))), -(hAPP(c_Finite__Set_Ocard(_1126575), hAPP(hAPP(c_Set_Oinsert(_1126575), _1126579), _1126577)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1126575), _1126577)))], (17723 ^ _784416) ^ [_1126733, _1126735, _1126737] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1126733), _1126735)), 17726 ^ _784416 : [(17727 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1126733), _1126737), _1126735)), -(hAPP(c_Finite__Set_Ocard(_1126733), hAPP(hAPP(c_Set_Oinsert(_1126733), _1126737), _1126735)) = hAPP(c_Finite__Set_Ocard(_1126733), _1126735))], (17733 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1126733), _1126737), _1126735))), -(hAPP(c_Finite__Set_Ocard(_1126733), hAPP(hAPP(c_Set_Oinsert(_1126733), _1126737), _1126735)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1126733), _1126735)))]]], (17739 ^ _784416) ^ [_1127027, _1127029, _1127031] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1127027), _1127029)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127027), _1127031)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1127027), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1127027, tc_HOL_Obool)), _1127029), _1127031))), hAPP(c_Finite__Set_Ocard(_1127027), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127027, tc_HOL_Obool)), _1127029), _1127031))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1127027), _1127029)), hAPP(c_Finite__Set_Ocard(_1127027), _1127031)))], (17749 ^ _784416) ^ [_1127284, _1127286, _1127288] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1127284), _1127286)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127284), _1127288)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1127284), _1127286)), hAPP(c_Finite__Set_Ocard(_1127284), _1127288)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1127284), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1127284, tc_HOL_Obool)), _1127286), _1127288))), hAPP(c_Finite__Set_Ocard(_1127284), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127284, tc_HOL_Obool)), _1127286), _1127288))))], (17759 ^ _784416) ^ [_1127541, _1127543, _1127545] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1127541), _1127543)), -(hAPP(c_Finite__Set_Ocard(_1127541), hAPP(hAPP(c_Set_Oinsert(_1127541), _1127545), _1127543)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1127541), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1127541, tc_HOL_Obool)), _1127543), hAPP(hAPP(c_Set_Oinsert(_1127541), _1127545), c_Orderings_Obot__class_Obot(tc_fun(_1127541, tc_HOL_Obool)))))))], (17765 ^ _784416) ^ [_1127718, _1127720, _1127722] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1127718), _1127720)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127718), _1127722)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127718, tc_HOL_Obool)), _1127720), _1127722) = c_Orderings_Obot__class_Obot(tc_fun(_1127718, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1127718), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1127718, tc_HOL_Obool)), _1127720), _1127722)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1127718), _1127720)), hAPP(c_Finite__Set_Ocard(_1127718), _1127722)))], (17779 ^ _784416) ^ [_1128017, _1128019, _1128021] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1128017), _1128019)), -(hBOOL(hAPP(hAPP(c_member(_1128017), _1128021), _1128019))), -(hAPP(c_Finite__Set_Ocard(_1128017), hAPP(hAPP(c_Set_Oinsert(_1128017), _1128021), _1128019)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1128017), _1128019)))], (17789 ^ _784416) ^ [_1128175, _1128177, _1128179, _1128181, _1128183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128175), _1128177)), 17792 ^ _784416 : [(17793 ^ _784416) ^ [] : [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), _1128175), _1128179)), _1128181)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128177), _1128179)), _1128183))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1128181), 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), _1128177), _1128175)), _1128179)), _1128183))))], (17799 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1128181), 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), _1128177), _1128175)), _1128179)), _1128183))), -(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), _1128175), _1128179)), _1128181)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128177), _1128179)), _1128183))))]]], (17805 ^ _784416) ^ [_1128566, _1128568, _1128570, _1128572, _1128574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128566), _1128568)), 17808 ^ _784416 : [(17809 ^ _784416) ^ [] : [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), _1128568), _1128570)), _1128572)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128566), _1128570)), _1128574))), -(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), _1128568), _1128566)), _1128570)), _1128572)), _1128574)))], (17815 ^ _784416) ^ [] : [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), _1128568), _1128566)), _1128570)), _1128572)), _1128574)), -(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), _1128568), _1128570)), _1128572)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128566), _1128570)), _1128574))))]]], (17821 ^ _784416) ^ [_1128957, _1128959, _1128961, _1128963, _1128965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128957), _1128959)), 17824 ^ _784416 : [(17825 ^ _784416) ^ [] : [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), _1128959), _1128961)), _1128963)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128957), _1128961)), _1128965))), -(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), _1128959), _1128957)), _1128961)), _1128963)), _1128965)))], (17831 ^ _784416) ^ [] : [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), _1128959), _1128957)), _1128961)), _1128963)), _1128965)), -(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), _1128959), _1128961)), _1128963)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128957), _1128961)), _1128965))))]]], (17837 ^ _784416) ^ [_1129348, _1129350, _1129352, _1129354, _1129356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129348), _1129350)), -(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), _1129350), _1129352)), _1129354)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129348), _1129352)), _1129356)) = 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), _1129350), _1129348)), _1129352)), _1129354)), _1129356))], (17843 ^ _784416) ^ [_1129549, _1129551, _1129553, _1129555, _1129557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129549), _1129551)), 17846 ^ _784416 : [(17847 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129551), _1129553)), _1129555) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129549), _1129553)), _1129557), -(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), _1129551), _1129549)), _1129553)), _1129555) = _1129557)], (17853 ^ _784416) ^ [] : [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), _1129551), _1129549)), _1129553)), _1129555) = _1129557, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129551), _1129553)), _1129555) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129549), _1129553)), _1129557))]]], (17859 ^ _784416) ^ [_1129910, _1129912, _1129914, _1129916, _1129918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129910), _1129912)), 17862 ^ _784416 : [(17863 ^ _784416) ^ [] : [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), _1129910), _1129914)), _1129916)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129912), _1129914)), _1129918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129916), 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), _1129912), _1129910)), _1129914)), _1129918))))], (17869 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1129916), 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), _1129912), _1129910)), _1129914)), _1129918))), -(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), _1129910), _1129914)), _1129916)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129912), _1129914)), _1129918))))]]], (17875 ^ _784416) ^ [_1130301, _1130303, _1130305, _1130307, _1130309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130301), _1130303)), -(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), _1130301), _1130305)), _1130307)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1130303), _1130305)), _1130309)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1130307), 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), _1130303), _1130301)), _1130305)), _1130309)))], (17881 ^ _784416) ^ [_1130502, _1130504, _1130506, _1130508] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1130502), _1130504)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1130506), _1130504)), _1130508)) = 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), _1130502), _1130506)), _1130504)), _1130508))], (17883 ^ _784416) ^ [_1130573, _1130575, _1130577, _1130579, _1130581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130573), _1130575)), 17886 ^ _784416 : [(17887 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1130573), _1130577)), _1130579) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1130575), _1130577)), _1130581), -(_1130579 = 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), _1130575), _1130573)), _1130577)), _1130581))], (17893 ^ _784416) ^ [] : [_1130579 = 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), _1130575), _1130573)), _1130577)), _1130581), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1130573), _1130577)), _1130579) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1130575), _1130577)), _1130581))]]], (17899 ^ _784416) ^ [_1130934, _1130936] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1130934), hAPP(c_Nat_OSuc, _1130936)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1130934), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1130936))], (17901 ^ _784416) ^ [_1130980] : [-(hAPP(c_Nat_OSuc, _1130980) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1130980), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (17903 ^ _784416) ^ [_1131012] : [-(hAPP(c_Nat_OSuc, _1131012) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1131012))], (17905 ^ _784416) ^ [_1131041, _1131043] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1131041, _1131043)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1131041, _1131043), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1131043), c_Orderings_Otop__class_Otop(tc_fun(_1131043, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1131041), c_Orderings_Otop__class_Otop(tc_fun(_1131041, tc_HOL_Obool)))))], (17915 ^ _784416) ^ [_1131201, _1131203, _1131205] : [class_Groups_Olinordered__ab__semigroup__add(_1131201), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131201), _1131203)), -(_1131203 = c_Orderings_Obot__class_Obot(tc_fun(_1131201, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131201), _1131205), c_Big__Operators_Olinorder__class_OMax(_1131201, _1131203)) = c_Big__Operators_Olinorder__class_OMax(_1131201, hAPP(c_Set_OCollect(_1131201), hAPP(hAPP(c_COMBB(tc_fun(_1131201, tc_HOL_Obool), tc_HOL_Obool, _1131201), c_HOL_OEx(_1131201)), hAPP(hAPP(c_COMBC(_1131201, tc_fun(_1131201, tc_HOL_Obool), tc_fun(_1131201, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1131201, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1131201, tc_HOL_Obool), tc_fun(_1131201, tc_HOL_Obool)), _1131201), c_COMBS(_1131201, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1131201, tc_HOL_Obool), tc_fun(_1131201, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1131201), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1131201), c_fconj)), hAPP(hAPP(c_COMBC(_1131201, tc_fun(_1131201, _1131201), tc_fun(_1131201, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1131201, tc_HOL_Obool), tc_fun(tc_fun(_1131201, _1131201), tc_fun(_1131201, tc_HOL_Obool)), _1131201), c_COMBB(_1131201, tc_HOL_Obool, _1131201)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1131201), _1131205))))), hAPP(hAPP(c_COMBC(_1131201, tc_fun(_1131201, tc_HOL_Obool), tc_HOL_Obool), c_member(_1131201)), _1131203))))))], (17929 ^ _784416) ^ [_1131687, _1131689, _1131691] : [class_Groups_Olinordered__ab__semigroup__add(_1131687), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131687), _1131689)), -(_1131689 = c_Orderings_Obot__class_Obot(tc_fun(_1131687, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131687), _1131691), c_Big__Operators_Olinorder__class_OMin(_1131687, _1131689)) = c_Big__Operators_Olinorder__class_OMin(_1131687, hAPP(c_Set_OCollect(_1131687), hAPP(hAPP(c_COMBB(tc_fun(_1131687, tc_HOL_Obool), tc_HOL_Obool, _1131687), c_HOL_OEx(_1131687)), hAPP(hAPP(c_COMBC(_1131687, tc_fun(_1131687, tc_HOL_Obool), tc_fun(_1131687, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1131687, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1131687, tc_HOL_Obool), tc_fun(_1131687, tc_HOL_Obool)), _1131687), c_COMBS(_1131687, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1131687, tc_HOL_Obool), tc_fun(_1131687, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1131687), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1131687), c_fconj)), hAPP(hAPP(c_COMBC(_1131687, tc_fun(_1131687, _1131687), tc_fun(_1131687, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1131687, tc_HOL_Obool), tc_fun(tc_fun(_1131687, _1131687), tc_fun(_1131687, tc_HOL_Obool)), _1131687), c_COMBB(_1131687, tc_HOL_Obool, _1131687)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1131687), _1131691))))), hAPP(hAPP(c_COMBC(_1131687, tc_fun(_1131687, tc_HOL_Obool), tc_HOL_Obool), c_member(_1131687)), _1131689))))))], (17943 ^ _784416) ^ [_1132182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1132182), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17945 ^ _784416) ^ [_1132210] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1132210)))], (17947 ^ _784416) ^ [_1132235] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1132235))))], (17949 ^ _784416) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17951 ^ _784416) ^ [_1132281, _1132283] : [class_Groups_Ozero(_1132281), 17954 ^ _784416 : [(17955 ^ _784416) ^ [] : [c_Groups_Ozero__class_Ozero(_1132281) = _1132283, -(_1132283 = c_Groups_Ozero__class_Ozero(_1132281))], (17961 ^ _784416) ^ [] : [_1132283 = c_Groups_Ozero__class_Ozero(_1132281), -(c_Groups_Ozero__class_Ozero(_1132281) = _1132283)]]], (17967 ^ _784416) ^ [_1132498, _1132500, _1132502] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1132498), 17970 ^ _784416 : [(17971 ^ _784416) ^ [] : [_1132500 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132498), _1132500), _1132502), -(_1132502 = c_Groups_Ozero__class_Ozero(_1132498))], (17977 ^ _784416) ^ [] : [_1132502 = c_Groups_Ozero__class_Ozero(_1132498), -(_1132500 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132498), _1132500), _1132502))]]], (17983 ^ _784416) ^ [_1132739, _1132741] : [class_Rings_Ocomm__semiring__1(_1132739), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132739), _1132741), c_Groups_Ozero__class_Ozero(_1132739)) = _1132741)], (17989 ^ _784416) ^ [_1132834, _1132836] : [class_Rings_Ocomm__semiring__1(_1132834), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132834), c_Groups_Ozero__class_Ozero(_1132834)), _1132836) = _1132836)], (17995 ^ _784416) ^ [_1132929, _1132931] : [class_Groups_Omonoid__add(_1132929), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132929), c_Groups_Ozero__class_Ozero(_1132929)), _1132931) = _1132931)], (18001 ^ _784416) ^ [_1133024, _1133026] : [class_Groups_Ocomm__monoid__add(_1133024), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133024), c_Groups_Ozero__class_Ozero(_1133024)), _1133026) = _1133026)], (18007 ^ _784416) ^ [_1133119, _1133121] : [class_Groups_Olinordered__ab__group__add(_1133119), 18010 ^ _784416 : [(18011 ^ _784416) ^ [] : [c_Groups_Ozero__class_Ozero(_1133119) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133119), _1133121), _1133121), -(_1133121 = c_Groups_Ozero__class_Ozero(_1133119))], (18017 ^ _784416) ^ [] : [_1133121 = c_Groups_Ozero__class_Ozero(_1133119), -(c_Groups_Ozero__class_Ozero(_1133119) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133119), _1133121), _1133121))]]], (18023 ^ _784416) ^ [_1133360, _1133362] : [class_Groups_Omonoid__add(_1133360), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133360), _1133362), c_Groups_Ozero__class_Ozero(_1133360)) = _1133362)], (18029 ^ _784416) ^ [_1133455, _1133457] : [class_Groups_Ocomm__monoid__add(_1133455), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133455), _1133457), c_Groups_Ozero__class_Ozero(_1133455)) = _1133457)], (18035 ^ _784416) ^ [_1133550, _1133552] : [class_Rings_Ocomm__semiring__1(_1133550), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133550), _1133552), c_Groups_Ozero__class_Ozero(_1133550)) = c_Groups_Ozero__class_Ozero(_1133550))], (18041 ^ _784416) ^ [_1133649, _1133651] : [class_Rings_Ocomm__semiring__1(_1133649), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133649), c_Groups_Ozero__class_Ozero(_1133649)), _1133651) = c_Groups_Ozero__class_Ozero(_1133649))], (18047 ^ _784416) ^ [_1133748, _1133750] : [class_Rings_Omult__zero(_1133748), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133748), c_Groups_Ozero__class_Ozero(_1133748)), _1133750) = c_Groups_Ozero__class_Ozero(_1133748))], (18053 ^ _784416) ^ [_1133847, _1133849] : [class_Rings_Omult__zero(_1133847), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133847), _1133849), c_Groups_Ozero__class_Ozero(_1133847)) = c_Groups_Ozero__class_Ozero(_1133847))], (18059 ^ _784416) ^ [_1133946, _1133948, _1133950] : [class_Rings_Oring__no__zero__divisors(_1133946), 18062 ^ _784416 : [(18073 ^ _784416) ^ [] : [18074 ^ _784416 : [(18075 ^ _784416) ^ [] : [_1133948 = c_Groups_Ozero__class_Ozero(_1133946)], (18077 ^ _784416) ^ [] : [_1133950 = c_Groups_Ozero__class_Ozero(_1133946)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133946), _1133948), _1133950) = c_Groups_Ozero__class_Ozero(_1133946))], (18063 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133946), _1133948), _1133950) = c_Groups_Ozero__class_Ozero(_1133946), -(_1133948 = c_Groups_Ozero__class_Ozero(_1133946)), -(_1133950 = c_Groups_Ozero__class_Ozero(_1133946))]]], (18081 ^ _784416) ^ [_1134244, _1134246, _1134248] : [class_Rings_Ono__zero__divisors(_1134244), -(_1134246 = c_Groups_Ozero__class_Ozero(_1134244)), -(_1134248 = c_Groups_Ozero__class_Ozero(_1134244)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134244), _1134246), _1134248) = c_Groups_Ozero__class_Ozero(_1134244)], (18095 ^ _784416) ^ [_1134464, _1134466, _1134468] : [class_Rings_Ono__zero__divisors(_1134464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134464), _1134466), _1134468) = c_Groups_Ozero__class_Ozero(_1134464), -(_1134466 = c_Groups_Ozero__class_Ozero(_1134464)), -(_1134468 = c_Groups_Ozero__class_Ozero(_1134464))], (18109 ^ _784416) ^ [_1134636, _1134638, _1134640] : [class_Groups_Ogroup__add(_1134636), 18112 ^ _784416 : [(18113 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1134636), _1134638), _1134640) = c_Groups_Ozero__class_Ozero(_1134636), -(_1134638 = _1134640)], (18119 ^ _784416) ^ [] : [_1134638 = _1134640, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1134636), _1134638), _1134640) = c_Groups_Ozero__class_Ozero(_1134636))]]], (18125 ^ _784416) ^ [_1134877, _1134879, _1134881] : [class_Groups_Oab__group__add(_1134877), 18128 ^ _784416 : [(18129 ^ _784416) ^ [] : [_1134879 = _1134881, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1134877), _1134879), _1134881) = c_Groups_Ozero__class_Ozero(_1134877))], (18135 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1134877), _1134879), _1134881) = c_Groups_Ozero__class_Ozero(_1134877), -(_1134879 = _1134881)]]], (18141 ^ _784416) ^ [_1135118, _1135120] : [class_Groups_Ogroup__add(_1135118), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1135118), _1135120), _1135120) = c_Groups_Ozero__class_Ozero(_1135118))], (18147 ^ _784416) ^ [_1135213, _1135215] : [class_Groups_Ogroup__add(_1135213), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1135213), _1135215), c_Groups_Ozero__class_Ozero(_1135213)) = _1135215)], (18153 ^ _784416) ^ [_1135308] : [class_Rings_Ozero__neq__one(_1135308), c_Groups_Oone__class_Oone(_1135308) = c_Groups_Ozero__class_Ozero(_1135308)], (18159 ^ _784416) ^ [_1135390] : [class_Rings_Ozero__neq__one(_1135390), c_Groups_Ozero__class_Ozero(_1135390) = c_Groups_Oone__class_Oone(_1135390)], (18165 ^ _784416) ^ [_1135472] : [class_Groups_Ogroup__add(_1135472), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1135472), c_Groups_Ozero__class_Ozero(_1135472)) = c_Groups_Ozero__class_Ozero(_1135472))], (18171 ^ _784416) ^ [_1135563, _1135565] : [class_Groups_Ogroup__add(_1135563), 18174 ^ _784416 : [(18175 ^ _784416) ^ [] : [c_Groups_Ozero__class_Ozero(_1135563) = hAPP(c_Groups_Ouminus__class_Ouminus(_1135563), _1135565), -(c_Groups_Ozero__class_Ozero(_1135563) = _1135565)], (18181 ^ _784416) ^ [] : [c_Groups_Ozero__class_Ozero(_1135563) = _1135565, -(c_Groups_Ozero__class_Ozero(_1135563) = hAPP(c_Groups_Ouminus__class_Ouminus(_1135563), _1135565))]]], (18187 ^ _784416) ^ [_1135795, _1135797] : [class_Groups_Olinordered__ab__group__add(_1135795), 18190 ^ _784416 : [(18191 ^ _784416) ^ [] : [_1135797 = hAPP(c_Groups_Ouminus__class_Ouminus(_1135795), _1135797), -(_1135797 = c_Groups_Ozero__class_Ozero(_1135795))], (18197 ^ _784416) ^ [] : [_1135797 = c_Groups_Ozero__class_Ozero(_1135795), -(_1135797 = hAPP(c_Groups_Ouminus__class_Ouminus(_1135795), _1135797))]]], (18203 ^ _784416) ^ [_1136021, _1136023] : [class_Groups_Ogroup__add(_1136021), 18206 ^ _784416 : [(18207 ^ _784416) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1136021), _1136023) = c_Groups_Ozero__class_Ozero(_1136021), -(_1136023 = c_Groups_Ozero__class_Ozero(_1136021))], (18213 ^ _784416) ^ [] : [_1136023 = c_Groups_Ozero__class_Ozero(_1136021), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1136021), _1136023) = c_Groups_Ozero__class_Ozero(_1136021))]]], (18219 ^ _784416) ^ [_1136253, _1136255] : [class_Groups_Olinordered__ab__group__add(_1136253), 18222 ^ _784416 : [(18223 ^ _784416) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1136253), _1136255) = _1136255, -(_1136255 = c_Groups_Ozero__class_Ozero(_1136253))], (18229 ^ _784416) ^ [] : [_1136255 = c_Groups_Ozero__class_Ozero(_1136253), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1136253), _1136255) = _1136255)]]], (18235 ^ _784416) ^ [_1136488] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1136488)], (18237 ^ _784416) ^ [_1136523] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1136523)], (18239 ^ _784416) ^ [_1136558] : [hAPP(c_Nat_OSuc, _1136558) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18241 ^ _784416) ^ [_1136593] : [hAPP(c_Nat_OSuc, _1136593) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18243 ^ _784416) ^ [_1136628] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1136628)], (18245 ^ _784416) ^ [_1136663] : [hAPP(c_Nat_OSuc, _1136663) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18247 ^ _784416) ^ [_1136698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1136698), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18249 ^ _784416) ^ [_1136732] : [-(_1136732 = 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)), _1136732)))], (18255 ^ _784416) ^ [_1136764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1136764)), _1136764 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18261 ^ _784416) ^ [_1136855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1136855), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18263 ^ _784416) ^ [_1136883, _1136885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1136883), _1136885)), _1136885 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18269 ^ _784416) ^ [_1136967] : [-(_1136967 = 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)), _1136967)))], (18275 ^ _784416) ^ [_1137003] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1137003) = _1137003)], (18277 ^ _784416) ^ [_1137029] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1137029), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1137029)], (18279 ^ _784416) ^ [_1137073, _1137075] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1137073), _1137075) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 18282 ^ _784416 : [(18283 ^ _784416) ^ [] : [-(_1137073 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18285 ^ _784416) ^ [] : [-(_1137075 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (18287 ^ _784416) ^ [_1137184, _1137186] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1137184), _1137186) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1137184 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1137186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18297 ^ _784416) ^ [_1137327, _1137329] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1137327), _1137329) = _1137327, -(_1137329 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18303 ^ _784416) ^ [_1137428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1137428), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1137428 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18309 ^ _784416) ^ [_1137509] : [_1137509 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1137509), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18315 ^ _784416) ^ [_1137596] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1137596)))], (18317 ^ _784416) ^ [_1137621] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1137621) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18319 ^ _784416) ^ [_1137647] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1137647), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1137647)], (18321 ^ _784416) ^ [_1137676] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1137676), _1137676) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18323 ^ _784416) ^ [_1137705, _1137707] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1137705), _1137707) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1137707), _1137705) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1137705 = _1137707)], (18343 ^ _784416) ^ [_1137988, _1137990, _1137992] : [18344 ^ _784416 : [(18345 ^ _784416) ^ [] : [_1137988 = _1137992], (18347 ^ _784416) ^ [] : [_1137990 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1137988), _1137990) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1137992), _1137990))], (18333 ^ _784416) ^ [_1137876, _1137878, _1137880] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1137876), _1137878) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1137880), _1137878), -(_1137876 = _1137880), -(_1137878 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18361 ^ _784416) ^ [_1138261, _1138263, _1138265] : [18362 ^ _784416 : [(18363 ^ _784416) ^ [] : [_1138263 = _1138265], (18365 ^ _784416) ^ [] : [_1138261 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1138261), _1138263) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1138261), _1138265))], (18351 ^ _784416) ^ [_1138149, _1138151, _1138153] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1138149), _1138151) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1138149), _1138153), -(_1138151 = _1138153), -(_1138149 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18379 ^ _784416) ^ [_1138517, _1138519] : [18380 ^ _784416 : [(18381 ^ _784416) ^ [] : [_1138517 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18383 ^ _784416) ^ [] : [_1138519 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1138517), _1138519) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18369 ^ _784416) ^ [_1138419, _1138421] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1138419), _1138421) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1138419 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1138421 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18387 ^ _784416) ^ [_1138646] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1138646), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18389 ^ _784416) ^ [_1138675] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1138675) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18401 ^ _784416) ^ [_1138831, _1138833, _1138835] : [18402 ^ _784416 : [(18403 ^ _784416) ^ [] : [_1138831 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18405 ^ _784416) ^ [] : [_1138833 = _1138835]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1138831), _1138833) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1138831), _1138835))], (18391 ^ _784416) ^ [_1138719, _1138721, _1138723] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1138719), _1138721) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1138719), _1138723), -(_1138719 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1138721 = _1138723)], (18409 ^ _784416) ^ [_1138974, _1138976, _1138978] : [class_Rings_Olinordered__ring__strict(_1138974), 18412 ^ _784416 : [(18413 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1138974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138974), _1138976), _1138976)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138974), _1138978), _1138978)) = c_Groups_Ozero__class_Ozero(_1138974), 18416 ^ _784416 : [(18417 ^ _784416) ^ [] : [-(_1138976 = c_Groups_Ozero__class_Ozero(_1138974))], (18419 ^ _784416) ^ [] : [-(_1138978 = c_Groups_Ozero__class_Ozero(_1138974))]]], (18421 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1138974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138974), _1138976), _1138976)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138974), _1138978), _1138978)) = c_Groups_Ozero__class_Ozero(_1138974)), _1138976 = c_Groups_Ozero__class_Ozero(_1138974), _1138978 = c_Groups_Ozero__class_Ozero(_1138974)]]], (18431 ^ _784416) ^ [_1139349, _1139351] : [hBOOL(hAPP(_1139349, _1139351)), -(hBOOL(hAPP(_1139349, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1139349) = hAPP(c_Nat_OSuc, c_Orderings_Oord__class_OLeast(tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat), _1139349), c_Nat_OSuc))))], (18441 ^ _784416) ^ [_1139479, _1139481, _1139483] : [class_Rings_Olinordered__ring__strict(_1139479), 18444 ^ _784416 : [(18445 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139479), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139479), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139479), _1139481), _1139481)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139479), _1139483), _1139483))), c_Groups_Ozero__class_Ozero(_1139479))), 18448 ^ _784416 : [(18449 ^ _784416) ^ [] : [-(_1139481 = c_Groups_Ozero__class_Ozero(_1139479))], (18451 ^ _784416) ^ [] : [-(_1139483 = c_Groups_Ozero__class_Ozero(_1139479))]]], (18453 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139479), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139479), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139479), _1139481), _1139481)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139479), _1139483), _1139483))), c_Groups_Ozero__class_Ozero(_1139479)))), _1139481 = c_Groups_Ozero__class_Ozero(_1139479), _1139483 = c_Groups_Ozero__class_Ozero(_1139479)]]], (18463 ^ _784416) ^ [_1139875, _1139877, _1139879] : [class_Rings_Olinordered__ring(_1139875), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139875), c_Groups_Ozero__class_Ozero(_1139875)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139875), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139875), _1139877), _1139877)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1139875), _1139879), _1139879)))))], (18469 ^ _784416) ^ [_1140018, _1140020, _1140022] : [class_Rings_Olinordered__ring__strict(_1140018), 18472 ^ _784416 : [(18483 ^ _784416) ^ [] : [18484 ^ _784416 : [(18485 ^ _784416) ^ [] : [-(_1140020 = c_Groups_Ozero__class_Ozero(_1140018))], (18487 ^ _784416) ^ [] : [-(_1140022 = c_Groups_Ozero__class_Ozero(_1140018))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140018), c_Groups_Ozero__class_Ozero(_1140018)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140018), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140018), _1140020), _1140020)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140018), _1140022), _1140022)))))], (18473 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140018), c_Groups_Ozero__class_Ozero(_1140018)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140018), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140018), _1140020), _1140020)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140018), _1140022), _1140022)))), _1140020 = c_Groups_Ozero__class_Ozero(_1140018), _1140022 = c_Groups_Ozero__class_Ozero(_1140018)]]], (18491 ^ _784416) ^ [_1140393, _1140395, _1140397] : [class_Rings_Olinordered__ring(_1140393), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140393), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140393), _1140395), _1140395)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140393), _1140397), _1140397))), c_Groups_Ozero__class_Ozero(_1140393)))], (18497 ^ _784416) ^ [_1140537, _1140539] : [class_Groups_Olinordered__ab__group__add(_1140537), 18500 ^ _784416 : [(18501 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140537), c_Groups_Ozero__class_Ozero(_1140537)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140537), _1140539), _1140539))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140537), c_Groups_Ozero__class_Ozero(_1140537)), _1140539)))], (18507 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140537), c_Groups_Ozero__class_Ozero(_1140537)), _1140539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140537), c_Groups_Ozero__class_Ozero(_1140537)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140537), _1140539), _1140539))))]]], (18513 ^ _784416) ^ [_1140820, _1140822] : [class_Groups_Olinordered__ab__group__add(_1140820), 18516 ^ _784416 : [(18517 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140820), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140820), _1140822), _1140822)), c_Groups_Ozero__class_Ozero(_1140820))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140820), _1140822), c_Groups_Ozero__class_Ozero(_1140820))))], (18523 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140820), _1140822), c_Groups_Ozero__class_Ozero(_1140820))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140820), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140820), _1140822), _1140822)), c_Groups_Ozero__class_Ozero(_1140820))))]]], (18529 ^ _784416) ^ [_1141103, _1141105, _1141107] : [class_Groups_Oordered__comm__monoid__add(_1141103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141103), c_Groups_Ozero__class_Ozero(_1141103)), _1141105)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141103), c_Groups_Ozero__class_Ozero(_1141103)), _1141107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141103), c_Groups_Ozero__class_Ozero(_1141103)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1141103), _1141105), _1141107))))], (18543 ^ _784416) ^ [_1141358, _1141360, _1141362] : [class_Groups_Oordered__comm__monoid__add(_1141358), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141358), c_Groups_Ozero__class_Ozero(_1141358)), _1141360)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141358), c_Groups_Ozero__class_Ozero(_1141358)), _1141362)), 18554 ^ _784416 : [(18555 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1141358), _1141360), _1141362) = c_Groups_Ozero__class_Ozero(_1141358), 18558 ^ _784416 : [(18559 ^ _784416) ^ [] : [-(_1141360 = c_Groups_Ozero__class_Ozero(_1141358))], (18561 ^ _784416) ^ [] : [-(_1141362 = c_Groups_Ozero__class_Ozero(_1141358))]]], (18563 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1141358), _1141360), _1141362) = c_Groups_Ozero__class_Ozero(_1141358)), _1141360 = c_Groups_Ozero__class_Ozero(_1141358), _1141362 = c_Groups_Ozero__class_Ozero(_1141358)]]], (18573 ^ _784416) ^ [_1141829, _1141831, _1141833, _1141835] : [class_Groups_Oordered__comm__monoid__add(_1141829), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141829), c_Groups_Ozero__class_Ozero(_1141829)), _1141831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141829), _1141833), _1141835)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141829), _1141833), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1141829), _1141831), _1141835))))], (18587 ^ _784416) ^ [_1142082, _1142084, _1142086, _1142088] : [class_Groups_Oordered__comm__monoid__add(_1142082), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142082), c_Groups_Ozero__class_Ozero(_1142082)), _1142084)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142082), _1142086), _1142088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142082), _1142086), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142082), _1142088), _1142084))))], (18601 ^ _784416) ^ [_1142335, _1142337, _1142339] : [class_Groups_Oordered__comm__monoid__add(_1142335), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142335), _1142337), c_Groups_Ozero__class_Ozero(_1142335))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142335), _1142339), c_Groups_Ozero__class_Ozero(_1142335))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142335), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142335), _1142337), _1142339)), c_Groups_Ozero__class_Ozero(_1142335))))], (18615 ^ _784416) ^ [_1142590, _1142592] : [class_Rings_Olinordered__ring(_1142590), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142590), c_Groups_Ozero__class_Ozero(_1142590)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142590), _1142592), _1142592))))], (18621 ^ _784416) ^ [_1142699, _1142701, _1142703] : [class_Rings_Olinordered__ring__strict(_1142699), 18624 ^ _784416 : [(18625 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142699), c_Groups_Ozero__class_Ozero(_1142699)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142699), _1142701), _1142703))), 18630 ^ _784416 : [(18631 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142699), c_Groups_Ozero__class_Ozero(_1142699)), _1142701)))], (18633 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142699), c_Groups_Ozero__class_Ozero(_1142699)), _1142703)))]], 18634 ^ _784416 : [(18635 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142699), _1142701), c_Groups_Ozero__class_Ozero(_1142699))))], (18637 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142699), _1142703), c_Groups_Ozero__class_Ozero(_1142699))))]]], (18639 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142699), c_Groups_Ozero__class_Ozero(_1142699)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142699), _1142701), _1142703)))), 18640 ^ _784416 : [(18641 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142699), c_Groups_Ozero__class_Ozero(_1142699)), _1142701)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142699), c_Groups_Ozero__class_Ozero(_1142699)), _1142703))], (18647 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142699), _1142701), c_Groups_Ozero__class_Ozero(_1142699))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1142699), _1142703), c_Groups_Ozero__class_Ozero(_1142699)))]]]]], (18655 ^ _784416) ^ [_1143289, _1143291, _1143293] : [class_Rings_Olinordered__ring__strict(_1143289), 18658 ^ _784416 : [(18659 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143289), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143289), _1143291), _1143293)), c_Groups_Ozero__class_Ozero(_1143289))), 18664 ^ _784416 : [(18665 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143289), c_Groups_Ozero__class_Ozero(_1143289)), _1143291)))], (18667 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143289), _1143293), c_Groups_Ozero__class_Ozero(_1143289))))]], 18668 ^ _784416 : [(18669 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143289), _1143291), c_Groups_Ozero__class_Ozero(_1143289))))], (18671 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143289), c_Groups_Ozero__class_Ozero(_1143289)), _1143293)))]]], (18673 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143289), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143289), _1143291), _1143293)), c_Groups_Ozero__class_Ozero(_1143289)))), 18674 ^ _784416 : [(18675 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143289), c_Groups_Ozero__class_Ozero(_1143289)), _1143291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143289), _1143293), c_Groups_Ozero__class_Ozero(_1143289)))], (18681 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143289), _1143291), c_Groups_Ozero__class_Ozero(_1143289))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143289), c_Groups_Ozero__class_Ozero(_1143289)), _1143293))]]]]], (18689 ^ _784416) ^ [_1143879, _1143881, _1143883] : [class_Rings_Oordered__cancel__semiring(_1143879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143879), c_Groups_Ozero__class_Ozero(_1143879)), _1143881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143879), c_Groups_Ozero__class_Ozero(_1143879)), _1143883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1143879), c_Groups_Ozero__class_Ozero(_1143879)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143879), _1143881), _1143883))))], (18703 ^ _784416) ^ [_1144134, _1144136, _1144138] : [class_Rings_Oordered__cancel__semiring(_1144134), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144134), c_Groups_Ozero__class_Ozero(_1144134)), _1144136)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144134), _1144138), c_Groups_Ozero__class_Ozero(_1144134))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144134), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144134), _1144136), _1144138)), c_Groups_Ozero__class_Ozero(_1144134))))], (18717 ^ _784416) ^ [_1144389, _1144391, _1144393] : [class_Rings_Oordered__cancel__semiring(_1144389), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144389), c_Groups_Ozero__class_Ozero(_1144389)), _1144391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144389), _1144393), c_Groups_Ozero__class_Ozero(_1144389))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144389), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144389), _1144393), _1144391)), c_Groups_Ozero__class_Ozero(_1144389))))], (18731 ^ _784416) ^ [_1144644, _1144646, _1144648] : [class_Rings_Oordered__cancel__semiring(_1144644), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144644), _1144646), c_Groups_Ozero__class_Ozero(_1144644))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144644), c_Groups_Ozero__class_Ozero(_1144644)), _1144648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144644), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144644), _1144646), _1144648)), c_Groups_Ozero__class_Ozero(_1144644))))], (18745 ^ _784416) ^ [_1144899, _1144901, _1144903] : [class_Rings_Oordered__ring(_1144899), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144899), _1144901), c_Groups_Ozero__class_Ozero(_1144899))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144899), _1144903), c_Groups_Ozero__class_Ozero(_1144899))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144899), c_Groups_Ozero__class_Ozero(_1144899)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144899), _1144901), _1144903))))], (18759 ^ _784416) ^ [_1145154, _1145156, _1145158, _1145160] : [class_Rings_Oordered__semiring(_1145154), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145154), _1145156), _1145158)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145154), c_Groups_Ozero__class_Ozero(_1145154)), _1145160)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145154), _1145156), _1145160)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145154), _1145158), _1145160))))], (18773 ^ _784416) ^ [_1145423, _1145425, _1145427, _1145429] : [class_Rings_Oordered__semiring(_1145423), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145423), _1145425), _1145427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145423), c_Groups_Ozero__class_Ozero(_1145423)), _1145429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145423), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145423), _1145429), _1145425)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145423), _1145429), _1145427))))], (18787 ^ _784416) ^ [_1145692, _1145694, _1145696, _1145698] : [class_Rings_Oordered__comm__semiring(_1145692), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145692), _1145694), _1145696)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145692), c_Groups_Ozero__class_Ozero(_1145692)), _1145698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145692), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145692), _1145698), _1145694)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145692), _1145698), _1145696))))], (18801 ^ _784416) ^ [_1145961, _1145963, _1145965, _1145967] : [class_Rings_Oordered__ring(_1145961), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145961), _1145963), _1145965)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145961), _1145967), c_Groups_Ozero__class_Ozero(_1145961))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145961), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145961), _1145965), _1145967)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145961), _1145963), _1145967))))], (18815 ^ _784416) ^ [_1146230, _1146232, _1146234, _1146236] : [class_Rings_Oordered__ring(_1146230), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146230), _1146232), _1146234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146230), _1146236), c_Groups_Ozero__class_Ozero(_1146230))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146230), _1146236), _1146234)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146230), _1146236), _1146232))))], (18829 ^ _784416) ^ [_1146499, _1146501, _1146503, _1146505, _1146507] : [class_Rings_Oordered__semiring(_1146499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146499), _1146501), _1146503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146499), _1146505), _1146507)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146499), c_Groups_Ozero__class_Ozero(_1146499)), _1146501)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146499), c_Groups_Ozero__class_Ozero(_1146499)), _1146505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146499), _1146501), _1146505)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146499), _1146503), _1146507))))], (18851 ^ _784416) ^ [_1146922, _1146924, _1146926, _1146928, _1146930] : [class_Rings_Oordered__semiring(_1146922), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146922), _1146924), _1146926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146922), _1146928), _1146930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146922), c_Groups_Ozero__class_Ozero(_1146922)), _1146926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146922), c_Groups_Ozero__class_Ozero(_1146922)), _1146928)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146922), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146922), _1146924), _1146928)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146922), _1146926), _1146930))))], (18873 ^ _784416) ^ [_1147345, _1147347, _1147349] : [class_Rings_Oordered__ring(_1147345), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147345), c_Groups_Ozero__class_Ozero(_1147345)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147345), _1147347), _1147349)))), 18878 ^ _784416 : [(18879 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147345), c_Groups_Ozero__class_Ozero(_1147345)), _1147347)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147345), c_Groups_Ozero__class_Ozero(_1147345)), _1147349))], (18885 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147345), _1147347), c_Groups_Ozero__class_Ozero(_1147345))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147345), _1147349), c_Groups_Ozero__class_Ozero(_1147345)))]]], (18893 ^ _784416) ^ [_1147721, _1147723, _1147725] : [class_Rings_Oordered__cancel__semiring(_1147721), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147721), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147721), _1147723), _1147725)), c_Groups_Ozero__class_Ozero(_1147721)))), 18898 ^ _784416 : [(18899 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147721), c_Groups_Ozero__class_Ozero(_1147721)), _1147723)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147721), _1147725), c_Groups_Ozero__class_Ozero(_1147721)))], (18905 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147721), _1147723), c_Groups_Ozero__class_Ozero(_1147721))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147721), c_Groups_Ozero__class_Ozero(_1147721)), _1147725))]]], (18913 ^ _784416) ^ [_1148097, _1148099, _1148101, _1148103] : [class_Rings_Olinordered__semidom(_1148097), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148097), c_Groups_Ozero__class_Ozero(_1148097)), _1148099)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148097), _1148101), _1148103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148097), _1148101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148097), _1148099), _1148103))))], (18927 ^ _784416) ^ [_1148350, _1148352] : [class_Groups_Olinordered__ab__group__add(_1148350), 18930 ^ _784416 : [(18931 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148350), c_Groups_Ozero__class_Ozero(_1148350)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148350), _1148352), _1148352))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148350), c_Groups_Ozero__class_Ozero(_1148350)), _1148352)))], (18937 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148350), c_Groups_Ozero__class_Ozero(_1148350)), _1148352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148350), c_Groups_Ozero__class_Ozero(_1148350)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148350), _1148352), _1148352))))]]], (18943 ^ _784416) ^ [_1148633, _1148635] : [class_Groups_Olinordered__ab__group__add(_1148633), 18946 ^ _784416 : [(18947 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148633), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148633), _1148635), _1148635)), c_Groups_Ozero__class_Ozero(_1148633))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148633), _1148635), c_Groups_Ozero__class_Ozero(_1148633))))], (18953 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148633), _1148635), c_Groups_Ozero__class_Ozero(_1148633))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148633), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148633), _1148635), _1148635)), c_Groups_Ozero__class_Ozero(_1148633))))]]], (18959 ^ _784416) ^ [_1148916, _1148918, _1148920] : [class_Groups_Oordered__comm__monoid__add(_1148916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148916), c_Groups_Ozero__class_Ozero(_1148916)), _1148918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148916), c_Groups_Ozero__class_Ozero(_1148916)), _1148920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148916), c_Groups_Ozero__class_Ozero(_1148916)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148916), _1148918), _1148920))))], (18973 ^ _784416) ^ [_1149171, _1149173, _1149175] : [class_Groups_Oordered__comm__monoid__add(_1149171), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149171), _1149173), c_Groups_Ozero__class_Ozero(_1149171))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149171), _1149175), c_Groups_Ozero__class_Ozero(_1149171))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149171), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149171), _1149173), _1149175)), c_Groups_Ozero__class_Ozero(_1149171))))], (18987 ^ _784416) ^ [_1149426, _1149428, _1149430, _1149432] : [class_Rings_Olinordered__ring__strict(_1149426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149426), _1149428), _1149430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149426), _1149432), c_Groups_Ozero__class_Ozero(_1149426))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149426), _1149432), _1149430)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149426), _1149432), _1149428))))], (19001 ^ _784416) ^ [_1149695, _1149697, _1149699, _1149701] : [class_Rings_Olinordered__ring__strict(_1149695), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149695), _1149697), _1149699)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149695), _1149701), c_Groups_Ozero__class_Ozero(_1149695))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149695), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149695), _1149699), _1149701)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149695), _1149697), _1149701))))], (19015 ^ _784416) ^ [_1149964, _1149966, _1149968, _1149970] : [class_Rings_Olinordered__comm__semiring__strict(_1149964), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149964), _1149966), _1149968)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149964), c_Groups_Ozero__class_Ozero(_1149964)), _1149970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149964), _1149970), _1149966)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149964), _1149970), _1149968))))], (19029 ^ _784416) ^ [_1150233, _1150235, _1150237, _1150239] : [class_Rings_Olinordered__semiring__strict(_1150233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150233), _1150235), _1150237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150233), c_Groups_Ozero__class_Ozero(_1150233)), _1150239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150233), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150233), _1150239), _1150235)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150233), _1150239), _1150237))))], (19043 ^ _784416) ^ [_1150502, _1150504, _1150506, _1150508] : [class_Rings_Olinordered__semiring__strict(_1150502), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150502), _1150504), _1150506)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150502), c_Groups_Ozero__class_Ozero(_1150502)), _1150508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150502), _1150504), _1150508)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150502), _1150506), _1150508))))], (19057 ^ _784416) ^ [_1150771, _1150773, _1150775] : [class_Rings_Olinordered__ring__strict(_1150771), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150771), _1150773), c_Groups_Ozero__class_Ozero(_1150771))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150771), _1150775), c_Groups_Ozero__class_Ozero(_1150771))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150771), c_Groups_Ozero__class_Ozero(_1150771)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1150771), _1150773), _1150775))))], (19071 ^ _784416) ^ [_1151026, _1151028, _1151030] : [class_Rings_Olinordered__semiring__strict(_1151026), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151026), _1151028), c_Groups_Ozero__class_Ozero(_1151026))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151026), c_Groups_Ozero__class_Ozero(_1151026)), _1151030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151026), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151026), _1151028), _1151030)), c_Groups_Ozero__class_Ozero(_1151026))))], (19085 ^ _784416) ^ [_1151281, _1151283, _1151285, _1151287] : [class_Rings_Olinordered__ring__strict(_1151281), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151281), _1151283), c_Groups_Ozero__class_Ozero(_1151281))), 19092 ^ _784416 : [(19093 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151281), _1151283), _1151285)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151281), _1151283), _1151287))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151281), _1151287), _1151285)))], (19099 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151281), _1151287), _1151285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151281), _1151283), _1151285)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151281), _1151283), _1151287))))]]], (19105 ^ _784416) ^ [_1151662, _1151664, _1151666] : [class_Rings_Olinordered__semiring__strict(_1151662), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151662), c_Groups_Ozero__class_Ozero(_1151662)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151662), _1151664), _1151666))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151662), c_Groups_Ozero__class_Ozero(_1151662)), _1151666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151662), c_Groups_Ozero__class_Ozero(_1151662)), _1151664)))], (19119 ^ _784416) ^ [_1151917, _1151919, _1151921] : [class_Rings_Olinordered__semiring__strict(_1151917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151917), c_Groups_Ozero__class_Ozero(_1151917)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151917), _1151919), _1151921))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151917), c_Groups_Ozero__class_Ozero(_1151917)), _1151919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1151917), c_Groups_Ozero__class_Ozero(_1151917)), _1151921)))], (19133 ^ _784416) ^ [_1152172, _1152174, _1152176] : [class_Rings_Olinordered__semiring__strict(_1152172), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152172), c_Groups_Ozero__class_Ozero(_1152172)), _1152174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152172), _1152176), c_Groups_Ozero__class_Ozero(_1152172))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152172), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152172), _1152176), _1152174)), c_Groups_Ozero__class_Ozero(_1152172))))], (19147 ^ _784416) ^ [_1152427, _1152429, _1152431] : [class_Rings_Olinordered__semiring__strict(_1152427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152427), c_Groups_Ozero__class_Ozero(_1152427)), _1152429)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152427), _1152431), c_Groups_Ozero__class_Ozero(_1152427))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152427), _1152429), _1152431)), c_Groups_Ozero__class_Ozero(_1152427))))], (19161 ^ _784416) ^ [_1152682, _1152684, _1152686] : [class_Rings_Olinordered__semiring__strict(_1152682), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152682), c_Groups_Ozero__class_Ozero(_1152682)), _1152684)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152682), c_Groups_Ozero__class_Ozero(_1152682)), _1152686)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152682), c_Groups_Ozero__class_Ozero(_1152682)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152682), _1152684), _1152686))))], (19175 ^ _784416) ^ [_1152937, _1152939, _1152941, _1152943] : [class_Rings_Olinordered__ring__strict(_1152937), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152937), c_Groups_Ozero__class_Ozero(_1152937)), _1152939)), 19182 ^ _784416 : [(19183 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152937), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152937), _1152939), _1152941)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152937), _1152939), _1152943))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152937), _1152941), _1152943)))], (19189 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152937), _1152941), _1152943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1152937), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152937), _1152939), _1152941)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152937), _1152939), _1152943))))]]], (19195 ^ _784416) ^ [_1153318, _1153320, _1153322, _1153324] : [class_Rings_Olinordered__ring__strict(_1153318), 19198 ^ _784416 : [(19199 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153318), _1153320), _1153322)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153318), _1153320), _1153324))), 19204 ^ _784416 : [(19205 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153318), c_Groups_Ozero__class_Ozero(_1153318)), _1153320)))], (19207 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153318), _1153322), _1153324)))]], 19208 ^ _784416 : [(19209 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153318), _1153320), c_Groups_Ozero__class_Ozero(_1153318))))], (19211 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153318), _1153324), _1153322)))]]], (19213 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153318), _1153320), _1153322)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153318), _1153320), _1153324)))), 19214 ^ _784416 : [(19215 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153318), c_Groups_Ozero__class_Ozero(_1153318)), _1153320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153318), _1153322), _1153324))], (19221 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153318), _1153320), c_Groups_Ozero__class_Ozero(_1153318))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153318), _1153324), _1153322))]]]]], (19229 ^ _784416) ^ [_1153924, _1153926, _1153928, _1153930] : [class_Rings_Olinordered__ring__strict(_1153924), 19232 ^ _784416 : [(19233 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153924), _1153926), _1153928)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153924), _1153930), _1153928))), 19238 ^ _784416 : [(19239 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153924), c_Groups_Ozero__class_Ozero(_1153924)), _1153928)))], (19241 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153924), _1153926), _1153930)))]], 19242 ^ _784416 : [(19243 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153924), _1153928), c_Groups_Ozero__class_Ozero(_1153924))))], (19245 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153924), _1153930), _1153926)))]]], (19247 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153924), _1153926), _1153928)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153924), _1153930), _1153928)))), 19248 ^ _784416 : [(19249 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153924), c_Groups_Ozero__class_Ozero(_1153924)), _1153928)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153924), _1153926), _1153930))], (19255 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153924), _1153928), c_Groups_Ozero__class_Ozero(_1153924))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153924), _1153930), _1153926))]]]]], (19263 ^ _784416) ^ [_1154530, _1154532] : [class_Rings_Olinordered__ring(_1154530), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154530), _1154532), _1154532)), c_Groups_Ozero__class_Ozero(_1154530)))], (19269 ^ _784416) ^ [_1154640, _1154642, _1154644] : [class_Groups_Oordered__ab__group__add(_1154640), 19272 ^ _784416 : [(19273 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154640), _1154642), _1154644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154640), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1154640), _1154642), _1154644)), c_Groups_Ozero__class_Ozero(_1154640))))], (19279 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154640), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1154640), _1154642), _1154644)), c_Groups_Ozero__class_Ozero(_1154640))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154640), _1154642), _1154644)))]]], (19285 ^ _784416) ^ [_1154923, _1154925, _1154927] : [class_Groups_Oordered__ab__group__add(_1154923), 19288 ^ _784416 : [(19289 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154923), _1154925), _1154927)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154923), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1154923), _1154925), _1154927)), c_Groups_Ozero__class_Ozero(_1154923))))], (19295 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154923), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1154923), _1154925), _1154927)), c_Groups_Ozero__class_Ozero(_1154923))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154923), _1154925), _1154927)))]]], (19301 ^ _784416) ^ [_1155206, _1155208, _1155210, _1155212, _1155214, _1155216] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1155206), -(_1155208 = c_Groups_Ozero__class_Ozero(_1155206)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155206), _1155210), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155206), _1155208), _1155214)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155206), _1155212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155206), _1155208), _1155216)), _1155210 = _1155212, -(_1155214 = _1155216)], (19319 ^ _784416) ^ [_1155544] : [class_Rings_Olinordered__semidom(_1155544), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155544), c_Groups_Ozero__class_Ozero(_1155544)), c_Groups_Oone__class_Oone(_1155544))))], (19325 ^ _784416) ^ [_1155639] : [class_Rings_Olinordered__semidom(_1155639), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155639), c_Groups_Oone__class_Oone(_1155639)), c_Groups_Ozero__class_Ozero(_1155639)))], (19331 ^ _784416) ^ [_1155735] : [class_Rings_Olinordered__semidom(_1155735), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155735), c_Groups_Ozero__class_Ozero(_1155735)), c_Groups_Oone__class_Oone(_1155735))))], (19337 ^ _784416) ^ [_1155830] : [class_Rings_Olinordered__semidom(_1155830), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155830), c_Groups_Oone__class_Oone(_1155830)), c_Groups_Ozero__class_Ozero(_1155830)))], (19343 ^ _784416) ^ [_1155926, _1155928] : [class_Groups_Olinordered__ab__group__add(_1155926), 19346 ^ _784416 : [(19347 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155926), hAPP(c_Groups_Ouminus__class_Ouminus(_1155926), _1155928)), _1155928)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155926), c_Groups_Ozero__class_Ozero(_1155926)), _1155928)))], (19353 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155926), c_Groups_Ozero__class_Ozero(_1155926)), _1155928)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155926), hAPP(c_Groups_Ouminus__class_Ouminus(_1155926), _1155928)), _1155928)))]]], (19359 ^ _784416) ^ [_1156194, _1156196] : [class_Groups_Oordered__ab__group__add(_1156194), 19362 ^ _784416 : [(19363 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156194), hAPP(c_Groups_Ouminus__class_Ouminus(_1156194), _1156196)), c_Groups_Ozero__class_Ozero(_1156194))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156194), c_Groups_Ozero__class_Ozero(_1156194)), _1156196)))], (19369 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156194), c_Groups_Ozero__class_Ozero(_1156194)), _1156196)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156194), hAPP(c_Groups_Ouminus__class_Ouminus(_1156194), _1156196)), c_Groups_Ozero__class_Ozero(_1156194))))]]], (19375 ^ _784416) ^ [_1156468, _1156470] : [class_Groups_Olinordered__ab__group__add(_1156468), 19378 ^ _784416 : [(19379 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156468), _1156470), hAPP(c_Groups_Ouminus__class_Ouminus(_1156468), _1156470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156468), _1156470), c_Groups_Ozero__class_Ozero(_1156468))))], (19385 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156468), _1156470), c_Groups_Ozero__class_Ozero(_1156468))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156468), _1156470), hAPP(c_Groups_Ouminus__class_Ouminus(_1156468), _1156470))))]]], (19391 ^ _784416) ^ [_1156736, _1156738] : [class_Groups_Oordered__ab__group__add(_1156736), 19394 ^ _784416 : [(19395 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156736), c_Groups_Ozero__class_Ozero(_1156736)), hAPP(c_Groups_Ouminus__class_Ouminus(_1156736), _1156738))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156736), _1156738), c_Groups_Ozero__class_Ozero(_1156736))))], (19401 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156736), _1156738), c_Groups_Ozero__class_Ozero(_1156736))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156736), c_Groups_Ozero__class_Ozero(_1156736)), hAPP(c_Groups_Ouminus__class_Ouminus(_1156736), _1156738))))]]], (19407 ^ _784416) ^ [_1157010, _1157012] : [class_Groups_Olinordered__ab__group__add(_1157010), 19410 ^ _784416 : [(19411 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157010), hAPP(c_Groups_Ouminus__class_Ouminus(_1157010), _1157012)), _1157012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157010), c_Groups_Ozero__class_Ozero(_1157010)), _1157012)))], (19417 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157010), c_Groups_Ozero__class_Ozero(_1157010)), _1157012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157010), hAPP(c_Groups_Ouminus__class_Ouminus(_1157010), _1157012)), _1157012)))]]], (19423 ^ _784416) ^ [_1157278, _1157280] : [class_Groups_Oordered__ab__group__add(_1157278), 19426 ^ _784416 : [(19427 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157278), hAPP(c_Groups_Ouminus__class_Ouminus(_1157278), _1157280)), c_Groups_Ozero__class_Ozero(_1157278))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157278), c_Groups_Ozero__class_Ozero(_1157278)), _1157280)))], (19433 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157278), c_Groups_Ozero__class_Ozero(_1157278)), _1157280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157278), hAPP(c_Groups_Ouminus__class_Ouminus(_1157278), _1157280)), c_Groups_Ozero__class_Ozero(_1157278))))]]], (19439 ^ _784416) ^ [_1157552, _1157554] : [class_Groups_Oordered__ab__group__add(_1157552), 19442 ^ _784416 : [(19443 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157552), c_Groups_Ozero__class_Ozero(_1157552)), hAPP(c_Groups_Ouminus__class_Ouminus(_1157552), _1157554))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157552), _1157554), c_Groups_Ozero__class_Ozero(_1157552))))], (19449 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157552), _1157554), c_Groups_Ozero__class_Ozero(_1157552))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157552), c_Groups_Ozero__class_Ozero(_1157552)), hAPP(c_Groups_Ouminus__class_Ouminus(_1157552), _1157554))))]]], (19455 ^ _784416) ^ [_1157826, _1157828] : [class_Rings_Olinordered__idom(_1157826), 19458 ^ _784416 : [(19459 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157826), _1157828), hAPP(c_Groups_Ouminus__class_Ouminus(_1157826), _1157828))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157826), _1157828), c_Groups_Ozero__class_Ozero(_1157826))))], (19465 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157826), _1157828), c_Groups_Ozero__class_Ozero(_1157826))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157826), _1157828), hAPP(c_Groups_Ouminus__class_Ouminus(_1157826), _1157828))))]]], (19471 ^ _784416) ^ [_1158094, _1158096] : [class_Groups_Olinordered__ab__group__add(_1158094), hBOOL(hAPP(c_Finite__Set_Ofinite(_1158094), _1158096)), -(_1158096 = c_Orderings_Obot__class_Obot(tc_fun(_1158094, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1158094), c_Big__Operators_Olinorder__class_OMin(_1158094, _1158096)) = c_Big__Operators_Olinorder__class_OMax(_1158094, hAPP(c_Set_Oimage(_1158094, _1158094, c_Groups_Ouminus__class_Ouminus(_1158094)), _1158096)))], (19485 ^ _784416) ^ [_1158294, _1158296] : [class_Groups_Olinordered__ab__group__add(_1158294), hBOOL(hAPP(c_Finite__Set_Ofinite(_1158294), _1158296)), -(_1158296 = c_Orderings_Obot__class_Obot(tc_fun(_1158294, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1158294), c_Big__Operators_Olinorder__class_OMax(_1158294, _1158296)) = c_Big__Operators_Olinorder__class_OMin(_1158294, hAPP(c_Set_Oimage(_1158294, _1158294, c_Groups_Ouminus__class_Ouminus(_1158294)), _1158296)))], (19499 ^ _784416) ^ [_1158494, _1158496] : [class_Groups_Ogroup__add(_1158494), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1158494), _1158496), hAPP(c_Groups_Ouminus__class_Ouminus(_1158494), _1158496)) = c_Groups_Ozero__class_Ozero(_1158494))], (19505 ^ _784416) ^ [_1158599, _1158601, _1158603] : [class_Groups_Ogroup__add(_1158599), 19508 ^ _784416 : [(19509 ^ _784416) ^ [] : [_1158601 = hAPP(c_Groups_Ouminus__class_Ouminus(_1158599), _1158603), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1158599), _1158601), _1158603) = c_Groups_Ozero__class_Ozero(_1158599))], (19515 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1158599), _1158601), _1158603) = c_Groups_Ozero__class_Ozero(_1158599), -(_1158601 = hAPP(c_Groups_Ouminus__class_Ouminus(_1158599), _1158603))]]], (19521 ^ _784416) ^ [_1158855, _1158857] : [class_Groups_Ogroup__add(_1158855), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1158855), hAPP(c_Groups_Ouminus__class_Ouminus(_1158855), _1158857)), _1158857) = c_Groups_Ozero__class_Ozero(_1158855))], (19527 ^ _784416) ^ [_1158960, _1158962] : [class_Groups_Oab__group__add(_1158960), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1158960), hAPP(c_Groups_Ouminus__class_Ouminus(_1158960), _1158962)), _1158962) = c_Groups_Ozero__class_Ozero(_1158960))], (19533 ^ _784416) ^ [_1159065, _1159067, _1159069] : [class_Groups_Ogroup__add(_1159065), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1159065), _1159067), _1159069) = c_Groups_Ozero__class_Ozero(_1159065), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1159065), _1159067) = _1159069)], (19543 ^ _784416) ^ [_1159226, _1159228] : [class_Groups_Ogroup__add(_1159226), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1159226), c_Groups_Ozero__class_Ozero(_1159226)), _1159228) = hAPP(c_Groups_Ouminus__class_Ouminus(_1159226), _1159228))], (19549 ^ _784416) ^ [_1159346, _1159348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1159346), hAPP(c_Nat_OSuc, _1159348))), -(_1159346 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 19557 ^ _784416 : [(19558 ^ _784416) ^ [] : [-(_1159346 = hAPP(c_Nat_OSuc, 19556 ^ [_1159346, _1159348]))], (19560 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19556 ^ [_1159346, _1159348]), _1159348)))]]], (19562 ^ _784416) ^ [_1159526, _1159528] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1159526), hAPP(c_Nat_OSuc, _1159528)))), 19563 ^ _784416 : [(19564 ^ _784416) ^ [] : [_1159526 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19566 ^ _784416) ^ [_1159614] : [_1159526 = hAPP(c_Nat_OSuc, _1159614), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1159614), _1159528))]]], (19574 ^ _784416) ^ [_1159760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1159760), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1159760 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19580 ^ _784416) ^ [_1159841] : [_1159841 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1159841), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (19586 ^ _784416) ^ [_1159940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1159940)), -(_1159940 = hAPP(c_Nat_OSuc, 19589 ^ [_1159940]))], (19593 ^ _784416) ^ [_1160031] : [19594 ^ _784416 : [(19595 ^ _784416) ^ [_1160073] : [_1160031 = hAPP(c_Nat_OSuc, _1160073)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1160031)))], (19599 ^ _784416) ^ [_1160146, _1160148] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160146), _1160148), 19604 ^ _784416 : [(19605 ^ _784416) ^ [] : [-(_1160146 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19607 ^ _784416) ^ [] : [-(_1160148 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 19608 ^ _784416 : [(19609 ^ _784416) ^ [] : [-(_1160146 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19611 ^ _784416) ^ [] : [-(_1160148 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (19613 ^ _784416) ^ [_1160330, _1160332] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160330), _1160332)), 19614 ^ _784416 : [(19615 ^ _784416) ^ [] : [_1160330 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1160332 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19621 ^ _784416) ^ [] : [_1160330 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1160332 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (19629 ^ _784416) ^ [_1160571, _1160573] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160571), _1160573) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 19634 ^ _784416 : [(19635 ^ _784416) ^ [] : [-(_1160571 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19637 ^ _784416) ^ [] : [-(_1160573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 19638 ^ _784416 : [(19639 ^ _784416) ^ [] : [-(_1160571 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19641 ^ _784416) ^ [] : [-(_1160573 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (19643 ^ _784416) ^ [_1160755, _1160757] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160755), _1160757) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 19644 ^ _784416 : [(19645 ^ _784416) ^ [] : [_1160755 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1160757 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19651 ^ _784416) ^ [] : [_1160755 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1160757 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (19669 ^ _784416) ^ [_1161106, _1161108] : [19670 ^ _784416 : [(19671 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161106))], (19673 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161108))]], -(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), _1161106), _1161108))))], (19659 ^ _784416) ^ [_1160996, _1160998] : [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), _1160996), _1160998))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1160996))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1160998)))], (19677 ^ _784416) ^ [_1161247] : [-(hAPP(c_Finite__Set_Ocard(_1161247), c_Orderings_Obot__class_Obot(tc_fun(_1161247, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19679 ^ _784416) ^ [_1161276, _1161278] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1161276), _1161278))), -(hAPP(c_Finite__Set_Ocard(_1161276), _1161278) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19685 ^ _784416) ^ [_1161336, _1161338] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161336), _1161338) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 19688 ^ _784416 : [(19689 ^ _784416) ^ [] : [-(_1161336 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19691 ^ _784416) ^ [] : [-(_1161338 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (19693 ^ _784416) ^ [_1161447, _1161449] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161447), _1161449) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1161447 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161449 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19703 ^ _784416) ^ [_1161605, _1161607] : [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), _1161605), _1161607))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1161607), _1161605)))], (19709 ^ _784416) ^ [_1161704, _1161706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1161706), _1161704)), -(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), _1161704), _1161706))))], (19715 ^ _784416) ^ [_1161809, _1161811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161809)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161811)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1161811), _1161809)), _1161811)))], (19725 ^ _784416) ^ [_1161968, _1161970, _1161972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1161968), _1161970)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161972)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161972), _1161968)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161972), _1161970))))], (19735 ^ _784416) ^ [_1162149, _1162151, _1162153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162149), _1162151)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162149), _1162153)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162151), _1162153))))], (19745 ^ _784416) ^ [_1162348, _1162350, _1162352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162348), _1162350)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162352), _1162350))), 19748 ^ _784416 : [(19749 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162350)))], (19751 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162348), _1162352)))]]], (19753 ^ _784416) ^ [_1162497, _1162499, _1162501] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162497), _1162499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162501), _1162499)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162499)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162497), _1162501))], (19763 ^ _784416) ^ [_1162698, _1162700, _1162702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162698), _1162700)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162698), _1162702))), 19766 ^ _784416 : [(19767 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162698)))], (19769 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162700), _1162702)))]]], (19771 ^ _784416) ^ [_1162847, _1162849, _1162851] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162847), _1162849)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162847), _1162851)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162847)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1162849), _1162851))], (19781 ^ _784416) ^ [_1163045, _1163047] : [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), _1163045), _1163047))), 19784 ^ _784416 : [(19785 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1163045)))], (19787 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1163047)))]]], (19789 ^ _784416) ^ [_1163168, _1163170] : [-(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), _1163168), _1163170)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1163168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1163170))], (19799 ^ _784416) ^ [_1163323, _1163325, _1163327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1163323)), 19802 ^ _784416 : [(19803 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163323), _1163325)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163323), _1163327))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1163325), _1163327)))], (19809 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1163325), _1163327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163323), _1163325)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163323), _1163327))))]]], (19815 ^ _784416) ^ [_1163606, _1163608, _1163610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1163606)), 19818 ^ _784416 : [(19819 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163606), _1163608) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163606), _1163610), -(_1163608 = _1163610)], (19825 ^ _784416) ^ [] : [_1163608 = _1163610, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163606), _1163608) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163606), _1163610))]]], (19831 ^ _784416) ^ [_1163859, _1163861] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1163859), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1163859), _1163861)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19833 ^ _784416) ^ [_1163911, _1163913] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1163911), _1163913) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1163911), _1163913)))], (19839 ^ _784416) ^ [_1164006, _1164008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1164006), _1164008)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1164006), _1164008) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19845 ^ _784416) ^ [_1164107, _1164109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1164107), _1164109)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1164107), _1164109) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19851 ^ _784416) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (19853 ^ _784416) ^ [_1164224, _1164226] : [class_Orderings_Olinorder(_1164224), -(c_Big__Operators_Olinorder__class_OMax(_1164224, hAPP(hAPP(c_Set_Oinsert(_1164224), _1164226), c_Orderings_Obot__class_Obot(tc_fun(_1164224, tc_HOL_Obool)))) = _1164226)], (19859 ^ _784416) ^ [_1164331, _1164333] : [class_Orderings_Olinorder(_1164331), -(c_Big__Operators_Olinorder__class_OMin(_1164331, hAPP(hAPP(c_Set_Oinsert(_1164331), _1164333), c_Orderings_Obot__class_Obot(tc_fun(_1164331, tc_HOL_Obool)))) = _1164333)], (19865 ^ _784416) ^ [_1164438, _1164440] : [_1164438 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1164438), _1164440), -(_1164440 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1164438 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19875 ^ _784416) ^ [_1164540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1164540)), -(_1164540 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1164540), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (19881 ^ _784416) ^ [_1164646, _1164648] : [_1164646 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1164646), _1164648) = _1164648)], (19887 ^ _784416) ^ [_1164729, _1164731] : [-(_1164729 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1164729), _1164731) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1164729), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1164731)))], (19893 ^ _784416) ^ [_1164788, _1164790, _1164792] : [class_Groups_Oordered__comm__monoid__add(_1164788), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164788), c_Groups_Ozero__class_Ozero(_1164788)), _1164790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164788), c_Groups_Ozero__class_Ozero(_1164788)), _1164792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164788), c_Groups_Ozero__class_Ozero(_1164788)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164788), _1164790), _1164792))))], (19907 ^ _784416) ^ [_1165043, _1165045, _1165047] : [class_Groups_Oordered__comm__monoid__add(_1165043), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165043), c_Groups_Ozero__class_Ozero(_1165043)), _1165045)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165043), c_Groups_Ozero__class_Ozero(_1165043)), _1165047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165043), c_Groups_Ozero__class_Ozero(_1165043)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165043), _1165045), _1165047))))], (19921 ^ _784416) ^ [_1165298, _1165300, _1165302, _1165304] : [class_Groups_Oordered__comm__monoid__add(_1165298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165298), c_Groups_Ozero__class_Ozero(_1165298)), _1165300)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165298), _1165302), _1165304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165298), _1165302), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165298), _1165300), _1165304))))], (19935 ^ _784416) ^ [_1165551, _1165553, _1165555, _1165557] : [class_Groups_Oordered__comm__monoid__add(_1165551), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165551), c_Groups_Ozero__class_Ozero(_1165551)), _1165553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165551), _1165555), _1165557)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165551), _1165555), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165551), _1165553), _1165557))))], (19949 ^ _784416) ^ [_1165804, _1165806, _1165808] : [class_Groups_Oordered__comm__monoid__add(_1165804), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165804), _1165806), c_Groups_Ozero__class_Ozero(_1165804))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165804), _1165808), c_Groups_Ozero__class_Ozero(_1165804))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165804), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165804), _1165806), _1165808)), c_Groups_Ozero__class_Ozero(_1165804))))], (19963 ^ _784416) ^ [_1166059, _1166061, _1166063] : [class_Groups_Oordered__comm__monoid__add(_1166059), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166059), _1166061), c_Groups_Ozero__class_Ozero(_1166059))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166059), _1166063), c_Groups_Ozero__class_Ozero(_1166059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166059), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166059), _1166061), _1166063)), c_Groups_Ozero__class_Ozero(_1166059))))], (19977 ^ _784416) ^ [_1166314, _1166316, _1166318, _1166320] : [class_Rings_Olinordered__ring__strict(_1166314), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166314), c_Groups_Ozero__class_Ozero(_1166314)), _1166316)), 19984 ^ _784416 : [(19985 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166314), _1166316), _1166318)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166314), _1166316), _1166320))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166314), _1166318), _1166320)))], (19991 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166314), _1166318), _1166320)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166314), _1166316), _1166318)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166314), _1166316), _1166320))))]]], (19997 ^ _784416) ^ [_1166695, _1166697, _1166699, _1166701] : [class_Rings_Olinordered__ring__strict(_1166695), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166695), _1166697), c_Groups_Ozero__class_Ozero(_1166695))), 20004 ^ _784416 : [(20005 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166695), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166695), _1166697), _1166699)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166695), _1166697), _1166701))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166695), _1166701), _1166699)))], (20011 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166695), _1166701), _1166699)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166695), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166695), _1166697), _1166699)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166695), _1166697), _1166701))))]]], (20017 ^ _784416) ^ [_1167076, _1167078, _1167080, _1167082, _1167084] : [class_Rings_Olinordered__semiring__strict(_1167076), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167076), _1167078), _1167080)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167076), _1167082), _1167084)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167076), c_Groups_Ozero__class_Ozero(_1167076)), _1167080)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167076), c_Groups_Ozero__class_Ozero(_1167076)), _1167082)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167076), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167076), _1167078), _1167082)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167076), _1167080), _1167084))))], (20039 ^ _784416) ^ [_1167499, _1167501, _1167503, _1167505, _1167507] : [class_Rings_Olinordered__semiring__strict(_1167499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167499), _1167501), _1167503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167499), _1167505), _1167507)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167499), c_Groups_Ozero__class_Ozero(_1167499)), _1167501)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167499), c_Groups_Ozero__class_Ozero(_1167499)), _1167505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167499), _1167501), _1167505)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167499), _1167503), _1167507))))], (20061 ^ _784416) ^ [_1167922, _1167924, _1167926, _1167928, _1167930] : [class_Rings_Olinordered__semiring__strict(_1167922), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167922), _1167924), _1167926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167922), _1167928), _1167930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167922), c_Groups_Ozero__class_Ozero(_1167922)), _1167924)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167922), c_Groups_Ozero__class_Ozero(_1167922)), _1167928)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167922), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167922), _1167924), _1167928)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167922), _1167926), _1167930))))], (20083 ^ _784416) ^ [_1168345, _1168347, _1168349, _1168351, _1168353] : [class_Rings_Olinordered__semiring__strict(_1168345), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168345), _1168347), _1168349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168345), _1168351), _1168353)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168345), c_Groups_Ozero__class_Ozero(_1168345)), _1168347)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168345), c_Groups_Ozero__class_Ozero(_1168345)), _1168351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168345), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168345), _1168347), _1168351)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168345), _1168349), _1168353))))], (20105 ^ _784416) ^ [_1168768, _1168770, _1168772, _1168774] : [class_Rings_Olinordered__semiring(_1168768), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168768), _1168770), _1168772)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168768), _1168774), _1168772))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168768), c_Groups_Ozero__class_Ozero(_1168768)), _1168772)), 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hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1173715)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1173717))], (20399 ^ _784416) ^ [_1174065, _1174067, _1174069] : [20400 ^ _784416 : [(20401 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174065)))], (20403 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1174067), _1174069))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174065), _1174067)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174065), _1174069))))], (20389 ^ _784416) ^ [_1173888, _1173890, _1173892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 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[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1174586), _1174588)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174584), _1174586)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174584), _1174588))))]]], (20441 ^ _784416) ^ [_1174867, _1174869, _1174871] : [class_Orderings_Olinorder(_1174867), hBOOL(hAPP(c_Finite__Set_Ofinite(_1174867), _1174869)), hBOOL(hAPP(hAPP(c_member(_1174867), _1174871), _1174869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1174867), c_Big__Operators_Olinorder__class_OMin(_1174867, _1174869)), _1174871)))], (20455 ^ _784416) ^ [_1175094, _1175096, _1175098] : [class_Orderings_Olinorder(_1175094), hBOOL(hAPP(c_Finite__Set_Ofinite(_1175094), _1175096)), hBOOL(hAPP(hAPP(c_member(_1175094), _1175098), _1175096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1175094), _1175098), c_Big__Operators_Olinorder__class_OMax(_1175094, _1175096))))], (20469 ^ _784416) ^ [_1175321, _1175323] : [class_Orderings_Olinorder(_1175321), hBOOL(hAPP(c_Finite__Set_Ofinite(_1175321), _1175323)), -(_1175323 = c_Orderings_Obot__class_Obot(tc_fun(_1175321, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1175321), c_Big__Operators_Olinorder__class_OMax(_1175321, _1175323)), _1175323)))], (20483 ^ _784416) ^ [_1175501, _1175503] : [class_Orderings_Olinorder(_1175501), hBOOL(hAPP(c_Finite__Set_Ofinite(_1175501), _1175503)), -(_1175503 = c_Orderings_Obot__class_Obot(tc_fun(_1175501, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1175501), c_Big__Operators_Olinorder__class_OMin(_1175501, _1175503)), _1175503)))], (20497 ^ _784416) ^ [_1175677, _1175679] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175677))), -(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)), _1175677))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1175679)))) = 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)), _1175677))), 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, _1175679))))))], (20503 ^ _784416) ^ [_1175760, _1175762] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175760)), 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)), _1175760))), 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, _1175762))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20509 ^ _784416) ^ [_1175890, _1175892] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175890)), -(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)), _1175890))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1175892))))) = 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)), _1175890))), 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, _1175892))))))], (20515 ^ _784416) ^ [_1176067, _1176069, _1176071, _1176073, _1176075, _1176077] : [class_Rings_Olinordered__semiring__1(_1176067), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176067), _1176069), _1176071)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176067), _1176073), _1176071)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176067), c_Groups_Ozero__class_Ozero(_1176067)), _1176075)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176067), c_Groups_Ozero__class_Ozero(_1176067)), _1176077)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176067), _1176075), _1176077) = c_Groups_Oone__class_Oone(_1176067), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176067), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176067), _1176075), _1176069)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1176067), _1176077), _1176073))), _1176071)))], (20541 ^ _784416) ^ [_1176611, _1176613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1176611), _1176613))), 20544 ^ _784416 : [(20545 ^ _784416) ^ [] : [_1176613 = c_Orderings_Obot__class_Obot(tc_fun(_1176611, tc_HOL_Obool))], (20547 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1176611), _1176613)))]]], (20549 ^ _784416) ^ [_1176752, _1176754] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1176752), _1176754)))), -(_1176754 = c_Orderings_Obot__class_Obot(tc_fun(_1176752, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1176752), _1176754))], (20559 ^ _784416) ^ [_1176918] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1176918), c_Orderings_Otop__class_Otop(tc_fun(_1176918, 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(_1176918), c_Orderings_Otop__class_Otop(tc_fun(_1176918, tc_HOL_Obool))))))], (20565 ^ _784416) ^ [_1177035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1177035)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1177035), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1177035)], (20571 ^ _784416) ^ [_1177132, _1177134, _1177136] : [class_Orderings_Olinorder(_1177132), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1177132, tc_HOL_Obool)), _1177134), _1177136)), -(_1177134 = c_Orderings_Obot__class_Obot(tc_fun(_1177132, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1177132), _1177136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177132), c_Big__Operators_Olinorder__class_OMax(_1177132, _1177134)), c_Big__Operators_Olinorder__class_OMax(_1177132, _1177136))))], (20589 ^ _784416) ^ [_1177438, _1177440, _1177442] : [class_Orderings_Olinorder(_1177438), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1177438, tc_HOL_Obool)), _1177440), _1177442)), -(_1177440 = c_Orderings_Obot__class_Obot(tc_fun(_1177438, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1177438), _1177442)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177438), c_Big__Operators_Olinorder__class_OMin(_1177438, _1177442)), c_Big__Operators_Olinorder__class_OMin(_1177438, _1177440))))], (20607 ^ _784416) ^ [_1177753, _1177755] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1177753), _1177755)), -(hAPP(c_Finite__Set_Ocard(_1177753), _1177755) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1177753, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1177753), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1177755))], (20613 ^ _784416) ^ [_1177880, _1177882] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1177880), _1177882))), -(hAPP(c_Finite__Set_Ocard(_1177880), _1177882) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20619 ^ _784416) ^ [_1177927, _1177929] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1177927), _1177929)), -(hAPP(c_Finite__Set_Ocard(_1177927), _1177929) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1177927, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1177927), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1177929))], (20625 ^ _784416) ^ [_1178060, _1178062, _1178064, _1178066, _1178068, _1178070] : [class_Rings_Olinordered__semiring__1__strict(_1178060), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178060), _1178062), _1178064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178060), _1178066), _1178064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178060), c_Groups_Ozero__class_Ozero(_1178060)), _1178068)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178060), c_Groups_Ozero__class_Ozero(_1178060)), _1178070)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178060), _1178068), _1178070) = c_Groups_Oone__class_Oone(_1178060), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178060), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178060), _1178068), _1178062)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178060), _1178070), _1178066))), _1178064)))], (20651 ^ _784416) ^ [_1178589, _1178591] : [class_Rings_Olinordered__idom(_1178589), 20654 ^ _784416 : [(20655 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178589), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178589), _1178591), _1178591)), c_Groups_Ozero__class_Ozero(_1178589))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178589), _1178591), c_Groups_Ozero__class_Ozero(_1178589))))], (20661 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178589), _1178591), c_Groups_Ozero__class_Ozero(_1178589))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178589), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178589), _1178591), _1178591)), c_Groups_Ozero__class_Ozero(_1178589))))]]], (20667 ^ _784416) ^ [_1178872, _1178874, _1178876] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1178872), _1178874)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1178872), _1178876)), 20677 ^ _784416 : [(20678 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1178872), 20676 ^ [_1178872, _1178874, _1178876]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1178872, tc_HOL_Obool)), _1178874), _1178876))))], (20680 ^ _784416) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1178872), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1178872, tc_HOL_Obool)), _1178874), _1178876)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1178872), _1178874)), hAPP(c_Finite__Set_Ocard(_1178872), _1178876)))], (20684 ^ _784416) ^ [_1179234, _1179236, _1179238] : [hAPP(c_Finite__Set_Ocard(_1179234), _1179236) = hAPP(c_Nat_OSuc, _1179238), 20689 ^ _784416 : [(20690 ^ _784416) ^ [] : [-(_1179236 = hAPP(hAPP(c_Set_Oinsert(_1179234), 20687 ^ [_1179234, _1179236, _1179238]), 20688 ^ [_1179234, _1179236, _1179238]))], (20692 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1179234), 20687 ^ [_1179234, _1179236, _1179238]), 20688 ^ [_1179234, _1179236, _1179238]))], (20694 ^ _784416) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1179234), 20688 ^ [_1179234, _1179236, _1179238]) = _1179238)], (20696 ^ _784416) ^ [] : [_1179238 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(20688 ^ [_1179234, _1179236, _1179238] = c_Orderings_Obot__class_Obot(tc_fun(_1179234, tc_HOL_Obool)))]]], (20702 ^ _784416) ^ [_1179652, _1179654, _1179656] : [-(hAPP(c_Finite__Set_Ocard(_1179652), _1179654) = hAPP(c_Nat_OSuc, _1179656)), 20703 ^ _784416 : [(20704 ^ _784416) ^ [_1179752, _1179754] : [_1179654 = hAPP(hAPP(c_Set_Oinsert(_1179652), _1179754), _1179752), -(hBOOL(hAPP(hAPP(c_member(_1179652), _1179754), _1179752))), hAPP(c_Finite__Set_Ocard(_1179652), _1179752) = _1179656, 20715 ^ _784416 : [(20716 ^ _784416) ^ [] : [-(_1179656 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20718 ^ _784416) ^ [] : [_1179752 = c_Orderings_Obot__class_Obot(tc_fun(_1179652, tc_HOL_Obool))]]]]], (20722 ^ _784416) ^ [_1180074, _1180076, _1180078] : [-(c_Option_Ooption_Ooption__size(_1180074, _1180076, hAPP(c_Option_Ooption_OSome(_1180074), _1180078)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1180076, _1180078)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20724 ^ _784416) ^ [_1180119, _1180121] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1180119), _1180121)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1180119, tc_HOL_Obool)), hAPP(c_Set_OPow(_1180119), _1180121)) = 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(_1180119), _1180121)))], (20730 ^ _784416) ^ [_1180246, _1180248] : [class_Groups_Olinordered__ab__group__add(_1180246), 20733 ^ _784416 : [(20734 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180246), _1180248), _1180248) = c_Groups_Ozero__class_Ozero(_1180246), -(_1180248 = c_Groups_Ozero__class_Ozero(_1180246))], (20740 ^ _784416) ^ [] : [_1180248 = c_Groups_Ozero__class_Ozero(_1180246), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180246), _1180248), _1180248) = c_Groups_Ozero__class_Ozero(_1180246))]]], (20756 ^ _784416) ^ [_1180707, _1180709, _1180711, _1180713] : [20757 ^ _784416 : [(20758 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1180707), _1180709)))], (20760 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1180711), _1180713)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1180707, _1180711)), c_Sum__Type_OPlus(_1180707, _1180711, _1180709, _1180713)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20746 ^ _784416) ^ [_1180502, _1180504, _1180506, _1180508] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1180502, _1180506)), c_Sum__Type_OPlus(_1180502, _1180506, _1180504, _1180508)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1180502), _1180504)), hAPP(c_Finite__Set_Ocard(_1180506), _1180508))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1180502), _1180504)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1180506), _1180508))], (20764 ^ _784416) ^ [_1180807, _1180809, _1180811, _1180813] : [class_Rings_Ocomm__semiring__1(_1180807), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1180807), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180807), _1180809), _1180811)), _1180813) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180807), hAPP(hAPP(c_Power_Opower__class_Opower(_1180807), _1180809), _1180813)), hAPP(hAPP(c_Power_Opower__class_Opower(_1180807), _1180811), _1180813)))], (20770 ^ _784416) ^ [_1180966, _1180968, _1180970, _1180972] : [class_Rings_Ocomm__semiring__1(_1180966), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1180966), hAPP(hAPP(c_Power_Opower__class_Opower(_1180966), _1180968), _1180970)), _1180972) = hAPP(hAPP(c_Power_Opower__class_Opower(_1180966), _1180968), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1180970), _1180972)))], (20776 ^ _784416) ^ [_1181105, _1181107] : [class_Rings_Ocomm__semiring__1(_1181105), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1181105), _1181107), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1181107)], (20782 ^ _784416) ^ [_1181196, _1181198, _1181200] : [class_Rings_Ocomm__semiring__1(_1181196), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1181196), _1181198), hAPP(c_Nat_OSuc, _1181200)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181196), _1181198), hAPP(hAPP(c_Power_Opower__class_Opower(_1181196), _1181198), _1181200)))], (20788 ^ _784416) ^ [_1181327, _1181329, _1181331] : [class_Rings_Ocomm__semiring__1(_1181327), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181327), _1181329), hAPP(hAPP(c_Power_Opower__class_Opower(_1181327), _1181329), _1181331)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1181327), _1181329), hAPP(c_Nat_OSuc, _1181331)))], (20794 ^ _784416) ^ [_1181458, _1181460, _1181462] : [class_Rings_Ocomm__semiring__1(_1181458), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181458), hAPP(hAPP(c_Power_Opower__class_Opower(_1181458), _1181460), _1181462)), _1181460) = hAPP(hAPP(c_Power_Opower__class_Opower(_1181458), _1181460), hAPP(c_Nat_OSuc, _1181462)))], (20800 ^ _784416) ^ [_1181589, _1181591] : [class_Rings_Ocomm__semiring__1(_1181589), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1181589), _1181591), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1181589))], (20806 ^ _784416) ^ [_1181684, _1181686, _1181688, _1181690] : [class_Rings_Ocomm__semiring__1(_1181684), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181684), hAPP(hAPP(c_Power_Opower__class_Opower(_1181684), _1181686), _1181688)), hAPP(hAPP(c_Power_Opower__class_Opower(_1181684), _1181686), _1181690)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1181684), _1181686), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1181688), _1181690)))], (20812 ^ _784416) ^ [_1181839, _1181841] : [-(c_Option_Ooption_Ooption__size(_1181839, _1181841, c_Option_Ooption_ONone(_1181839)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20814 ^ _784416) ^ [_1181879, _1181881] : [_1181879 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1181881), _1181879) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20820 ^ _784416) ^ [_1181962, _1181964] : [-(_1181962 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1181964), _1181962) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1181964), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1181964), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1181962), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (20826 ^ _784416) ^ [_1182024, _1182026, _1182028, _1182030] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1182024, _1182026)), c_Sum__Type_OPlus(_1182024, _1182026, _1182028, _1182030))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1182026), _1182030)))], (20832 ^ _784416) ^ [_1182137, _1182139, _1182141, _1182143] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1182137, _1182139)), c_Sum__Type_OPlus(_1182137, _1182139, _1182141, _1182143))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1182137), _1182141)))], (20838 ^ _784416) ^ [_1182250, _1182252, _1182254, _1182256] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1182250), _1182252)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1182254), _1182256)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1182250, _1182254)), c_Sum__Type_OPlus(_1182250, _1182254, _1182252, _1182256))))], (20848 ^ _784416) ^ [_1182448, _1182450, _1182452, _1182454] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1182448, _1182450)), c_Sum__Type_OPlus(_1182448, _1182450, _1182452, _1182454))), 20851 ^ _784416 : [(20852 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1182448), _1182452)))], (20854 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1182450), _1182454)))]]], (20856 ^ _784416) ^ [_1182591, _1182593, _1182595, _1182597] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1182591, _1182593)), c_Sum__Type_OPlus(_1182591, _1182593, _1182595, _1182597)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1182591), _1182595)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1182593), _1182597))], (20866 ^ _784416) ^ [_1182770, _1182772, _1182774, _1182776] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1182770), _1182772)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1182774), _1182776)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1182770, _1182774)), c_Sum__Type_OPlus(_1182770, _1182774, _1182772, _1182776)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1182770), _1182772)), hAPP(c_Finite__Set_Ocard(_1182774), _1182776)))], (20876 ^ _784416) ^ [_1182981, _1182983, _1182985, _1182987] : [class_Rings_Olinordered__semidom(_1182981), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182981), _1182983), _1182985)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182981), c_Groups_Ozero__class_Ozero(_1182981)), _1182983)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1182987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182981), hAPP(hAPP(c_Power_Opower__class_Opower(_1182981), _1182983), _1182987)), hAPP(hAPP(c_Power_Opower__class_Opower(_1182981), _1182985), _1182987))))], (20894 ^ _784416) ^ [_1183310, _1183312, _1183314] : [class_Rings_Olinordered__semidom(_1183310), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183310), c_Groups_Oone__class_Oone(_1183310)), _1183312)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1183314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183310), c_Groups_Oone__class_Oone(_1183310)), hAPP(hAPP(c_Power_Opower__class_Opower(_1183310), _1183312), _1183314))))], (20908 ^ _784416) ^ [_1183551, _1183553, _1183555, _1183557] : [class_Rings_Olinordered__semidom(_1183551), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183551), c_Groups_Oone__class_Oone(_1183551)), _1183553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183551), hAPP(hAPP(c_Power_Opower__class_Opower(_1183551), _1183553), _1183555)), hAPP(hAPP(c_Power_Opower__class_Opower(_1183551), _1183553), _1183557))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1183555), _1183557)))], (20922 ^ _784416) ^ [_1183816, _1183818, _1183820, _1183822] : [class_Rings_Olinordered__semidom(_1183816), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183816), c_Groups_Oone__class_Oone(_1183816)), _1183818)), 20929 ^ _784416 : [(20930 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183816), hAPP(hAPP(c_Power_Opower__class_Opower(_1183816), _1183818), _1183820)), hAPP(hAPP(c_Power_Opower__class_Opower(_1183816), _1183818), _1183822))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1183820), _1183822)))], (20936 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1183820), _1183822)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183816), hAPP(hAPP(c_Power_Opower__class_Opower(_1183816), _1183818), _1183820)), hAPP(hAPP(c_Power_Opower__class_Opower(_1183816), _1183818), _1183822))))]]], (20942 ^ _784416) ^ [_1184191, _1184193, _1184195, _1184197] : [class_Rings_Olinordered__semidom(_1184191), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1184193), _1184195)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184191), c_Groups_Ozero__class_Ozero(_1184191)), _1184197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184191), _1184197), c_Groups_Oone__class_Oone(_1184191))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184191), hAPP(hAPP(c_Power_Opower__class_Opower(_1184191), _1184197), _1184195)), hAPP(hAPP(c_Power_Opower__class_Opower(_1184191), _1184197), _1184193))))], (20960 ^ _784416) ^ [_1184530, _1184532, _1184534, _1184536] : [class_Rings_Olinordered__semidom(_1184530), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1184532), _1184534)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184530), c_Groups_Ozero__class_Ozero(_1184530)), _1184536)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184530), _1184536), c_Groups_Oone__class_Oone(_1184530))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184530), hAPP(hAPP(c_Power_Opower__class_Opower(_1184530), _1184536), _1184534)), hAPP(hAPP(c_Power_Opower__class_Opower(_1184530), _1184536), _1184532))))], (20978 ^ _784416) ^ [_1184869, _1184871, _1184873] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1184869), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1184871), _1184873)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1184869), _1184871)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1184869), _1184873)))], (20980 ^ _784416) ^ [_1184926, _1184928, _1184930] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1184926), _1184928)), _1184930) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1184926), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184928), _1184930)))], (20982 ^ _784416) ^ [_1184977, _1184979, _1184981] : [class_Rings_Oring__1__no__zero__divisors(_1184977), -(_1184979 = c_Groups_Ozero__class_Ozero(_1184977)), hAPP(hAPP(c_Power_Opower__class_Opower(_1184977), _1184979), _1184981) = c_Groups_Ozero__class_Ozero(_1184977)], (20992 ^ _784416) ^ [_1185136, _1185138, _1185140, _1185142] : [class_Groups_Ocomm__monoid__mult(_1185136), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1185136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185136), _1185138), _1185140)), _1185142) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185136), hAPP(hAPP(c_Power_Opower__class_Opower(_1185136), _1185138), _1185142)), hAPP(hAPP(c_Power_Opower__class_Opower(_1185136), _1185140), _1185142)))], (20998 ^ _784416) ^ [_1185295, _1185297, _1185299] : [class_Groups_Omonoid__mult(_1185295), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185295), hAPP(hAPP(c_Power_Opower__class_Opower(_1185295), _1185297), _1185299)), _1185297) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185295), _1185297), hAPP(hAPP(c_Power_Opower__class_Opower(_1185295), _1185297), _1185299)))], (21004 ^ _784416) ^ [_1185436, _1185438] : [class_Groups_Omonoid__mult(_1185436), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1185436), c_Groups_Oone__class_Oone(_1185436)), _1185438) = c_Groups_Oone__class_Oone(_1185436))], (21010 ^ _784416) ^ [_1185535, _1185537, _1185539, _1185541] : [class_Groups_Omonoid__mult(_1185535), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1185535), _1185537), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185539), _1185541)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1185535), hAPP(hAPP(c_Power_Opower__class_Opower(_1185535), _1185537), _1185539)), _1185541))], (21016 ^ _784416) ^ [_1185674, _1185676] : [class_Groups_Omonoid__mult(_1185674), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1185674), _1185676), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1185676)], (21022 ^ _784416) ^ [_1185765, _1185767, _1185769, _1185771] : [class_Rings_Olinordered__semidom(_1185765), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185765), _1185767), _1185769)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185765), c_Groups_Ozero__class_Ozero(_1185765)), _1185767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185765), hAPP(hAPP(c_Power_Opower__class_Opower(_1185765), _1185767), _1185771)), hAPP(hAPP(c_Power_Opower__class_Opower(_1185765), _1185769), _1185771))))], (21036 ^ _784416) ^ [_1186034, _1186036, _1186038] : [class_Rings_Olinordered__semidom(_1186034), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186034), c_Groups_Ozero__class_Ozero(_1186034)), _1186036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186034), c_Groups_Ozero__class_Ozero(_1186034)), hAPP(hAPP(c_Power_Opower__class_Opower(_1186034), _1186036), _1186038))))], (21046 ^ _784416) ^ [_1186217, _1186219, _1186221] : [class_Rings_Olinordered__semidom(_1186217), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186217), c_Groups_Ozero__class_Ozero(_1186217)), _1186219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186217), c_Groups_Ozero__class_Ozero(_1186217)), hAPP(hAPP(c_Power_Opower__class_Opower(_1186217), _1186219), _1186221))))], (21056 ^ _784416) ^ [_1186400, _1186402, _1186404] : [class_Power_Opower(_1186400), class_Rings_Omult__zero(_1186400), class_Rings_Ono__zero__divisors(_1186400), class_Rings_Ozero__neq__one(_1186400), 21071 ^ _784416 : [(21072 ^ _784416) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1186400), _1186402), _1186404) = c_Groups_Ozero__class_Ozero(_1186400), 21075 ^ _784416 : [(21076 ^ _784416) ^ [] : [-(_1186402 = c_Groups_Ozero__class_Ozero(_1186400))], (21078 ^ _784416) ^ [] : [_1186404 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (21080 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1186400), _1186402), _1186404) = c_Groups_Ozero__class_Ozero(_1186400)), _1186402 = c_Groups_Ozero__class_Ozero(_1186400), -(_1186404 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (21090 ^ _784416) ^ [_1186892, _1186894, _1186896] : [class_Rings_Olinordered__semidom(_1186892), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186892), c_Groups_Oone__class_Oone(_1186892)), _1186894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186892), c_Groups_Oone__class_Oone(_1186892)), hAPP(hAPP(c_Power_Opower__class_Opower(_1186892), _1186894), _1186896))))], (21100 ^ _784416) ^ [_1187075, _1187077] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1187075), c_Groups_Ozero__class_Ozero(_1187075)), hAPP(c_Nat_OSuc, _1187077)) = c_Groups_Ozero__class_Ozero(_1187075)), class_Power_Opower(_1187075), class_Rings_Osemiring__0(_1187075)], (21110 ^ _784416) ^ [_1187230, _1187232, _1187234, _1187236] : [class_Rings_Olinordered__semidom(_1187230), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187230), c_Groups_Oone__class_Oone(_1187230)), _1187232)), 21117 ^ _784416 : [(21118 ^ _784416) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1187230), _1187232), _1187234) = hAPP(hAPP(c_Power_Opower__class_Opower(_1187230), _1187232), _1187236), -(_1187234 = _1187236)], (21124 ^ _784416) ^ [] : [_1187234 = _1187236, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1187230), _1187232), _1187234) = hAPP(hAPP(c_Power_Opower__class_Opower(_1187230), _1187232), _1187236))]]], (21130 ^ _784416) ^ [_1187569, _1187571, _1187573] : [class_Groups_Omonoid__mult(_1187569), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1187569), _1187571), hAPP(c_Nat_OSuc, _1187573)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187569), hAPP(hAPP(c_Power_Opower__class_Opower(_1187569), _1187571), _1187573)), _1187571))], (21136 ^ _784416) ^ [_1187700, _1187702, _1187704] : [class_Power_Opower(_1187700), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1187700), _1187702), hAPP(c_Nat_OSuc, _1187704)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187700), _1187702), hAPP(hAPP(c_Power_Opower__class_Opower(_1187700), _1187702), _1187704)))], (21142 ^ _784416) ^ [_1187831, _1187833] : [class_Power_Opower(_1187831), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1187831), _1187833), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1187831))], (21148 ^ _784416) ^ [_1187926, _1187928, _1187930, _1187932] : [class_Groups_Omonoid__mult(_1187926), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1187926), _1187928), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1187930), _1187932)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187926), hAPP(hAPP(c_Power_Opower__class_Opower(_1187926), _1187928), _1187930)), hAPP(hAPP(c_Power_Opower__class_Opower(_1187926), _1187928), _1187932)))], (21154 ^ _784416) ^ [_1188081] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1188081) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21166 ^ _784416) ^ [_1188220, _1188222] : [21167 ^ _784416 : [(21168 ^ _784416) ^ [] : [_1188222 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21170 ^ _784416) ^ [] : [_1188220 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1188220), _1188222) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21156 ^ _784416) ^ [_1188122, _1188124] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1188122), _1188124) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1188124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1188122 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21184 ^ _784416) ^ [_1188470, _1188472] : [21185 ^ _784416 : [(21186 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188470))], (21188 ^ _784416) ^ [] : [_1188472 = 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), _1188470), _1188472))))], (21174 ^ _784416) ^ [_1188364, _1188366] : [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), _1188364), _1188366))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188364))), -(_1188366 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21192 ^ _784416) ^ [_1188607, _1188609, _1188611] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188607)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1188607), _1188609)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1188607), _1188611))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1188609), _1188611)))], (21202 ^ _784416) ^ [_1188788, _1188790, _1188792, _1188794] : [class_Rings_Olinordered__semidom(_1188788), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188788), hAPP(hAPP(c_Power_Opower__class_Opower(_1188788), _1188790), _1188792)), hAPP(hAPP(c_Power_Opower__class_Opower(_1188788), _1188794), _1188792))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1188788), c_Groups_Ozero__class_Ozero(_1188788)), _1188794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188788), _1188790), _1188794)))], (21216 ^ _784416) ^ [_1189057, _1189059, _1189061, _1189063] : [class_Rings_Olinordered__semidom(_1189057), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189057), hAPP(hAPP(c_Power_Opower__class_Opower(_1189057), _1189059), hAPP(c_Nat_OSuc, _1189061))), hAPP(hAPP(c_Power_Opower__class_Opower(_1189057), _1189063), hAPP(c_Nat_OSuc, _1189061)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189057), c_Groups_Ozero__class_Ozero(_1189057)), _1189063)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189057), _1189059), _1189063)))], (21230 ^ _784416) ^ [_1189338, _1189340, _1189342, _1189344] : [class_Rings_Olinordered__semidom(_1189338), hAPP(hAPP(c_Power_Opower__class_Opower(_1189338), _1189340), hAPP(c_Nat_OSuc, _1189342)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1189338), _1189344), hAPP(c_Nat_OSuc, _1189342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189338), c_Groups_Ozero__class_Ozero(_1189338)), _1189340)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189338), c_Groups_Ozero__class_Ozero(_1189338)), _1189344)), -(_1189340 = _1189344)], (21248 ^ _784416) ^ [_1189665, _1189667, _1189669] : [class_Rings_Olinordered__semidom(_1189665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189665), c_Groups_Oone__class_Oone(_1189665)), _1189667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189665), c_Groups_Oone__class_Oone(_1189665)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189665), _1189667), hAPP(hAPP(c_Power_Opower__class_Opower(_1189665), _1189667), _1189669)))))], (21258 ^ _784416) ^ [_1189864, _1189866, _1189868] : [class_Rings_Olinordered__semidom(_1189864), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189864), c_Groups_Oone__class_Oone(_1189864)), _1189866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189864), hAPP(hAPP(c_Power_Opower__class_Opower(_1189864), _1189866), _1189868)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189864), _1189866), hAPP(hAPP(c_Power_Opower__class_Opower(_1189864), _1189866), _1189868)))))], (21268 ^ _784416) ^ [_1190075, _1190077] : [class_Power_Opower(_1190075), class_Rings_Osemiring__0(_1190075), 21275 ^ _784416 : [(21276 ^ _784416) ^ [] : [_1190077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1190075), c_Groups_Ozero__class_Ozero(_1190075)), _1190077) = c_Groups_Oone__class_Oone(_1190075))], (21282 ^ _784416) ^ [] : [-(_1190077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1190075), c_Groups_Ozero__class_Ozero(_1190075)), _1190077) = c_Groups_Ozero__class_Ozero(_1190075))]]], (21288 ^ _784416) ^ [_1190349, _1190351, _1190353] : [class_Rings_Olinordered__semidom(_1190349), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190349), c_Groups_Oone__class_Oone(_1190349)), _1190351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190349), c_Groups_Oone__class_Oone(_1190349)), hAPP(hAPP(c_Power_Opower__class_Opower(_1190349), _1190351), hAPP(c_Nat_OSuc, _1190353)))))], (21298 ^ _784416) ^ [_1190538, _1190540, _1190542, _1190544] : [class_Rings_Olinordered__semidom(_1190538), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190538), c_Groups_Oone__class_Oone(_1190538)), _1190540)), 21305 ^ _784416 : [(21306 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190538), hAPP(hAPP(c_Power_Opower__class_Opower(_1190538), _1190540), _1190542)), hAPP(hAPP(c_Power_Opower__class_Opower(_1190538), _1190540), _1190544))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1190542), _1190544)))], (21312 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1190542), _1190544)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190538), hAPP(hAPP(c_Power_Opower__class_Opower(_1190538), _1190540), _1190542)), hAPP(hAPP(c_Power_Opower__class_Opower(_1190538), _1190540), _1190544))))]]], (21318 ^ _784416) ^ [_1190913, _1190915, _1190917, _1190919] : [class_Rings_Olinordered__semidom(_1190913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190913), c_Groups_Oone__class_Oone(_1190913)), _1190915)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190913), hAPP(hAPP(c_Power_Opower__class_Opower(_1190913), _1190915), _1190917)), hAPP(hAPP(c_Power_Opower__class_Opower(_1190913), _1190915), _1190919))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1190917), _1190919)))], (21332 ^ _784416) ^ [_1191178, _1191180, _1191182, _1191184] : [class_Rings_Olinordered__semidom(_1191178), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1191180), _1191182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191178), c_Groups_Oone__class_Oone(_1191178)), _1191184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191178), hAPP(hAPP(c_Power_Opower__class_Opower(_1191178), _1191184), _1191180)), hAPP(hAPP(c_Power_Opower__class_Opower(_1191178), _1191184), _1191182))))], (21346 ^ _784416) ^ [_1191443, _1191445, _1191447, _1191449] : [class_Rings_Olinordered__semidom(_1191443), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1191445), _1191447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191443), c_Groups_Oone__class_Oone(_1191443)), _1191449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191443), hAPP(hAPP(c_Power_Opower__class_Opower(_1191443), _1191449), _1191445)), hAPP(hAPP(c_Power_Opower__class_Opower(_1191443), _1191449), _1191447))))], (21360 ^ _784416) ^ [_1191708, _1191710, _1191712] : [class_Rings_Oring__1(_1191708), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1191708), hAPP(c_Groups_Ouminus__class_Ouminus(_1191708), _1191710)), _1191712) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191708), hAPP(hAPP(c_Power_Opower__class_Opower(_1191708), hAPP(c_Groups_Ouminus__class_Ouminus(_1191708), c_Groups_Oone__class_Oone(_1191708))), _1191712)), hAPP(hAPP(c_Power_Opower__class_Opower(_1191708), _1191710), _1191712)))], (21366 ^ _784416) ^ [_1191873, _1191875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1191873)), -(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), _1191873), _1191875))))], (21372 ^ _784416) ^ [_1191970, _1191972, _1191974] : [class_Rings_Olinordered__semidom(_1191970), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191970), c_Groups_Ozero__class_Ozero(_1191970)), _1191972)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191970), _1191972), c_Groups_Oone__class_Oone(_1191970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191970), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191970), _1191972), hAPP(hAPP(c_Power_Opower__class_Opower(_1191970), _1191972), _1191974))), hAPP(hAPP(c_Power_Opower__class_Opower(_1191970), _1191972), _1191974))))], (21386 ^ _784416) ^ [_1192253, _1192255, _1192257, _1192259] : [class_Rings_Olinordered__semidom(_1192253), hAPP(hAPP(c_Power_Opower__class_Opower(_1192253), _1192255), _1192257) = hAPP(hAPP(c_Power_Opower__class_Opower(_1192253), _1192259), _1192257), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192253), c_Groups_Ozero__class_Ozero(_1192253)), _1192255)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192253), c_Groups_Ozero__class_Ozero(_1192253)), _1192259)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1192257)), -(_1192255 = _1192259)], (21408 ^ _784416) ^ [_1192628, _1192630, _1192632] : [class_Rings_Olinordered__semidom(_1192628), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192628), c_Groups_Ozero__class_Ozero(_1192628)), _1192630)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192628), _1192630), c_Groups_Oone__class_Oone(_1192628))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192628), hAPP(hAPP(c_Power_Opower__class_Opower(_1192628), _1192630), hAPP(c_Nat_OSuc, _1192632))), c_Groups_Oone__class_Oone(_1192628))))], (21422 ^ _784416) ^ [_1192889, _1192891] : [-(c_Sum__Type_OPlus(_1192889, _1192891, c_Orderings_Otop__class_Otop(tc_fun(_1192889, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1192891, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1192889, _1192891), tc_HOL_Obool)))], (21424 ^ _784416) ^ [_1192937] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1192937)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1192937)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21426 ^ _784416) ^ [_1192994, _1192996, _1192998, _1193000] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1192994, _1192994)), hAPP(hAPP(c_Product__Type_OPair(_1192994, _1192994), _1192996), _1192998)), hAPP(c_Wellfounded_Omeasure(_1192994), _1193000))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1193000, _1192996)), hAPP(_1193000, _1192998))))], (21432 ^ _784416) ^ [_1193141, _1193143, _1193145, _1193147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1193147, _1193143)), hAPP(_1193147, _1193145))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1193141, _1193141)), hAPP(hAPP(c_Product__Type_OPair(_1193141, _1193141), _1193143), _1193145)), hAPP(c_Wellfounded_Omeasure(_1193141), _1193147))))], (21438 ^ _784416) ^ [_1193315, _1193317, _1193319, _1193321] : [c_Sum__Type_OPlus(_1193315, _1193317, _1193319, _1193321) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1193315, _1193317), tc_HOL_Obool)), 21441 ^ _784416 : [(21442 ^ _784416) ^ [] : [-(_1193319 = c_Orderings_Obot__class_Obot(tc_fun(_1193315, tc_HOL_Obool)))], (21444 ^ _784416) ^ [] : [-(_1193321 = c_Orderings_Obot__class_Obot(tc_fun(_1193317, tc_HOL_Obool)))]]], (21446 ^ _784416) ^ [_1193464, _1193466, _1193468, _1193470] : [-(c_Sum__Type_OPlus(_1193464, _1193466, _1193468, _1193470) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1193464, _1193466), tc_HOL_Obool))), _1193468 = c_Orderings_Obot__class_Obot(tc_fun(_1193464, tc_HOL_Obool)), _1193470 = c_Orderings_Obot__class_Obot(tc_fun(_1193466, tc_HOL_Obool))], (21456 ^ _784416) ^ [_1193649] : [class_Power_Opower(_1193649), -(c_Power_Opower__class_Opower(_1193649) = c_Power_Opower_Opower(_1193649, c_Groups_Oone__class_Oone(_1193649), c_Groups_Otimes__class_Otimes(_1193649)))], (21462 ^ _784416) ^ [_1193742, _1193744, _1193746, _1193748, _1193750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1193742, _1193744)), hAPP(_1193742, _1193746))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1193748, _1193748)), hAPP(hAPP(c_Product__Type_OPair(_1193748, _1193748), _1193744), _1193746)), _1193750)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1193748, _1193748)), hAPP(hAPP(c_Product__Type_OPair(_1193748, _1193748), _1193744), _1193746)), c_Wellfounded_Omlex__prod(_1193748, _1193742, _1193750))))], (21472 ^ _784416) ^ [_1193989, _1193991, _1193993] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1193989), _1193991)), _1193993) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193989), _1193993)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193991), _1193993)))], (21474 ^ _784416) ^ [_1194046, _1194048, _1194050] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194046), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1194048), _1194050)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194046), _1194048)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194046), _1194050)))], (21476 ^ _784416) ^ [_1194103, _1194105] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1194103)), _1194105) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194103), _1194105)))], (21478 ^ _784416) ^ [_1194146, _1194148, _1194150] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194146), _1194148)), _1194150) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194146), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194148), _1194150)))], (21480 ^ _784416) ^ [_1194197, _1194199] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194197), _1194199) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194199), _1194197))], (21482 ^ _784416) ^ [_1194234, _1194236, _1194238] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1194234), _1194236)), _1194238) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194234), _1194238)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194236), _1194238)))], (21484 ^ _784416) ^ [_1194291, _1194293, _1194295] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194291), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1194293), _1194295)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194291), _1194293)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194291), _1194295)))], (21486 ^ _784416) ^ [_1194348] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194348), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1194348)], (21488 ^ _784416) ^ [_1194377] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1194377) = _1194377)], (21490 ^ _784416) ^ [_1194403, _1194405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194403)), 21493 ^ _784416 : [(21494 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194403), _1194405) = c_Groups_Oone__class_Oone(tc_Int_Oint), 21497 ^ _784416 : [(21498 ^ _784416) ^ [] : [-(_1194403 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (21500 ^ _784416) ^ [] : [-(_1194405 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (21502 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194403), _1194405) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1194403 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1194405 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (21512 ^ _784416) ^ [_1194704, _1194706, _1194708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1194704), _1194706)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1194708)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194708), _1194704)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194708), _1194706))))], (21522 ^ _784416) ^ [_1194885, _1194887, _1194889, _1194891] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1194885, _1194887, _1194889), _1194891), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1194887)], (21524 ^ _784416) ^ [_1194924, _1194926, _1194928, _1194930, _1194932] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1194924, _1194926, _1194928), _1194930), hAPP(c_Nat_OSuc, _1194932)) = hAPP(hAPP(_1194928, _1194930), hAPP(hAPP(c_Power_Opower_Opower(_1194924, _1194926, _1194928), _1194930), _1194932)))], (21526 ^ _784416) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21528 ^ _784416) ^ [_1195002, _1195004, _1195006, _1195008, _1195010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1195002, _1195004)), hAPP(_1195002, _1195006))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1195008, _1195008)), hAPP(hAPP(c_Product__Type_OPair(_1195008, _1195008), _1195004), _1195006)), c_Wellfounded_Omlex__prod(_1195008, _1195002, _1195010))))], (21534 ^ _784416) ^ [_1195153] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1195153)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1195153)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21536 ^ _784416) ^ [_1195191, _1195193] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_1195191)), hAPP(c_Option_Ooption_OSome(_1195191), _1195193)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21538 ^ _784416) ^ [_1195228] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_1195228)), c_Option_Ooption_ONone(_1195228)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21540 ^ _784416) ^ [_1195260, _1195262] : [class_Rings_Olinordered__idom(_1195260), hBOOL(hAPP(hAPP(c_member(_1195260), _1195262), c_Int_Oring__1__class_OInts(_1195260))), 21547 ^ _784416 : [(21548 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195260), c_Groups_Oone__class_Oone(_1195260)), _1195262)), _1195262)), c_Groups_Ozero__class_Ozero(_1195260))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195260), _1195262), c_Groups_Ozero__class_Ozero(_1195260))))], (21554 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195260), _1195262), c_Groups_Ozero__class_Ozero(_1195260))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195260), c_Groups_Oone__class_Oone(_1195260)), _1195262)), _1195262)), c_Groups_Ozero__class_Ozero(_1195260))))]]], (21560 ^ _784416) ^ [_1195676, _1195678, _1195680, _1195682, _1195684, _1195686, _1195688, _1195690] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1195676, _1195678), tc_prod(_1195676, _1195678))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1195676, _1195678), tc_prod(_1195676, _1195678)), hAPP(hAPP(c_Product__Type_OPair(_1195676, _1195678), _1195680), _1195682)), hAPP(hAPP(c_Product__Type_OPair(_1195676, _1195678), _1195684), _1195686))), c_Wellfounded_Olex__prod(_1195676, _1195678, _1195688, _1195690))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1195676, _1195676)), hAPP(hAPP(c_Product__Type_OPair(_1195676, _1195676), _1195680), _1195684)), _1195688))), 21567 ^ _784416 : [(21568 ^ _784416) ^ [] : [-(_1195680 = _1195684)], (21570 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1195678, _1195678)), hAPP(hAPP(c_Product__Type_OPair(_1195678, _1195678), _1195682), _1195686)), _1195690)))]]], (21572 ^ _784416) ^ [_1196001, _1196003, _1196005, _1196007, _1196009, _1196011, _1196013, _1196015] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1196001, _1196003), tc_prod(_1196001, _1196003))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1196001, _1196003), tc_prod(_1196001, _1196003)), hAPP(hAPP(c_Product__Type_OPair(_1196001, _1196003), _1196005), _1196007)), hAPP(hAPP(c_Product__Type_OPair(_1196001, _1196003), _1196009), _1196011))), c_Wellfounded_Olex__prod(_1196001, _1196003, _1196013, _1196015)))), 21573 ^ _784416 : [(21574 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1196001, _1196001)), hAPP(hAPP(c_Product__Type_OPair(_1196001, _1196001), _1196005), _1196009)), _1196013))], (21576 ^ _784416) ^ [] : [_1196005 = _1196009, hBOOL(hAPP(hAPP(c_member(tc_prod(_1196003, _1196003)), hAPP(hAPP(c_Product__Type_OPair(_1196003, _1196003), _1196007), _1196011)), _1196015))]]], (21584 ^ _784416) ^ [_1196394, _1196396, _1196398] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1196394, tc_HOL_Obool), tc_fun(_1196394, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1196394, tc_HOL_Obool), tc_fun(_1196394, tc_HOL_Obool)), _1196396), _1196398)), c_Wellfounded_Ofinite__psubset(_1196394))), 21587 ^ _784416 : [(21588 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1196394, tc_HOL_Obool)), _1196396), _1196398)))], (21590 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1196394), _1196398)))]]], (21592 ^ _784416) ^ [_1196589, _1196591, _1196593] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1196589, tc_HOL_Obool), tc_fun(_1196589, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1196589, tc_HOL_Obool), tc_fun(_1196589, tc_HOL_Obool)), _1196591), _1196593)), c_Wellfounded_Ofinite__psubset(_1196589)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1196589, tc_HOL_Obool)), _1196591), _1196593)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1196589), _1196593))], (21602 ^ _784416) ^ [_1196830] : [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)), _1196830)), _1196830)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196830), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21608 ^ _784416) ^ [_1196939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196939), 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)), _1196939)), _1196939)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21614 ^ _784416) ^ [_1197063] : [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)), _1197063)), _1197063) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (21616 ^ _784416) ^ [_1197095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197095)), -(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)), _1197095))))], (21622 ^ _784416) ^ [_1197184] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1197184), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1197184)], (21624 ^ _784416) ^ [_1197213] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197213) = _1197213)], (21626 ^ _784416) ^ [_1197239] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197239)), _1197239) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21628 ^ _784416) ^ [_1197286, _1197288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197286), _1197288)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1197286), _1197288)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21634 ^ _784416) ^ [_1197391, _1197393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1197391), _1197393)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197391), _1197393)))], (21640 ^ _784416) ^ [] : [-(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))], (21642 ^ _784416) ^ [_1197532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1197532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197532)))], (21648 ^ _784416) ^ [_1197611] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197611)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1197611)))], (21654 ^ _784416) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (21656 ^ _784416) ^ [] : [-(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))))], (21658 ^ _784416) ^ [_1197753, _1197755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197753), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1197755), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197753), _1197755)))], (21664 ^ _784416) ^ [_1197858, _1197860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197858), _1197860)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1197858), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1197860), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21670 ^ _784416) ^ [_1197969] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1197969)) = _1197969)], (21672 ^ _784416) ^ [_1197994, _1197996] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197994), _1197996))), -(_1197994 = _1197996), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1197996), _1197994)))], (21682 ^ _784416) ^ [_1198047] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1198047) = _1198047)], (21684 ^ _784416) ^ [_1198088, _1198090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198088), _1198090)), 21687 ^ _784416 : [(21688 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1198088), _1198090)))], (21690 ^ _784416) ^ [] : [_1198088 = _1198090]]], (21692 ^ _784416) ^ [_1198215, _1198217] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198215), _1198217))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1198215), _1198217)), -(_1198215 = _1198217)], (21702 ^ _784416) ^ [_1198369, _1198371] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198369), _1198371)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198369)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198371)))], (21704 ^ _784416) ^ [_1198415, _1198417, _1198419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198415), _1198417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198415), _1198419)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198417), _1198419))))], (21710 ^ _784416) ^ [_1198538, _1198540] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198538), _1198540) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198540), _1198538))], (21712 ^ _784416) ^ [_1198575, _1198577, _1198579] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198575), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198577), _1198579)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198577), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198575), _1198579)))], (21714 ^ _784416) ^ [_1198626, _1198628, _1198630] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198626), _1198628)), _1198630) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198626), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198628), _1198630)))], (21716 ^ _784416) ^ [_1198677, _1198679, _1198681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1198677), _1198679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198681), _1198677)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198681), _1198679))))], (21722 ^ _784416) ^ [_1198800, _1198802, _1198804, _1198806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1198800), _1198802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1198804), _1198806)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198800), _1198804)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198802), _1198806))))], (21732 ^ _784416) ^ [_1198991, _1198993] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1198991), _1198993) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1198991), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198993)))], (21734 ^ _784416) ^ [_1199031, _1199033] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199031), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1199033)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1199031), _1199033))], (21736 ^ _784416) ^ [_1199086, _1199088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199086), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199088), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1199086), _1199088)))], (21742 ^ _784416) ^ [_1199191, _1199193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1199191), _1199193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199191), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199193), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21748 ^ _784416) ^ [_1199317, _1199319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199317), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1199319)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199317), _1199319)))], (21754 ^ _784416) ^ [_1199422, _1199424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199422), _1199424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199422), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1199424)))], (21760 ^ _784416) ^ [_1199533, _1199535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199533), _1199535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199533), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1199535)))], (21776 ^ _784416) ^ [_1199775, _1199777] : [21777 ^ _784416 : [(21778 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199775), _1199777))], (21780 ^ _784416) ^ [] : [_1199775 = _1199777]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199775), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199777), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21766 ^ _784416) ^ [_1199657, _1199659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199657), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1199659), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199657), _1199659))), -(_1199657 = _1199659)], (21784 ^ _784416) ^ [_1199924] : [class_Rings_Oring__1(_1199924), -(hBOOL(hAPP(hAPP(c_member(_1199924), c_Groups_Ozero__class_Ozero(_1199924)), c_Int_Oring__1__class_OInts(_1199924))))], (21790 ^ _784416) ^ [_1200019, _1200021, _1200023] : [class_Rings_Oring__1(_1200019), hBOOL(hAPP(hAPP(c_member(_1200019), _1200021), c_Int_Oring__1__class_OInts(_1200019))), hBOOL(hAPP(hAPP(c_member(_1200019), _1200023), c_Int_Oring__1__class_OInts(_1200019))), -(hBOOL(hAPP(hAPP(c_member(_1200019), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200019), _1200021), _1200023)), c_Int_Oring__1__class_OInts(_1200019))))], (21804 ^ _784416) ^ [_1200274, _1200276, _1200278] : [class_Rings_Oring__1(_1200274), hBOOL(hAPP(hAPP(c_member(_1200274), _1200276), c_Int_Oring__1__class_OInts(_1200274))), hBOOL(hAPP(hAPP(c_member(_1200274), _1200278), c_Int_Oring__1__class_OInts(_1200274))), -(hBOOL(hAPP(hAPP(c_member(_1200274), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200274), _1200276), _1200278)), c_Int_Oring__1__class_OInts(_1200274))))], (21818 ^ _784416) ^ [] : [-(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))], (21820 ^ _784416) ^ [_1200547, _1200549, _1200551] : [class_Rings_Oring__1(_1200547), hBOOL(hAPP(hAPP(c_member(_1200547), _1200549), c_Int_Oring__1__class_OInts(_1200547))), hBOOL(hAPP(hAPP(c_member(_1200547), _1200551), c_Int_Oring__1__class_OInts(_1200547))), -(hBOOL(hAPP(hAPP(c_member(_1200547), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1200547), _1200549), _1200551)), c_Int_Oring__1__class_OInts(_1200547))))], (21834 ^ _784416) ^ [_1200802] : [class_Rings_Oring__1(_1200802), -(hBOOL(hAPP(hAPP(c_member(_1200802), c_Groups_Oone__class_Oone(_1200802)), c_Int_Oring__1__class_OInts(_1200802))))], (21840 ^ _784416) ^ [_1200897, _1200899] : [class_Rings_Oring__1(_1200897), hBOOL(hAPP(hAPP(c_member(_1200897), _1200899), c_Int_Oring__1__class_OInts(_1200897))), -(hBOOL(hAPP(hAPP(c_member(_1200897), hAPP(c_Groups_Ouminus__class_Ouminus(_1200897), _1200899)), c_Int_Oring__1__class_OInts(_1200897))))], (21850 ^ _784416) ^ [_1201070, _1201072, _1201074] : [class_Rings_Oring__1(_1201070), hBOOL(hAPP(hAPP(c_member(_1201070), _1201072), c_Int_Oring__1__class_OInts(_1201070))), -(hBOOL(hAPP(hAPP(c_member(_1201070), hAPP(hAPP(c_Power_Opower__class_Opower(_1201070), _1201072), _1201074)), c_Int_Oring__1__class_OInts(_1201070))))], (21860 ^ _784416) ^ [_1201253, _1201255] : [class_Int_Oring__char__0(_1201253), hBOOL(hAPP(hAPP(c_member(_1201253), _1201255), c_Int_Oring__1__class_OInts(_1201253))), 21867 ^ _784416 : [(21868 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201253), _1201255), _1201255) = c_Groups_Ozero__class_Ozero(_1201253), -(_1201255 = c_Groups_Ozero__class_Ozero(_1201253))], (21874 ^ _784416) ^ [] : [_1201255 = c_Groups_Ozero__class_Ozero(_1201253), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201253), _1201255), _1201255) = c_Groups_Ozero__class_Ozero(_1201253))]]], (21880 ^ _784416) ^ [_1201564, _1201566] : [class_Int_Oring__char__0(_1201564), hBOOL(hAPP(hAPP(c_member(_1201564), _1201566), c_Int_Oring__1__class_OInts(_1201564))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201564), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201564), c_Groups_Oone__class_Oone(_1201564)), _1201566)), _1201566) = c_Groups_Ozero__class_Ozero(_1201564)], (21890 ^ _784416) ^ [_1201750, _1201752, _1201754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201750)), _1201750 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1201752), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201750), _1201754)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201752), _1201750)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1201754)))], (21904 ^ _784416) ^ [_1201979, _1201981, _1201983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201979)), _1201979 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1201981), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201979), _1201983)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1201983), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (21918 ^ _784416) ^ [_1202208, _1202210, _1202212] : [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), _1202208), _1202210)), _1202212))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202212), _1202208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202208)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202210)))], (21932 ^ _784416) ^ [_1202441, _1202443, _1202445] : [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), _1202441), _1202443)), _1202445)), 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)), _1202445)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202441)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1202443), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21946 ^ _784416) ^ [_1202680, _1202682, _1202684, _1202686, _1202688] : [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), _1202680), _1202682)), _1202684)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1202680), _1202686)), _1202688))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1202684)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202684), _1202680)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1202688), _1202680)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1202682), _1202686)))], (21964 ^ _784416) ^ [_1203029, _1203031, _1203033, _1203035, _1203037, _1203039] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1203029), _1203031)), _1203033) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1203035), _1203037)), _1203039), 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), _1203035), _1203037)), _1203039))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203039), _1203035)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203033)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203035)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203035), _1203029)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203031), _1203037)))], (21990 ^ _784416) ^ [_1203528, _1203530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203528), _1203530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203530), _1203528)), -(_1203528 = _1203530)], (22000 ^ _784416) ^ [_1203677, _1203679, _1203681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203677), _1203679)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203679), _1203681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203677), _1203681)))], (22010 ^ _784416) ^ [_1203836, _1203838] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203836), _1203838))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203838), _1203836)))], (22016 ^ _784416) ^ [_1203882] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203882), _1203882)))], (22018 ^ _784416) ^ [_1203910, _1203912, _1203914, _1203916, _1203918, _1203920] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1203910), _1203912)), _1203914) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1203916), _1203918)), _1203920), 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), _1203916), _1203918)), _1203920)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203914), _1203910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203920)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203916)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203916), _1203910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1203918), _1203912)))], (22044 ^ _784416) ^ [_1204415, _1204417, _1204419, _1204421, _1204423] : [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), _1204415), _1204417)), _1204419)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1204415), _1204421)), _1204423))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204423), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1204415), _1204423)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1204415), _1204419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1204421), _1204417)))], (22062 ^ _784416) ^ [_1204770, _1204772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204770)), -(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), _1204770), _1204772))))], (22068 ^ _784416) ^ [_1204867, _1204869, _1204871, _1204873, _1204875, _1204877, _1204879] : [hBOOL(hAPP(_1204867, _1204869)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1204871, _1204871)), hAPP(hAPP(c_Product__Type_OPair(_1204871, _1204871), _1204873), _1204875)), hAPP(_1204877, _1204869))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1204879, _1204871), tc_prod(_1204879, _1204871))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1204879, _1204871), tc_prod(_1204879, _1204871)), hAPP(hAPP(c_Product__Type_OPair(_1204879, _1204871), _1204869), _1204873)), hAPP(hAPP(c_Product__Type_OPair(_1204879, _1204871), _1204869), _1204875))), c_Recdef_Osame__fst(_1204879, _1204871, _1204867, _1204877))))], (22078 ^ _784416) ^ [_1205172, _1205174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205174)), -(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), _1205172), _1205174))))], (22088 ^ _784416) ^ [] : [-(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))))], (22090 ^ _784416) ^ [_1205343, _1205345] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205345)), -(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), _1205343), _1205345))))], (22100 ^ _784416) ^ [] : [-(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))))], (22102 ^ _784416) ^ [_1205523, _1205525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1205523), _1205525)), -(c_Nat__Transfer_Otsub(_1205525, _1205523) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1205525), _1205523))], (22108 ^ _784416) ^ [_1205622, _1205624] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1205622), _1205624))), -(c_Nat__Transfer_Otsub(_1205624, _1205622) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22114 ^ _784416) ^ [_1205668, _1205670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1205668)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205670)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1205670), _1205668)), _1205670) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1205670), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1205668), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (22124 ^ _784416) ^ [_1205853, _1205855, _1205857, _1205859] : [_1205853 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1205855), _1205857)), _1205859), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1205853, _1205855), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1205857), _1205859)))), 22131 ^ _784416 : [(22132 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205855)))], (22134 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205859)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205859), _1205855))]], 22139 ^ _784416 : [(22140 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205855))], (22142 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205855), _1205859)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1205859), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (22150 ^ _784416) ^ [_1206315, _1206317, _1206319, _1206321, _1206323, _1206325] : [class_Groups_Ocomm__monoid__mult(_1206315), hBOOL(hAPP(c_Finite__Set_Ofinite(_1206317), _1206319)), 22157 ^ _784416 : [(22158 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1206317), _1206321), _1206319)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1206317, _1206315), hAPP(hAPP(c_COMBC(_1206317, _1206315, _1206315), hAPP(hAPP(c_COMBS(_1206317, _1206315, tc_fun(_1206315, _1206315)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1206315, tc_fun(_1206315, _1206315)), _1206317), c_If(_1206315)), hAPP(hAPP(c_COMBC(_1206317, _1206317, tc_HOL_Obool), c_fequal), _1206321))), _1206323)), _1206325)), _1206319) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1206315), hAPP(_1206323, _1206321)), hAPP(hAPP(c_Power_Opower__class_Opower(_1206315), _1206325), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1206317), _1206319)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (22164 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1206317), _1206321), _1206319))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1206317, _1206315), hAPP(hAPP(c_COMBC(_1206317, _1206315, _1206315), hAPP(hAPP(c_COMBS(_1206317, _1206315, tc_fun(_1206315, _1206315)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1206315, tc_fun(_1206315, _1206315)), _1206317), c_If(_1206315)), hAPP(hAPP(c_COMBC(_1206317, _1206317, tc_HOL_Obool), c_fequal), _1206321))), _1206323)), _1206325)), _1206319) = hAPP(hAPP(c_Power_Opower__class_Opower(_1206315), _1206325), hAPP(c_Finite__Set_Ocard(_1206317), _1206319)))]]], (22170 ^ _784416) ^ [_1206926, _1206928] : [-(hBOOL(hAPP(_1206926, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1206926, _1206928)), 22178 ^ _784416 : [(22179 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 22177 ^ [_1206926, _1206928]), _1206928)))], (22187 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1206926, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 22177 ^ [_1206926, _1206928]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (22181 ^ _784416) ^ [_1207164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1207164), 22177 ^ [_1206926, _1206928])), hBOOL(hAPP(_1206926, _1207164))]]], (22189 ^ _784416) ^ [_1207316, _1207318, _1207320, _1207322, _1207324, _1207326] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1207316, tc_HOL_Obool), tc_fun(_1207316, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1207316, tc_HOL_Obool), tc_fun(_1207316, tc_HOL_Obool)), _1207318), _1207320)), c_Wellfounded_Omax__ext(_1207316, _1207322))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1207316, tc_HOL_Obool), tc_fun(_1207316, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1207316, tc_HOL_Obool), tc_fun(_1207316, tc_HOL_Obool)), _1207324), _1207326)), c_Wellfounded_Omax__ext(_1207316, _1207322))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1207316, tc_HOL_Obool), tc_fun(_1207316, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1207316, tc_HOL_Obool), tc_fun(_1207316, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1207316, tc_HOL_Obool)), _1207318), _1207324)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1207316, tc_HOL_Obool)), _1207320), _1207326))), c_Wellfounded_Omax__ext(_1207316, _1207322))))], (22199 ^ _784416) ^ [_1207709, _1207711, _1207713, _1207715] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1207709, _1207711), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1207713), _1207715))), -(_1207711 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1207709), _1207711) = _1207713)], (22209 ^ _784416) ^ [_1207839] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1207839) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22211 ^ _784416) ^ [_1207865, _1207867] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1207865)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1207867)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1207865), _1207867))], (22213 ^ _784416) ^ [_1207908, _1207910] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1207908), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1207910)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1207908)), _1207910))], (22215 ^ _784416) ^ [_1207951, _1207953] : [class_Divides_Osemiring__div(_1207951), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1207951), _1207953), c_Groups_Ozero__class_Ozero(_1207951)) = c_Groups_Ozero__class_Ozero(_1207951))], (22221 ^ _784416) ^ [_1208050, _1208052] : [class_Divides_Osemiring__div(_1208050), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208050), c_Groups_Ozero__class_Ozero(_1208050)), _1208052) = c_Groups_Ozero__class_Ozero(_1208050))], (22227 ^ _784416) ^ [_1208149, _1208151] : [class_Divides_Osemiring__div(_1208149), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1208149), _1208151), c_Groups_Oone__class_Oone(_1208149)) = _1208151)], (22233 ^ _784416) ^ [_1208244, _1208246, _1208248, _1208250, _1208252] : [class_Groups_Ocomm__monoid__mult(_1208244), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1208246, _1208244), hAPP(hAPP(c_COMBS(_1208246, _1208244, _1208244), hAPP(hAPP(c_COMBB(_1208244, tc_fun(_1208244, _1208244), _1208246), c_Groups_Otimes__class_Otimes(_1208244)), _1208248)), _1208250)), _1208252) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208244), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1208246, _1208244), _1208248), _1208252)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1208246, _1208244), _1208250), _1208252)))], (22239 ^ _784416) ^ [_1208445, _1208447, _1208449] : [class_Groups_Ocomm__monoid__mult(_1208445), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1208447, _1208445), hAPP(c_COMBK(_1208445, _1208447), c_Groups_Oone__class_Oone(_1208445))), _1208449) = c_Groups_Oone__class_Oone(_1208445))], (22245 ^ _784416) ^ [_1208556] : [-(_1208556 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1208556), 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)))))], (22251 ^ _784416) ^ [_1208595, _1208597, _1208599] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1208595, _1208595), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1208597), _1208599))), -(_1208595 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1208599 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22261 ^ _784416) ^ [_1208711, _1208713, _1208715, _1208717, _1208719, _1208721] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1208711, _1208713), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1208715), _1208717))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1208711, _1208713), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1208719), _1208721))), -(_1208713 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1208715 = _1208719)], (22275 ^ _784416) ^ [_1208915, _1208917, _1208919, _1208921, _1208923, _1208925] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1208915, _1208917), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1208919), _1208921))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1208915, _1208917), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1208923), _1208925))), -(_1208917 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1208921 = _1208925)], (22289 ^ _784416) ^ [_1209119, _1209121, _1209123, _1209125] : [class_Rings_Ocomm__semiring__1(_1209119), class_Rings_Ono__zero__divisors(_1209119), hBOOL(hAPP(c_Finite__Set_Ofinite(_1209121), _1209123)), 22300 ^ _784416 : [(22301 ^ _784416) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1209121, _1209119), _1209125), _1209123) = c_Groups_Ozero__class_Ozero(_1209119), 22305 ^ _784416 : [(22306 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1209121), 22304 ^ [_1209119, _1209121, _1209123, _1209125]), _1209123)))], (22308 ^ _784416) ^ [] : [-(hAPP(_1209125, 22304 ^ [_1209119, _1209121, _1209123, _1209125]) = c_Groups_Ozero__class_Ozero(_1209119))]]], (22310 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1209121, _1209119), _1209125), _1209123) = c_Groups_Ozero__class_Ozero(_1209119)), 22311 ^ _784416 : [(22312 ^ _784416) ^ [_1209497] : [hBOOL(hAPP(hAPP(c_member(_1209121), _1209497), _1209123)), hAPP(_1209125, _1209497) = c_Groups_Ozero__class_Ozero(_1209119)]]]]], (22320 ^ _784416) ^ [_1209652, _1209654, _1209656, _1209658] : [class_Rings_Ocomm__semiring__1(_1209652), hBOOL(hAPP(c_Finite__Set_Ofinite(_1209654), _1209656)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1209654, _1209652), _1209658), _1209656) = c_Groups_Ozero__class_Ozero(_1209652)), 22329 ^ _784416 : [(22330 ^ _784416) ^ [_1209833] : [hBOOL(hAPP(hAPP(c_member(_1209654), _1209833), _1209656)), hAPP(_1209658, _1209833) = c_Groups_Ozero__class_Ozero(_1209652)]]], (22338 ^ _784416) ^ [_1209982, _1209984, _1209986] : [class_Groups_Ocomm__monoid__mult(_1209982), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1209984, _1209982), _1209986), c_Orderings_Obot__class_Obot(tc_fun(_1209984, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1209982))], (22344 ^ _784416) ^ [_1210091, _1210093, _1210095] : [class_Groups_Ocomm__monoid__mult(_1210091), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1210093, _1210091), _1210095), c_Orderings_Obot__class_Obot(tc_fun(_1210093, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1210091))], (22350 ^ _784416) ^ [_1210200, _1210202, _1210204, _1210206] : [class_Groups_Ocomm__monoid__mult(_1210200), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1210202), _1210204))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1210202, _1210200), _1210206), _1210204) = c_Groups_Oone__class_Oone(_1210200))], (22360 ^ _784416) ^ [_1210324, _1210326, _1210328, _1210330] : [class_Groups_Ocomm__monoid__mult(_1210324), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1210326), _1210328))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1210326, _1210324), _1210330), _1210328) = c_Groups_Oone__class_Oone(_1210324))], (22370 ^ _784416) ^ [_1210448, _1210450, _1210452] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1210448), _1210450)), 22373 ^ _784416 : [(22384 ^ _784416) ^ [] : [22386 ^ _784416 : [(22387 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1210448), 22385 ^ [_1210448, _1210450, _1210452]), _1210450)))], (22389 ^ _784416) ^ [] : [hAPP(_1210452, 22385 ^ [_1210448, _1210450, _1210452]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1210448, tc_Nat_Onat), _1210452), _1210450) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (22374 ^ _784416) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1210448, tc_Nat_Onat), _1210452), _1210450) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 22377 ^ _784416 : [(22378 ^ _784416) ^ [_1210610] : [hBOOL(hAPP(hAPP(c_member(_1210448), _1210610), _1210450)), -(hAPP(_1210452, _1210610) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]]]], (22393 ^ _784416) ^ [_1210868, _1210870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210868)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1210868), _1210870))))], (22403 ^ _784416) ^ [_1211021, _1211023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211021), 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)), _1211023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1211021), _1211023)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22413 ^ _784416) ^ [_1211186, _1211188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211186), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22416 ^ _784416 : [(22417 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1211188), _1211186)), 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)), _1211188)))], (22423 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1211188), _1211186)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (22429 ^ _784416) ^ [_1211442, _1211444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211442)), 22432 ^ _784416 : [(22433 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1211444), _1211442)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211444), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22439 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211444), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1211444), _1211442)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (22445 ^ _784416) ^ [_1211697] : [-(_1211697 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1211697), _1211697) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22451 ^ _784416) ^ [_1211737, _1211739, _1211741, _1211743, _1211745] : [class_Groups_Ocomm__monoid__mult(_1211737), hBOOL(hAPP(c_Finite__Set_Ofinite(_1211739), _1211741)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1211739, _1211737), hAPP(hAPP(c_COMBS(_1211739, _1211737, _1211737), hAPP(hAPP(c_COMBB(_1211737, tc_fun(_1211737, _1211737), _1211739), c_Groups_Otimes__class_Otimes(_1211737)), _1211743)), _1211745)), _1211741) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1211737), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1211739, _1211737), _1211743), _1211741)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1211739, _1211737), _1211745), _1211741)))], (22461 ^ _784416) ^ [_1212004, _1212006, _1212008, _1212010] : [class_Divides_Osemiring__div(_1212004), 22464 ^ _784416 : [(22465 ^ _784416) ^ [] : [_1212006 = c_Groups_Ozero__class_Ozero(_1212004), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1212004), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212004), _1212006), _1212008)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212004), _1212006), _1212010)) = c_Groups_Ozero__class_Ozero(_1212004))], (22471 ^ _784416) ^ [] : [-(_1212006 = c_Groups_Ozero__class_Ozero(_1212004)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1212004), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212004), _1212006), _1212008)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212004), _1212006), _1212010)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1212004), _1212008), _1212010))]]], (22477 ^ _784416) ^ [_1212310, _1212312, _1212314] : [class_Divides_Osemiring__div(_1212310), -(_1212312 = c_Groups_Ozero__class_Ozero(_1212310)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1212310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212310), _1212314), _1212312)), _1212312) = _1212314)], (22487 ^ _784416) ^ [_1212438, _1212440, _1212442] : [class_Divides_Osemiring__div(_1212438), -(_1212440 = c_Groups_Ozero__class_Ozero(_1212438)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1212438), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212438), _1212440), _1212442)), _1212440) = _1212442)], (22497 ^ _784416) ^ [_1212566, _1212568, _1212570, _1212572] : [class_Divides_Osemiring__div(_1212566), -(_1212568 = c_Groups_Ozero__class_Ozero(_1212566)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1212566), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212566), _1212570), _1212568)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212566), _1212572), _1212568)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1212566), _1212570), _1212572))], (22507 ^ _784416) ^ [_1212728, _1212730, _1212732, _1212734] : [class_Divides_Osemiring__div(_1212728), -(_1212730 = c_Groups_Ozero__class_Ozero(_1212728)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1212728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212728), _1212730), _1212732)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212728), _1212730), _1212734)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1212728), _1212732), _1212734))], (22517 ^ _784416) ^ [_1212890, _1212892] : [class_Divides_Osemiring__div(_1212890), -(_1212892 = c_Groups_Ozero__class_Ozero(_1212890)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1212890), _1212892), _1212892) = c_Groups_Oone__class_Oone(_1212890))], (22527 ^ _784416) ^ [_1213004, _1213006, _1213008] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1213004), _1213006)), 22530 ^ _784416 : [(22541 ^ _784416) ^ [] : [22543 ^ _784416 : [(22544 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1213004), 22542 ^ [_1213004, _1213006, _1213008]), _1213006)))], (22546 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1213008, 22542 ^ [_1213004, _1213006, _1213008])))]], -(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(_1213004, tc_Nat_Onat), _1213008), _1213006))))], (22531 ^ _784416) ^ [] : [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(_1213004, tc_Nat_Onat), _1213008), _1213006))), 22534 ^ _784416 : [(22535 ^ _784416) ^ [_1213172] : [hBOOL(hAPP(hAPP(c_member(_1213004), _1213172), _1213006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1213008, _1213172))))]]]]], (22550 ^ _784416) ^ [_1213440, _1213442, _1213444, _1213446, _1213448, _1213450, _1213452, _1213454] : [class_Groups_Ocomm__monoid__mult(_1213440), c_Fun_Oinj__on(_1213442, _1213444, _1213446, _1213448), _1213450 = hAPP(c_Set_Oimage(_1213442, _1213444, _1213446), _1213448), _1213452 = hAPP(c_Fun_Ocomp(_1213444, _1213440, _1213442, _1213454), _1213446), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1213444, _1213440), _1213454), _1213450) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1213442, _1213440), _1213452), _1213448))], (22568 ^ _784416) ^ [_1213789, _1213791, _1213793, _1213795, _1213797, _1213799] : [class_Groups_Ocomm__monoid__mult(_1213789), c_Fun_Oinj__on(_1213791, _1213793, _1213795, _1213797), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1213793, _1213789), _1213799), hAPP(c_Set_Oimage(_1213791, _1213793, _1213795), _1213797)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1213791, _1213789), hAPP(c_Fun_Ocomp(_1213793, _1213789, _1213791, _1213799), _1213795)), _1213797))], (22578 ^ _784416) ^ [_1214002, _1214004, _1214006] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1214002, _1214002), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1214004), _1214006))), -(_1214002 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1214004 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22588 ^ _784416) ^ [_1214118, _1214120, _1214122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214118), _1214120)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214122), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214120), _1214122)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214118), _1214122))))], (22598 ^ _784416) ^ [_1214305, _1214307, _1214309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214305), _1214307)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214305), _1214309)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214307), _1214309))))], (22608 ^ _784416) ^ [_1214486, _1214488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214486), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214488), _1214486)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214486), _1214488) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22618 ^ _784416) ^ [_1214647, _1214649, _1214651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214647), 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)), _1214649)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214649), _1214651)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214647), _1214649)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214647), _1214651))))], (22632 ^ _784416) ^ [_1214892, _1214894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214892), 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)), _1214894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1214892), _1214894)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22642 ^ _784416) ^ [_1215057, _1215059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215057), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22645 ^ _784416 : [(22646 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215059), _1215057))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215059), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22652 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215059), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215059), _1215057))))]]], (22658 ^ _784416) ^ [_1215313, _1215315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215313)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215313), _1215315)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215313), _1215315) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22668 ^ _784416) ^ [_1215468, _1215470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215468)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215470), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215468), _1215470)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22678 ^ _784416) ^ [_1215633, _1215635, _1215637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215633)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215635), _1215637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215633), _1215637)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215633), _1215635))))], (22692 ^ _784416) ^ [_1215872, _1215874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215872)), 22695 ^ _784416 : [(22696 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215872), _1215874))), 22699 ^ _784416 : [(22700 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215874), _1215872)))], (22702 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215874)))]]], (22704 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1215872), _1215874)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215874), _1215872)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215874))]]], (22714 ^ _784416) ^ [_1216200, _1216202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216200)), 22717 ^ _784416 : [(22718 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1216202), _1216200))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1216200), _1216202)))], (22724 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1216200), _1216202)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1216202), _1216200))))]]], (22730 ^ _784416) ^ [_1216450, _1216452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216450)), 22733 ^ _784416 : [(22734 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1216452), _1216450))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216452)))], (22740 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1216452), _1216450))))]]], (22746 ^ _784416) ^ [_1216706, _1216708] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1216706), _1216708) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1216708 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22755 ^ _784416 : [(22756 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216706)))], (22758 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216706), _1216708)))]], 22759 ^ _784416 : [(22760 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1216706), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22762 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216708), _1216706)))]]], (22764 ^ _784416) ^ [_1216937, _1216939] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1216937), _1216939) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22765 ^ _784416 : [(22766 ^ _784416) ^ [] : [_1216939 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (22768 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216937), _1216939))], (22774 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1216937), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216939), _1216937))]]], (22782 ^ _784416) ^ [_1217232, _1217234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217232)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1217234)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1217232), _1217234)), _1217232)))], (22792 ^ _784416) ^ [_1217391, _1217393, _1217395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217391)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1217393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1217395), _1217391)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1217393), _1217395)), _1217391))], (22798 ^ _784416) ^ [_1217522, _1217524, _1217526, _1217528, _1217530] : [class_Groups_Ocomm__monoid__mult(_1217522), hBOOL(hAPP(c_Finite__Set_Ofinite(_1217524), _1217526)), 22805 ^ _784416 : [(22806 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1217524), _1217528), _1217526)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1217524, _1217522), hAPP(hAPP(c_COMBC(_1217524, _1217522, _1217522), hAPP(hAPP(c_COMBS(_1217524, _1217522, tc_fun(_1217522, _1217522)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1217522, tc_fun(_1217522, _1217522)), _1217524), c_If(_1217522)), hAPP(c_fequal, _1217528))), _1217530)), c_Groups_Oone__class_Oone(_1217522))), _1217526) = hAPP(_1217530, _1217528))], (22812 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1217524), _1217528), _1217526))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1217524, _1217522), hAPP(hAPP(c_COMBC(_1217524, _1217522, _1217522), hAPP(hAPP(c_COMBS(_1217524, _1217522, tc_fun(_1217522, _1217522)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1217522, tc_fun(_1217522, _1217522)), _1217524), c_If(_1217522)), hAPP(c_fequal, _1217528))), _1217530)), c_Groups_Oone__class_Oone(_1217522))), _1217526) = c_Groups_Oone__class_Oone(_1217522))]]], (22818 ^ _784416) ^ [_1218032, _1218034, _1218036, _1218038, _1218040] : [class_Groups_Ocomm__monoid__mult(_1218032), hBOOL(hAPP(c_Finite__Set_Ofinite(_1218034), _1218036)), 22825 ^ _784416 : [(22826 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1218034), _1218038), _1218036)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1218034, _1218032), hAPP(hAPP(c_COMBC(_1218034, _1218032, _1218032), hAPP(hAPP(c_COMBS(_1218034, _1218032, tc_fun(_1218032, _1218032)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1218032, tc_fun(_1218032, _1218032)), _1218034), c_If(_1218032)), hAPP(hAPP(c_COMBC(_1218034, _1218034, tc_HOL_Obool), c_fequal), _1218038))), _1218040)), c_Groups_Oone__class_Oone(_1218032))), _1218036) = hAPP(_1218040, _1218038))], (22832 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1218034), _1218038), _1218036))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1218034, _1218032), hAPP(hAPP(c_COMBC(_1218034, _1218032, _1218032), hAPP(hAPP(c_COMBS(_1218034, _1218032, tc_fun(_1218032, _1218032)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1218032, tc_fun(_1218032, _1218032)), _1218034), c_If(_1218032)), hAPP(hAPP(c_COMBC(_1218034, _1218034, tc_HOL_Obool), c_fequal), _1218038))), _1218040)), c_Groups_Oone__class_Oone(_1218032))), _1218036) = c_Groups_Oone__class_Oone(_1218032))]]], (22838 ^ _784416) ^ [_1218570, _1218572, _1218574, _1218576] : [class_Groups_Ocomm__monoid__mult(_1218570), hBOOL(hAPP(c_Finite__Set_Ofinite(_1218572), _1218574)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1218572, _1218570), hAPP(c_COMBK(_1218570, _1218572), _1218576)), _1218574) = hAPP(hAPP(c_Power_Opower__class_Opower(_1218570), _1218576), hAPP(c_Finite__Set_Ocard(_1218572), _1218574)))], (22848 ^ _784416) ^ [_1218769, _1218771, _1218773, _1218775] : [class_Divides_Osemiring__div(_1218769), -(_1218771 = c_Groups_Ozero__class_Ozero(_1218769)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1218769), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218769), _1218773), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218769), _1218771), _1218775))), _1218771) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218769), _1218775), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1218769), _1218773), _1218771)))], (22858 ^ _784416) ^ [_1218947, _1218949, _1218951, _1218953] : [class_Divides_Osemiring__div(_1218947), -(_1218949 = c_Groups_Ozero__class_Ozero(_1218947)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1218947), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218947), _1218951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218947), _1218953), _1218949))), _1218949) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218947), _1218953), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1218947), _1218951), _1218949)))], (22868 ^ _784416) ^ [_1219125, _1219127, _1219129] : [class_Divides_Osemiring__div(_1219125), -(_1219127 = c_Groups_Ozero__class_Ozero(_1219125)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1219125), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1219125), _1219127), _1219129)), _1219127) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1219125), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1219125), _1219129), _1219127)), c_Groups_Oone__class_Oone(_1219125)))], (22878 ^ _784416) ^ [_1219289, _1219291, _1219293] : [class_Divides_Osemiring__div(_1219289), -(_1219291 = c_Groups_Ozero__class_Ozero(_1219289)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1219289), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1219289), _1219293), _1219291)), _1219291) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1219289), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1219289), _1219293), _1219291)), c_Groups_Oone__class_Oone(_1219289)))], (22888 ^ _784416) ^ [_1219453, _1219455, _1219457, _1219459, _1219461] : [class_Groups_Ocomm__monoid__mult(_1219453), hBOOL(hAPP(c_Finite__Set_Ofinite(_1219455), _1219457)), -(hBOOL(hAPP(hAPP(c_member(_1219455), _1219459), _1219457))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1219455, _1219453), _1219461), hAPP(hAPP(c_Set_Oinsert(_1219455), _1219459), _1219457)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219453), hAPP(_1219461, _1219459)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1219455, _1219453), _1219461), _1219457)))], (22902 ^ _784416) ^ [_1219703, _1219705, _1219707, _1219709, _1219711] : [class_Groups_Ocomm__monoid__mult(_1219703), hBOOL(hAPP(c_Finite__Set_Ofinite(_1219705), _1219707)), -(hBOOL(hAPP(hAPP(c_member(_1219705), _1219709), _1219707))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1219705, _1219703), _1219711), hAPP(hAPP(c_Set_Oinsert(_1219705), _1219709), _1219707)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219703), hAPP(_1219711, _1219709)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1219705, _1219703), _1219711), _1219707)))], (22916 ^ _784416) ^ [_1219953, _1219955, _1219957, _1219959, _1219961] : [class_Groups_Ocomm__monoid__mult(_1219953), hBOOL(hAPP(c_Finite__Set_Ofinite(_1219955), _1219957)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1219955), _1219959)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219953), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1219955, _1219953), _1219961), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1219955, tc_HOL_Obool)), _1219957), _1219959))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1219955, _1219953), _1219961), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1219955, tc_HOL_Obool)), _1219957), _1219959))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219953), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1219955, _1219953), _1219961), _1219957)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1219955, _1219953), _1219961), _1219959)))], (22930 ^ _784416) ^ [_1220314, _1220316, _1220318, _1220320, _1220322] : [class_Groups_Ocomm__monoid__mult(_1220314), hBOOL(hAPP(c_Finite__Set_Ofinite(_1220316), _1220318)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1220316), _1220320)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220314), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1220316, _1220314), _1220322), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1220316, tc_HOL_Obool)), _1220318), _1220320))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1220316, _1220314), _1220322), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1220316, tc_HOL_Obool)), _1220318), _1220320))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220314), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1220316, _1220314), _1220322), _1220318)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1220316, _1220314), _1220322), _1220320)))], (22944 ^ _784416) ^ [_1220675, _1220677, _1220679, _1220681, _1220683] : [class_Groups_Ocomm__monoid__mult(_1220675), hBOOL(hAPP(c_Finite__Set_Ofinite(_1220677), _1220679)), c_Fun_Oinj__on(_1220677, _1220677, _1220681, _1220679), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1220677, _1220675), _1220683), hAPP(c_Set_Oimage(_1220677, _1220677, _1220681), _1220679)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1220677, _1220675), hAPP(c_Fun_Ocomp(_1220677, _1220675, _1220677, _1220683), _1220681)), _1220679))], (22958 ^ _784416) ^ [_1220950, _1220952, _1220954, _1220956] : [class_Groups_Ocomm__monoid__mult(_1220950), hBOOL(hAPP(c_Finite__Set_Ofinite(_1220952), _1220954)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1220952, _1220950), _1220956), _1220954) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1220950, _1220952, c_Groups_Otimes__class_Otimes(_1220950)), _1220956), c_Groups_Oone__class_Oone(_1220950)), _1220954))], (22968 ^ _784416) ^ [_1221145, _1221147, _1221149, _1221151] : [class_Groups_Ocomm__monoid__mult(_1221145), 22971 ^ _784416 : [(22972 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1221147), _1221149)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1221147, _1221145), _1221151), _1221149) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1221145, _1221147, c_Groups_Otimes__class_Otimes(_1221145)), _1221151), c_Groups_Oone__class_Oone(_1221145)), _1221149))], (22978 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1221147), _1221149))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1221147, _1221145), _1221151), _1221149) = c_Groups_Oone__class_Oone(_1221145))]]], (22984 ^ _784416) ^ [_1221417, _1221419, _1221421, _1221423, _1221425] : [class_Groups_Ocomm__monoid__mult(_1221417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1221419), _1221421)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1221419, _1221417), _1221423), hAPP(hAPP(c_Set_Oinsert(_1221419), _1221425), _1221421)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221417), hAPP(_1221423, _1221425)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1221419, _1221417), _1221423), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221419, tc_HOL_Obool)), _1221421), hAPP(hAPP(c_Set_Oinsert(_1221419), _1221425), c_Orderings_Obot__class_Obot(tc_fun(_1221419, tc_HOL_Obool)))))))], (22994 ^ _784416) ^ [_1221686, _1221688, _1221690, _1221692, _1221694] : [class_Groups_Ocomm__monoid__mult(_1221686), hBOOL(hAPP(c_Finite__Set_Ofinite(_1221688), _1221690)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1221688), _1221692)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1221688, tc_HOL_Obool)), _1221690), _1221692) = c_Orderings_Obot__class_Obot(tc_fun(_1221688, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1221688, _1221686), _1221694), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1221688, tc_HOL_Obool)), _1221690), _1221692)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221686), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1221688, _1221686), _1221694), _1221690)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1221688, _1221686), _1221694), _1221692)))], (23012 ^ _784416) ^ [_1222081, _1222083, _1222085, _1222087, _1222089] : [class_Groups_Ocomm__monoid__mult(_1222081), hBOOL(hAPP(c_Finite__Set_Ofinite(_1222083), _1222085)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1222083), _1222087)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222083, tc_HOL_Obool)), _1222085), _1222087) = c_Orderings_Obot__class_Obot(tc_fun(_1222083, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1222083, _1222081), _1222089), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1222083, tc_HOL_Obool)), _1222085), _1222087)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1222081), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1222083, _1222081), _1222089), _1222085)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1222083, _1222081), _1222089), _1222087)))], (23076 ^ _784416) ^ [_1223454, _1223456, _1223458] : [-(hBOOL(hAPP(_1223454, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1223456), _1223458)))), 23079 ^ _784416 : [(23080 ^ _784416) ^ [] : [-(_1223458 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23082 ^ _784416) ^ [] : [hBOOL(hAPP(_1223454, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 23085 ^ _784416 : [(23086 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223458)))], (23090 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23088 ^ [_1223454, _1223456, _1223458])))], (23092 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23088 ^ [_1223454, _1223456, _1223458]), _1223458)))], (23094 ^ _784416) ^ [] : [-(_1223456 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223458), 23087 ^ [_1223454, _1223456, _1223458])), 23088 ^ [_1223454, _1223456, _1223458]))], (23096 ^ _784416) ^ [] : [hBOOL(hAPP(_1223454, 23087 ^ [_1223454, _1223456, _1223458]))]], 23097 ^ _784416 : [(23098 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1223458), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23102 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1223458), 23100 ^ [_1223454, _1223456, _1223458])))], (23104 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23100 ^ [_1223454, _1223456, _1223458]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23106 ^ _784416) ^ [] : [-(_1223456 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223458), 23099 ^ [_1223454, _1223456, _1223458])), 23100 ^ [_1223454, _1223456, _1223458]))], (23108 ^ _784416) ^ [] : [hBOOL(hAPP(_1223454, 23099 ^ [_1223454, _1223456, _1223458]))]]], (23030 ^ _784416) ^ [_1222494, _1222496, _1222498] : [hBOOL(hAPP(_1222494, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1222496), _1222498))), 23033 ^ _784416 : [(23034 ^ _784416) ^ [] : [_1222498 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1222494, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23040 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222498)), 23043 ^ _784416 : [(23044 ^ _784416) ^ [_1222828] : [-(hBOOL(hAPP(_1222494, _1222828))), 23045 ^ _784416 : [(23046 ^ _784416) ^ [_1222899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222899)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1222899), _1222498)), _1222496 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1222498), _1222828)), _1222899)]]]]], (23058 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1222498), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23061 ^ _784416 : [(23062 ^ _784416) ^ [_1223158] : [-(hBOOL(hAPP(_1222494, _1223158))), 23063 ^ _784416 : [(23064 ^ _784416) ^ [_1223232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1222498), _1223232)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1223232), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1222496 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1222498), _1223158)), _1223232)]]]]]]], (23112 ^ _784416) ^ [_1224168, _1224170, _1224172, _1224174] : [_1224168 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224170), _1224172)), _1224174), -(_1224170 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1224168), _1224170) = _1224172), 23119 ^ _784416 : [(23120 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224170)))], (23122 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224174), _1224170))]], 23127 ^ _784416 : [(23128 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224170))], (23130 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224170), _1224174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224174), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (23142 ^ _784416) ^ [_1224637, _1224639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224637)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1224637, _1224639))))], (23152 ^ _784416) ^ [_1224784, _1224786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224784), _1224786)), -(c_Nat__Transfer_Otsub(_1224786, _1224784) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1224786), _1224784))], (23158 ^ _784416) ^ [_1224889, _1224891, _1224893, _1224895, _1224897] : [class_Groups_Ocomm__monoid__mult(_1224889), hBOOL(hAPP(c_Finite__Set_Ofinite(_1224891), _1224893)), hBOOL(hAPP(hAPP(c_member(_1224891), _1224895), _1224893)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1224891, _1224889), _1224897), _1224893) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1224889), hAPP(_1224897, _1224895)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1224891, _1224889), _1224897), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1224891, tc_HOL_Obool)), _1224893), hAPP(hAPP(c_Set_Oinsert(_1224891), _1224895), c_Orderings_Obot__class_Obot(tc_fun(_1224891, tc_HOL_Obool)))))))], (23172 ^ _784416) ^ [_1225214, _1225216, _1225218, _1225220] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1225214, _1225216), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1225218), _1225220))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1225214), _1225216), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1225220), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1225218)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1225218)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1225220), 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), _1225216), _1225220))))))], (23178 ^ _784416) ^ [_1225462, _1225464, _1225466, _1225468] : [c_Wellfounded_Omax__extp(_1225462, hAPP(hAPP(c_COMBC(_1225462, tc_fun(tc_prod(_1225462, _1225462), tc_HOL_Obool), tc_fun(_1225462, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1225462, tc_fun(tc_fun(tc_prod(_1225462, _1225462), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1225462, _1225462), tc_HOL_Obool), tc_fun(_1225462, tc_HOL_Obool)), _1225462), c_COMBC(_1225462, tc_fun(tc_prod(_1225462, _1225462), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1225462, tc_prod(_1225462, _1225462)), tc_fun(_1225462, tc_fun(tc_fun(tc_prod(_1225462, _1225462), tc_HOL_Obool), tc_HOL_Obool)), _1225462), hAPP(c_COMBB(tc_prod(_1225462, _1225462), tc_fun(tc_fun(tc_prod(_1225462, _1225462), tc_HOL_Obool), tc_HOL_Obool), _1225462), c_member(tc_prod(_1225462, _1225462)))), c_Product__Type_OPair(_1225462, _1225462)))), _1225464), _1225466, _1225468), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1225462, tc_HOL_Obool), tc_fun(_1225462, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1225462, tc_HOL_Obool), tc_fun(_1225462, tc_HOL_Obool)), _1225466), _1225468)), c_Wellfounded_Omax__ext(_1225462, _1225464))))], (23184 ^ _784416) ^ [_1225847, _1225849, _1225851, _1225853] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1225847, tc_HOL_Obool), tc_fun(_1225847, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1225847, tc_HOL_Obool), tc_fun(_1225847, tc_HOL_Obool)), _1225851), _1225853)), c_Wellfounded_Omax__ext(_1225847, _1225849))), -(c_Wellfounded_Omax__extp(_1225847, hAPP(hAPP(c_COMBC(_1225847, tc_fun(tc_prod(_1225847, _1225847), tc_HOL_Obool), tc_fun(_1225847, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1225847, tc_fun(tc_fun(tc_prod(_1225847, _1225847), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1225847, _1225847), tc_HOL_Obool), tc_fun(_1225847, tc_HOL_Obool)), _1225847), c_COMBC(_1225847, tc_fun(tc_prod(_1225847, _1225847), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1225847, tc_prod(_1225847, _1225847)), tc_fun(_1225847, tc_fun(tc_fun(tc_prod(_1225847, _1225847), tc_HOL_Obool), tc_HOL_Obool)), _1225847), hAPP(c_COMBB(tc_prod(_1225847, _1225847), tc_fun(tc_fun(tc_prod(_1225847, _1225847), tc_HOL_Obool), tc_HOL_Obool), _1225847), c_member(tc_prod(_1225847, _1225847)))), c_Product__Type_OPair(_1225847, _1225847)))), _1225849), _1225851, _1225853))], (23190 ^ _784416) ^ [_1226247, _1226249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226247)), -(c_SMT_Oz3div(_1226249, _1226247) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1226249), _1226247))], (23196 ^ _784416) ^ [_1226340, _1226342] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226340))), -(c_SMT_Oz3div(_1226342, _1226340) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1226342), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226340))))], (23202 ^ _784416) ^ [_1226404, _1226406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226404), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1226406, _1226404) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226406), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226404)))], (23208 ^ _784416) ^ [_1226510, _1226512] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226510), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 23211 ^ _784416 : [(23212 ^ _784416) ^ [] : [23213 ^ _784416 : [(23214 ^ _784416) ^ [] : [_1226512 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23216 ^ _784416) ^ [] : [_1226510 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1226512, _1226510) = 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)))], (23220 ^ _784416) ^ [] : [-(c_Nitpick_Onorm__frac(_1226512, _1226510) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1226512), _1226510)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1226512))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1226510)))), -(_1226512 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1226510 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (23230 ^ _784416) ^ [_1226808, _1226810, _1226812, _1226814, _1226816] : [class_Groups_Ocomm__monoid__mult(_1226808), hBOOL(hAPP(c_Finite__Set_Ofinite(_1226810), _1226812)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1226810), _1226814)), 23244 ^ _784416 : [(23245 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1226810), 23243 ^ [_1226808, _1226810, _1226812, _1226814, _1226816]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1226810, tc_HOL_Obool)), _1226812), _1226814))))], (23247 ^ _784416) ^ [] : [hAPP(_1226816, 23243 ^ [_1226808, _1226810, _1226812, _1226814, _1226816]) = c_Groups_Oone__class_Oone(_1226808)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1226810, _1226808), _1226816), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1226810, tc_HOL_Obool)), _1226812), _1226814)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226808), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1226810, _1226808), _1226816), _1226812)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1226810, _1226808), _1226816), _1226814)))], (23251 ^ _784416) ^ [_1227303, _1227305, _1227307, _1227309, _1227311] : [class_Groups_Ocomm__monoid__mult(_1227303), hBOOL(hAPP(c_Finite__Set_Ofinite(_1227305), _1227307)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1227305), _1227309)), 23265 ^ _784416 : [(23266 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1227305), 23264 ^ [_1227303, _1227305, _1227307, _1227309, _1227311]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1227305, tc_HOL_Obool)), _1227307), _1227309))))], (23268 ^ _784416) ^ [] : [hAPP(_1227311, 23264 ^ [_1227303, _1227305, _1227307, _1227309, _1227311]) = c_Groups_Oone__class_Oone(_1227303)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1227305, _1227303), _1227311), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1227305, tc_HOL_Obool)), _1227307), _1227309)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227303), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1227305, _1227303), _1227311), _1227307)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1227305, _1227303), _1227311), _1227309)))], (23272 ^ _784416) ^ [_1227798, _1227800, _1227802, _1227804, _1227806] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1227798, _1227800), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1227802), _1227804))), -(_1227800 = 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)), _1227806)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1227798, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1227800), _1227806)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1227802), _1227806)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1227800), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1227802, _1227806))), _1227804)))))], (23286 ^ _784416) ^ [_1228104, _1228106, _1228108, _1228110, _1228112, _1228114] : [class_Divides_Osemiring__div(_1228104), c_Divides_Odiv__class_Omod(_1228104, _1228106, _1228108) = c_Divides_Odiv__class_Omod(_1228104, _1228110, _1228108), c_Divides_Odiv__class_Omod(_1228104, _1228112, _1228108) = c_Divides_Odiv__class_Omod(_1228104, _1228114, _1228108), -(c_Divides_Odiv__class_Omod(_1228104, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228104), _1228106), _1228112), _1228108) = c_Divides_Odiv__class_Omod(_1228104, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228104), _1228110), _1228114), _1228108))], (23300 ^ _784416) ^ [_1228387, _1228389, _1228391, _1228393] : [class_Divides_Osemiring__div(_1228387), -(c_Divides_Odiv__class_Omod(_1228387, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228387), c_Divides_Odiv__class_Omod(_1228387, _1228389, _1228391)), _1228393), _1228391) = c_Divides_Odiv__class_Omod(_1228387, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228387), _1228389), _1228393), _1228391))], (23306 ^ _784416) ^ [_1228522, _1228524, _1228526, _1228528] : [class_Divides_Osemiring__div(_1228522), -(c_Divides_Odiv__class_Omod(_1228522, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228522), _1228524), c_Divides_Odiv__class_Omod(_1228522, _1228526, _1228528)), _1228528) = c_Divides_Odiv__class_Omod(_1228522, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228522), _1228524), _1228526), _1228528))], (23312 ^ _784416) ^ [_1228657, _1228659, _1228661, _1228663] : [class_Divides_Osemiring__div(_1228657), -(c_Divides_Odiv__class_Omod(_1228657, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228657), _1228659), _1228661), _1228663) = c_Divides_Odiv__class_Omod(_1228657, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228657), c_Divides_Odiv__class_Omod(_1228657, _1228659, _1228663)), c_Divides_Odiv__class_Omod(_1228657, _1228661, _1228663)), _1228663))], (23318 ^ _784416) ^ [_1228800, _1228802, _1228804, _1228806] : [class_Divides_Osemiring__div(_1228800), -(c_Divides_Odiv__class_Omod(_1228800, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228800), _1228802), _1228804), _1228806) = c_Divides_Odiv__class_Omod(_1228800, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228800), c_Divides_Odiv__class_Omod(_1228800, _1228802, _1228806)), _1228804), _1228806))], (23324 ^ _784416) ^ [_1228935, _1228937, _1228939, _1228941] : [class_Divides_Osemiring__div(_1228935), -(c_Divides_Odiv__class_Omod(_1228935, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228935), _1228937), _1228939), _1228941) = c_Divides_Odiv__class_Omod(_1228935, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1228935), _1228937), c_Divides_Odiv__class_Omod(_1228935, _1228939, _1228941)), _1228941))], (23330 ^ _784416) ^ [_1229070, _1229072, _1229074] : [class_Divides_Osemiring__div(_1229070), -(c_Divides_Odiv__class_Omod(_1229070, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1229070), _1229072), _1229074), _1229072) = c_Divides_Odiv__class_Omod(_1229070, _1229074, _1229072))], (23336 ^ _784416) ^ [_1229179, _1229181, _1229183] : [class_Divides_Osemiring__div(_1229179), -(c_Divides_Odiv__class_Omod(_1229179, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1229179), _1229181), _1229183), _1229183) = c_Divides_Odiv__class_Omod(_1229179, _1229181, _1229183))], (23342 ^ _784416) ^ [_1229288, _1229290, _1229292, _1229294, _1229296, _1229298] : [class_Divides_Osemiring__div(_1229288), c_Divides_Odiv__class_Omod(_1229288, _1229290, _1229292) = c_Divides_Odiv__class_Omod(_1229288, _1229294, _1229292), c_Divides_Odiv__class_Omod(_1229288, _1229296, _1229292) = c_Divides_Odiv__class_Omod(_1229288, _1229298, _1229292), -(c_Divides_Odiv__class_Omod(_1229288, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229288), _1229290), _1229296), _1229292) = c_Divides_Odiv__class_Omod(_1229288, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229288), _1229294), _1229298), _1229292))], (23356 ^ _784416) ^ [_1229571, _1229573, _1229575, _1229577] : [class_Divides_Osemiring__div(_1229571), -(c_Divides_Odiv__class_Omod(_1229571, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229571), c_Divides_Odiv__class_Omod(_1229571, _1229573, _1229575)), _1229577), _1229575) = c_Divides_Odiv__class_Omod(_1229571, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229571), _1229573), _1229577), _1229575))], (23362 ^ _784416) ^ [_1229706, _1229708, _1229710, _1229712] : [class_Divides_Osemiring__div(_1229706), -(c_Divides_Odiv__class_Omod(_1229706, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229706), _1229708), _1229710), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229706), _1229712), _1229710)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229706), c_Divides_Odiv__class_Omod(_1229706, _1229708, _1229712)), _1229710))], (23368 ^ _784416) ^ [_1229849, _1229851, _1229853, _1229855] : [class_Divides_Osemiring__div(_1229849), -(c_Divides_Odiv__class_Omod(_1229849, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229849), _1229851), _1229853), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229849), _1229851), _1229855)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229849), _1229851), c_Divides_Odiv__class_Omod(_1229849, _1229853, _1229855)))], (23374 ^ _784416) ^ [_1229992, _1229994, _1229996, _1229998] : [class_Divides_Osemiring__div(_1229992), -(c_Divides_Odiv__class_Omod(_1229992, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229992), _1229994), _1229996), _1229998) = c_Divides_Odiv__class_Omod(_1229992, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229992), c_Divides_Odiv__class_Omod(_1229992, _1229994, _1229998)), c_Divides_Odiv__class_Omod(_1229992, _1229996, _1229998)), _1229998))], (23380 ^ _784416) ^ [_1230135, _1230137, _1230139, _1230141] : [class_Divides_Osemiring__div(_1230135), -(c_Divides_Odiv__class_Omod(_1230135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230135), _1230137), _1230139), _1230141) = c_Divides_Odiv__class_Omod(_1230135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230135), c_Divides_Odiv__class_Omod(_1230135, _1230137, _1230141)), _1230139), _1230141))], (23386 ^ _784416) ^ [_1230270, _1230272, _1230274, _1230276] : [class_Divides_Osemiring__div(_1230270), -(c_Divides_Odiv__class_Omod(_1230270, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230270), _1230272), _1230274), _1230276) = c_Divides_Odiv__class_Omod(_1230270, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230270), _1230272), c_Divides_Odiv__class_Omod(_1230270, _1230274, _1230276)), _1230276))], (23392 ^ _784416) ^ [_1230405, _1230407] : [class_Divides_Osemiring__div(_1230405), -(c_Divides_Odiv__class_Omod(_1230405, _1230407, _1230407) = c_Groups_Ozero__class_Ozero(_1230405))], (23398 ^ _784416) ^ [_1230492, _1230494] : [class_Divides_Osemiring__div(_1230492), -(c_Divides_Odiv__class_Omod(_1230492, _1230494, c_Groups_Ozero__class_Ozero(_1230492)) = _1230494)], (23404 ^ _784416) ^ [_1230579, _1230581] : [class_Divides_Osemiring__div(_1230579), -(c_Divides_Odiv__class_Omod(_1230579, c_Groups_Ozero__class_Ozero(_1230579), _1230581) = c_Groups_Ozero__class_Ozero(_1230579))], (23410 ^ _784416) ^ [_1230670, _1230672, _1230674] : [class_Divides_Osemiring__div(_1230670), -(c_Divides_Odiv__class_Omod(_1230670, c_Divides_Odiv__class_Omod(_1230670, _1230672, _1230674), _1230674) = c_Divides_Odiv__class_Omod(_1230670, _1230672, _1230674))], (23416 ^ _784416) ^ [_1230771, _1230773, _1230775, _1230777, _1230779, _1230781] : [class_Divides_Oring__div(_1230771), c_Divides_Odiv__class_Omod(_1230771, _1230773, _1230775) = c_Divides_Odiv__class_Omod(_1230771, _1230777, _1230775), c_Divides_Odiv__class_Omod(_1230771, _1230779, _1230775) = c_Divides_Odiv__class_Omod(_1230771, _1230781, _1230775), -(c_Divides_Odiv__class_Omod(_1230771, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1230771), _1230773), _1230779), _1230775) = c_Divides_Odiv__class_Omod(_1230771, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1230771), _1230777), _1230781), _1230775))], (23430 ^ _784416) ^ [_1231054, _1231056, _1231058, _1231060] : [class_Divides_Oring__div(_1231054), -(c_Divides_Odiv__class_Omod(_1231054, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1231054), _1231056), _1231058), _1231060) = c_Divides_Odiv__class_Omod(_1231054, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1231054), c_Divides_Odiv__class_Omod(_1231054, _1231056, _1231060)), c_Divides_Odiv__class_Omod(_1231054, _1231058, _1231060)), _1231060))], (23436 ^ _784416) ^ [_1231197, _1231199, _1231201, _1231203] : [class_Divides_Oring__div(_1231197), -(c_Divides_Odiv__class_Omod(_1231197, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1231197), _1231199), _1231201), _1231203) = c_Divides_Odiv__class_Omod(_1231197, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1231197), c_Divides_Odiv__class_Omod(_1231197, _1231199, _1231203)), _1231201), _1231203))], (23442 ^ _784416) ^ [_1231332, _1231334, _1231336, _1231338] : [class_Divides_Oring__div(_1231332), -(c_Divides_Odiv__class_Omod(_1231332, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1231332), _1231334), _1231336), _1231338) = c_Divides_Odiv__class_Omod(_1231332, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1231332), _1231334), c_Divides_Odiv__class_Omod(_1231332, _1231336, _1231338)), _1231338))], (23448 ^ _784416) ^ [_1231467, _1231469, _1231471] : [class_Divides_Oring__div(_1231467), -(c_Divides_Odiv__class_Omod(_1231467, hAPP(c_Groups_Ouminus__class_Ouminus(_1231467), _1231469), _1231471) = c_Divides_Odiv__class_Omod(_1231467, hAPP(c_Groups_Ouminus__class_Ouminus(_1231467), c_Divides_Odiv__class_Omod(_1231467, _1231469, _1231471)), _1231471))], (23454 ^ _784416) ^ [_1231588, _1231590, _1231592, _1231594] : [class_Divides_Oring__div(_1231588), c_Divides_Odiv__class_Omod(_1231588, _1231590, _1231592) = c_Divides_Odiv__class_Omod(_1231588, _1231594, _1231592), -(c_Divides_Odiv__class_Omod(_1231588, hAPP(c_Groups_Ouminus__class_Ouminus(_1231588), _1231590), _1231592) = c_Divides_Odiv__class_Omod(_1231588, hAPP(c_Groups_Ouminus__class_Ouminus(_1231588), _1231594), _1231592))], (23464 ^ _784416) ^ [_1231775, _1231777, _1231779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1231775), _1231777)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1231775), _1231779)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1231777), _1231779))))], (23470 ^ _784416) ^ [_1231898, _1231900] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1231898), _1231900)), _1231898)))], (23472 ^ _784416) ^ [_1231934, _1231936, _1231938] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1231934), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1231936), _1231938)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1231934), _1231936)), _1231938))], (23474 ^ _784416) ^ [_1231985] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1231985) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23476 ^ _784416) ^ [_1232012] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1232012, _1232012) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23478 ^ _784416) ^ [_1232039, _1232041, _1232043] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232039), _1232041), _1232043) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232039), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1232041, _1232043)), _1232043))], (23480 ^ _784416) ^ [_1232090, _1232092, _1232094] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232090), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1232092, _1232094)), _1232094) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232090), _1232092), _1232094))], (23482 ^ _784416) ^ [_1232141, _1232143, _1232145] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1232141), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1232143, _1232145)), _1232145) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1232141), _1232143), _1232145))], (23484 ^ _784416) ^ [_1232192, _1232194, _1232196] : [-(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, _1232192, _1232194)), _1232196), _1232194) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1232192), _1232196), _1232194))], (23486 ^ _784416) ^ [_1232243, _1232245] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1232243, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1232245)) = 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), _1232243), _1232245)))], (23488 ^ _784416) ^ [_1232285, _1232287] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1232285), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1232287)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1232285, _1232287)))], (23490 ^ _784416) ^ [_1232327, _1232329] : [-(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, _1232327, _1232329)), _1232329) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1232327), _1232329))], (23492 ^ _784416) ^ [_1232370, _1232372, _1232374] : [-(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, _1232370, _1232372)), _1232374), _1232372) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1232370), _1232374), _1232372))], (23494 ^ _784416) ^ [_1232421, _1232423, _1232425] : [class_Divides_Osemiring__div(_1232421), -(c_Divides_Odiv__class_Omod(_1232421, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232421), _1232423), _1232425), _1232423) = c_Groups_Ozero__class_Ozero(_1232421))], (23500 ^ _784416) ^ [_1232526, _1232528, _1232530] : [class_Divides_Osemiring__div(_1232526), -(c_Divides_Odiv__class_Omod(_1232526, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232526), _1232528), _1232530), _1232530) = c_Groups_Ozero__class_Ozero(_1232526))], (23506 ^ _784416) ^ [_1232631, _1232633, _1232635, _1232637] : [class_Divides_Osemiring__div(_1232631), -(c_Divides_Odiv__class_Omod(_1232631, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1232631), _1232633), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232631), _1232635), _1232637)), _1232637) = c_Divides_Odiv__class_Omod(_1232631, _1232633, _1232637))], (23512 ^ _784416) ^ [_1232758, _1232760, _1232762, _1232764] : [class_Divides_Osemiring__div(_1232758), -(c_Divides_Odiv__class_Omod(_1232758, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1232758), _1232760), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232758), _1232762), _1232764)), _1232762) = c_Divides_Odiv__class_Omod(_1232758, _1232760, _1232762))], (23518 ^ _784416) ^ [_1232885, _1232887] : [class_Divides_Osemiring__div(_1232885), -(c_Divides_Odiv__class_Omod(_1232885, _1232887, c_Groups_Oone__class_Oone(_1232885)) = c_Groups_Ozero__class_Ozero(_1232885))], (23524 ^ _784416) ^ [_1232976, _1232978, _1232980] : [class_Divides_Osemiring__div(_1232976), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1232976), c_Divides_Odiv__class_Omod(_1232976, _1232978, _1232980)), _1232980) = c_Groups_Ozero__class_Ozero(_1232976))], (23530 ^ _784416) ^ [_1233081] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1233081), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1233081)], (23532 ^ _784416) ^ [_1233110, _1233112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1233110), _1233112)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1233110), _1233112) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23538 ^ _784416) ^ [_1233221, _1233223, _1233225] : [_1233221 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1233221), _1233223)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1233221), _1233225)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23544 ^ _784416) ^ [_1233330, _1233332, _1233334] : [-(_1233330 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1233330), _1233332)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1233330), _1233334)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1233332), _1233334))], (23550 ^ _784416) ^ [_1233394, _1233396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233394)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233394, _1233396)), _1233394)))], (23556 ^ _784416) ^ [_1233493, _1233495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233493)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233495)), -(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, _1233493, _1233495))))], (23566 ^ _784416) ^ [_1233642, _1233644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233644, _1233642)), _1233642)))], (23572 ^ _784416) ^ [_1233741, _1233743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233741), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233741), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233743, _1233741))))], (23578 ^ _784416) ^ [_1233861, _1233863] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233861, _1233863) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1233861 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1233863), 23581 ^ [_1233861, _1233863]))], (23585 ^ _784416) ^ [_1233966, _1233968] : [23586 ^ _784416 : [(23587 ^ _784416) ^ [_1234015] : [_1233966 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1233968), _1234015)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1233966, _1233968) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23591 ^ _784416) ^ [_1234077, _1234079] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234077), _1234079) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234077, _1234079) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23597 ^ _784416) ^ [_1234167, _1234169] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234167, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234169)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234167, _1234169) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23603 ^ _784416) ^ [_1234258, _1234260] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234258, _1234260)), _1234260) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23605 ^ _784416) ^ [_1234291] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234291), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23607 ^ _784416) ^ [_1234317] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234317, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1234317)], (23609 ^ _784416) ^ [_1234346, _1234348, _1234350] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1234346), _1234348)), _1234350) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234346), _1234350)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234348), _1234350))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234346, _1234350)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1234348, _1234350))), _1234350)))], (23611 ^ _784416) ^ [_1234429, _1234431, _1234433] : [class_Divides_Osemiring__div(_1234429), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1234429), c_Divides_Odiv__class_Omod(_1234429, _1234431, _1234433)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234429), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1234429), _1234431), _1234433)), _1234433)) = _1234431)], (23617 ^ _784416) ^ [_1234562, _1234564, _1234566] : [class_Divides_Osemiring__div(_1234562), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1234562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234562), _1234564), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1234562), _1234566), _1234564))), c_Divides_Odiv__class_Omod(_1234562, _1234566, _1234564)) = _1234566)], (23623 ^ _784416) ^ [_1234695, _1234697, _1234699] : [class_Divides_Osemiring__div(_1234695), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1234695), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234695), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1234695), _1234697), _1234699)), _1234699)), c_Divides_Odiv__class_Omod(_1234695, _1234697, _1234699)) = _1234697)], (23629 ^ _784416) ^ [_1234828, _1234830, _1234832, _1234834] : [class_Divides_Osemiring__div(_1234828), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1234828), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1234828), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234828), _1234830), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1234828), _1234832), _1234830))), c_Divides_Odiv__class_Omod(_1234828, _1234832, _1234830))), _1234834) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1234828), _1234832), _1234834))], (23635 ^ _784416) ^ [_1234995, _1234997, _1234999, _1235001] : [class_Divides_Osemiring__div(_1234995), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1234995), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1234995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1234995), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1234995), _1234997), _1234999)), _1234999)), c_Divides_Odiv__class_Omod(_1234995, _1234997, _1234999))), _1235001) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1234995), _1234997), _1235001))], (23641 ^ _784416) ^ [_1235162, _1235164, _1235166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1235162)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1235162), _1235164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235166), _1235164)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235166), _1235162))))], (23651 ^ _784416) ^ [_1235343, _1235345, _1235347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1235343)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1235343), _1235345)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1235343), _1235347)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235345), _1235347))], (23657 ^ _784416) ^ [_1235474, _1235476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1235474)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1235476), _1235474)), _1235474) = _1235476)], (23663 ^ _784416) ^ [_1235579, _1235581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1235579)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1235579), _1235581)), _1235579) = _1235581)], (23669 ^ _784416) ^ [_1235684, _1235686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1235684)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1235686)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1235686), _1235684)), _1235686)))], (23679 ^ _784416) ^ [_1235843, _1235845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235843)), -(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, _1235845, _1235843))))], (23685 ^ _784416) ^ [_1235936, _1235938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235936)), 23688 ^ _784416 : [(23689 ^ _784416) ^ [] : [-(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, _1235938, _1235936))))], (23691 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1235938, _1235936)), _1235936)))]]], (23693 ^ _784416) ^ [_1236073, _1236075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236073)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236073), _1236075)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236073, _1236075) = _1236073)], (23703 ^ _784416) ^ [_1236224, _1236226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236224), 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, _1236226, _1236224)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23709 ^ _784416) ^ [_1236329, _1236331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236329), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23712 ^ _784416 : [(23713 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236331, _1236329)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23715 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236329), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236331, _1236329))))]]], (23717 ^ _784416) ^ [_1236478, _1236480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1236478), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236480), _1236478)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236478, _1236480) = _1236478)], (23727 ^ _784416) ^ [_1236644, _1236646] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236644, _1236646) = 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), _1236644), _1236646) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23733 ^ _784416) ^ [_1236737, _1236739] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236737, _1236739) = 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), _1236737), _1236739) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1236739), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236737, _1236739)))], (23739 ^ _784416) ^ [_1236805, _1236807] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236805, _1236807) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236805, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1236807)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23745 ^ _784416) ^ [_1236898, _1236900] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236898, _1236900) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236898, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1236900)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236898, _1236900)), _1236900))], (23751 ^ _784416) ^ [_1236957, _1236959] : [-(_1236957 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1236959), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1236957), _1236959))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1236957, _1236959)))], (23753 ^ _784416) ^ [_1237004, _1237006, _1237008] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1237004), _1237006)), _1237008) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1237004), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1237006), _1237008))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1237004), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1237006, _1237008))), _1237008)))], (23755 ^ _784416) ^ [_1237077, _1237079, _1237081] : [-(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), _1237077), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1237079), _1237077))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1237079, _1237077))), _1237081) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1237079), _1237081))], (23757 ^ _784416) ^ [_1237138, _1237140, _1237142] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1237138), _1237140)), _1237140)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1237138, _1237140))), _1237142) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1237138), _1237142))], (23759 ^ _784416) ^ [_1237199, _1237201] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1237199, _1237201) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1237199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1237199), _1237201)), _1237201)))], (23761 ^ _784416) ^ [_1237246, _1237248] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1237246), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1237248), _1237246)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1237248), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1237248, _1237246)))], (23763 ^ _784416) ^ [_1237293, _1237295, _1237297, _1237299] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1237293, _1237295), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1237297), _1237299))), -(_1237295 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1237293, _1237295) = _1237299)], (23773 ^ _784416) ^ [_1237419, _1237421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1237419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237421), _1237419))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1237421), _1237419) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1237421), _1237419)), _1237419)))], (23783 ^ _784416) ^ [_1237567, _1237569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1237567)), 23786 ^ _784416 : [(23787 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237569), _1237567)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1237569), _1237567) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23793 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1237569), _1237567))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1237569), _1237567) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1237569), _1237567)), _1237567)))]]], (23823 ^ _784416) ^ [_1238276, _1238278, _1238280] : [-(hBOOL(hAPP(_1238276, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1238278), _1238280)))), 23826 ^ _784416 : [(23827 ^ _784416) ^ [] : [-(_1238280 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23829 ^ _784416) ^ [] : [hBOOL(hAPP(_1238276, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 23830 ^ _784416 : [(23831 ^ _784416) ^ [] : [_1238280 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23835 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 23833 ^ [_1238276, _1238278, _1238280]), _1238280)))], (23837 ^ _784416) ^ [] : [-(_1238278 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1238280), 23832 ^ [_1238276, _1238278, _1238280])), 23833 ^ [_1238276, _1238278, _1238280]))], (23839 ^ _784416) ^ [] : [hBOOL(hAPP(_1238276, 23832 ^ [_1238276, _1238278, _1238280]))]]], (23799 ^ _784416) ^ [_1237839, _1237841, _1237843] : [hBOOL(hAPP(_1237839, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1237841), _1237843))), 23802 ^ _784416 : [(23803 ^ _784416) ^ [] : [_1237843 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1237839, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23809 ^ _784416) ^ [] : [-(_1237843 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 23812 ^ _784416 : [(23813 ^ _784416) ^ [_1238091, _1238093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1238091), _1237843)), _1237841 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1237843), _1238093)), _1238091), -(hBOOL(hAPP(_1237839, _1238093)))]]]]], (23843 ^ _784416) ^ [_1238698, _1238700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238698)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1238698), _1238700)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1238698, _1238700) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1238698), _1238700))], (23853 ^ _784416) ^ [_1238869, _1238871] : [-(_1238869 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1238871, _1238869), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1238871), _1238869)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1238871, _1238869)))))], (23859 ^ _784416) ^ [_1238926, _1238928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1238926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1238926), _1238928)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1238928), _1238926) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1238928), _1238926)), _1238926)))], (23869 ^ _784416) ^ [_1239129, _1239131, _1239133] : [hBOOL(hAPP(_1239129, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1239131), _1239133))), 23874 ^ _784416 : [(23875 ^ _784416) ^ [] : [-(_1239133 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23877 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1239129, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 23879 ^ _784416 : [(23880 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1239133), 23878 ^ [_1239129, _1239131, _1239133])), _1239131)))], (23882 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1239131), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1239133), hAPP(c_Nat_OSuc, 23878 ^ [_1239129, _1239131, _1239133])))))], (23884 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1239129, 23878 ^ [_1239129, _1239131, _1239133])))]]], (23886 ^ _784416) ^ [_1239433, _1239435, _1239437] : [-(hBOOL(hAPP(_1239433, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1239435), _1239437)))), 23887 ^ _784416 : [(23888 ^ _784416) ^ [] : [_1239437 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1239433, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23894 ^ _784416) ^ [_1239601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1239437), _1239601)), _1239435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1239435), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1239437), hAPP(c_Nat_OSuc, _1239601)))), hBOOL(hAPP(_1239433, _1239601))]]], (23906 ^ _784416) ^ [_1239831, _1239833, _1239835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1239831)), 23909 ^ _784416 : [(23920 ^ _784416) ^ [] : [_1239833 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1239835), _1239831), 23923 ^ _784416 : [(23924 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1239831), _1239833)), _1239835)))], (23926 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1239835), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1239831), hAPP(c_Nat_OSuc, _1239833)))))]]], (23910 ^ _784416) ^ [] : [-(_1239833 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1239835), _1239831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1239831), _1239833)), _1239835)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1239835), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1239831), hAPP(c_Nat_OSuc, _1239833))))]]], (23928 ^ _784416) ^ [_1240215, _1240217, _1240219, _1240221] : [_1240215 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1240217), _1240219)), _1240221), -(_1240217 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1240215, _1240217) = _1240221), 23935 ^ _784416 : [(23936 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240217)))], (23938 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1240221), _1240217))]], 23943 ^ _784416 : [(23944 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240217))], (23946 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1240217), _1240221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1240221), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (23958 ^ _784416) ^ [_1240680, _1240682, _1240684, _1240686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240680)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1240682), _1240684)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1240684), 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), _1240682), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1240686, _1240680))), _1240684)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23972 ^ _784416) ^ [_1240939, _1240941, _1240943, _1240945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240939)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1240941), _1240943)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1240943), 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), _1240941), _1240939)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1240941), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1240945, _1240939))), _1240943))))], (23986 ^ _784416) ^ [_1241210, _1241212, _1241214, _1241216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241210)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241212)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241212), _1241214)), -(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), _1241214), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1241216, _1241210))), _1241212)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241214), _1241210))))], (24000 ^ _784416) ^ [_1241475, _1241477, _1241479, _1241481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241475)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241477), _1241479)), -(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), _1241479), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1241481, _1241475))), _1241477))))], (24060 ^ _784416) ^ [_1242617, _1242619, _1242621] : [-(hBOOL(hAPP(_1242617, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1242619, _1242621)))), 24063 ^ _784416 : [(24064 ^ _784416) ^ [] : [-(_1242621 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24066 ^ _784416) ^ [] : [hBOOL(hAPP(_1242617, _1242619))]], 24069 ^ _784416 : [(24070 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242621)))], (24074 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24072 ^ [_1242617, _1242619, _1242621])))], (24076 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24072 ^ [_1242617, _1242619, _1242621]), _1242621)))], (24078 ^ _784416) ^ [] : [-(_1242619 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242621), 24071 ^ [_1242617, _1242619, _1242621])), 24072 ^ [_1242617, _1242619, _1242621]))], (24080 ^ _784416) ^ [] : [hBOOL(hAPP(_1242617, 24072 ^ [_1242617, _1242619, _1242621]))]], 24081 ^ _784416 : [(24082 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1242621), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24086 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1242621), 24084 ^ [_1242617, _1242619, _1242621])))], (24088 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24084 ^ [_1242617, _1242619, _1242621]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24090 ^ _784416) ^ [] : [-(_1242619 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1242621), 24083 ^ [_1242617, _1242619, _1242621])), 24084 ^ [_1242617, _1242619, _1242621]))], (24092 ^ _784416) ^ [] : [hBOOL(hAPP(_1242617, 24084 ^ [_1242617, _1242619, _1242621]))]]], (24014 ^ _784416) ^ [_1241740, _1241742, _1241744] : [hBOOL(hAPP(_1241740, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1241742, _1241744))), 24017 ^ _784416 : [(24018 ^ _784416) ^ [] : [_1241744 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1241740, _1241742)))], (24024 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241744)), 24027 ^ _784416 : [(24028 ^ _784416) ^ [_1242070, _1242072] : [-(hBOOL(hAPP(_1241740, _1242070))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1242070), _1241744)), _1241742 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241744), _1242072)), _1242070)]]], (24042 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241744), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24045 ^ _784416 : [(24046 ^ _784416) ^ [_1242362, _1242364] : [-(hBOOL(hAPP(_1241740, _1242362))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241744), _1242362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1242362), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1241742 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1241744), _1242364)), _1242362)]]]]], (24096 ^ _784416) ^ [_1243329, _1243331, _1243333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243329)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243331, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1243333), _1243329)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1243333), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243331), _1243333), _1243329))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243331, _1243333)))], (24102 ^ _784416) ^ [_1243483, _1243485] : [-(_1243483 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24105 ^ _784416 : [(24106 ^ _784416) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243485, _1243483) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243485)), _1243483) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243485), _1243483)))], (24112 ^ _784416) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243485, _1243483) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243485)), _1243483) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243485), _1243483))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (24118 ^ _784416) ^ [_1243756, _1243758] : [-(_1243756 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24121 ^ _784416 : [(24122 ^ _784416) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243758, _1243756) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243758), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243756)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243758), _1243756)))], (24128 ^ _784416) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1243758, _1243756) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243758), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243756)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243758), _1243756))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (24134 ^ _784416) ^ [_1244030, _1244032, _1244034, _1244036, _1244038, _1244040, _1244042] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1244030, _1244032), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1244034), _1244036))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1244038, _1244032), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1244040), _1244042))), -(_1244032 = 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), _1244030), _1244038), _1244032), 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), _1244034), _1244040)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244036), _1244042)), _1244032))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244036), _1244042), _1244032)))))], (24148 ^ _784416) ^ [_1244340, _1244342, _1244344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1244340), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24151 ^ _784416 : [(24170 ^ _784416) ^ [] : [24173 ^ _784416 : [(24174 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1244340), 24172 ^ [_1244340, _1244342, _1244344])))], (24176 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24172 ^ [_1244340, _1244342, _1244344]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24178 ^ _784416) ^ [] : [-(_1244344 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244340), 24171 ^ [_1244340, _1244342, _1244344])), 24172 ^ [_1244340, _1244342, _1244344]))], (24180 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1244342, 24171 ^ [_1244340, _1244342, _1244344]), 24172 ^ [_1244340, _1244342, _1244344]))]], -(hBOOL(hAPP(hAPP(_1244342, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1244344), _1244340)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1244344, _1244340))))], (24152 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1244342, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1244344), _1244340)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1244344, _1244340))), 24155 ^ _784416 : [(24156 ^ _784416) ^ [_1244550, _1244552] : [-(hBOOL(hAPP(hAPP(_1244342, _1244552), _1244550))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1244340), _1244550)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1244550), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1244344 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244340), _1244552)), _1244550)]]]]], (24184 ^ _784416) ^ [_1245073, _1245075, _1245077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245073)), 24187 ^ _784416 : [(24206 ^ _784416) ^ [] : [24209 ^ _784416 : [(24210 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24208 ^ [_1245073, _1245075, _1245077])))], (24212 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24208 ^ [_1245073, _1245075, _1245077]), _1245073)))], (24214 ^ _784416) ^ [] : [-(_1245077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1245073), 24207 ^ [_1245073, _1245075, _1245077])), 24208 ^ [_1245073, _1245075, _1245077]))], (24216 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1245075, 24207 ^ [_1245073, _1245075, _1245077]), 24208 ^ [_1245073, _1245075, _1245077]))]], -(hBOOL(hAPP(hAPP(_1245075, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1245077), _1245073)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1245077, _1245073))))], (24188 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1245075, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1245077), _1245073)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1245077, _1245073))), 24191 ^ _784416 : [(24192 ^ _784416) ^ [_1245274, _1245276] : [-(hBOOL(hAPP(hAPP(_1245075, _1245276), _1245274))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245274)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1245274), _1245073)), _1245077 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1245073), _1245276)), _1245274)]]]]], (24220 ^ _784416) ^ [_1245788, _1245790, _1245792, _1245794, _1245796] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1245788, _1245790), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1245792), _1245794))), -(_1245790 = 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), _1245796), _1245788), _1245790), 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), _1245796), _1245792)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1245796), _1245794)), _1245790))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1245796), _1245794), _1245790)))))], (24230 ^ _784416) ^ [_1246019, _1246021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246019)), -(c_SMT_Oz3mod(_1246021, _1246019) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1246021, _1246019))], (24236 ^ _784416) ^ [_1246108, _1246110] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246108))), -(c_SMT_Oz3mod(_1246110, _1246108) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1246110, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1246108)))], (24242 ^ _784416) ^ [_1246158, _1246160] : [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), _1246158), _1246160))), 24245 ^ _784416 : [(24246 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1246160), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1246158, _1246160) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1246158), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1246160)))], (24252 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1246160), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 24255 ^ _784416 : [(24256 ^ _784416) ^ [] : [24257 ^ _784416 : [(24258 ^ _784416) ^ [] : [_1246158 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (24260 ^ _784416) ^ [] : [_1246160 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1246158, _1246160) = 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)))], (24264 ^ _784416) ^ [] : [-(c_Nitpick_Onorm__frac(_1246158, _1246160) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1246158), _1246160)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1246158))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1246160)))), -(_1246158 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1246160 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]]]], (24274 ^ _784416) ^ [_1246650, _1246652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1246650), 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)), _1246652)), -(c_Divides_OnegDivAlg(_1246650, _1246652) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1246650), _1246652)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1246650, _1246652)))], (24284 ^ _784416) ^ [_1246831, _1246833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246833)), -(c_Divides_OposDivAlg(_1246831, _1246833) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1246831), _1246833)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1246831, _1246833)))], (24294 ^ _784416) ^ [_1247006, _1247008] : [-(c_Divides_Odivmod__int(_1247006, _1247008) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1247006), _1247008)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1247006, _1247008)))], (24296 ^ _784416) ^ [_1247050, _1247052, _1247054, _1247056] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1247050, _1247052), _1247054)), hBOOL(hAPP(hAPP(_1247052, _1247056), _1247054)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1247050, _1247052), _1247056)))], (24316 ^ _784416) ^ [_1247421, _1247423, _1247425] : [24318 ^ _784416 : [(24319 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1247423, 24317 ^ [_1247421, _1247423, _1247425]), _1247425)))], (24321 ^ _784416) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1247421, _1247423), 24317 ^ [_1247421, _1247423, _1247425]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1247421, _1247423), _1247425)))], (24306 ^ _784416) ^ [_1247235, _1247237, _1247239] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1247235, _1247237), _1247239)), 24309 ^ _784416 : [(24310 ^ _784416) ^ [_1247320] : [hBOOL(hAPP(hAPP(_1247237, _1247320), _1247239)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1247235, _1247237), _1247320)))]]], (24335 ^ _784416) ^ [_1247811, _1247813, _1247815] : [24337 ^ _784416 : [(24338 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1247813, 24336 ^ [_1247811, _1247813, _1247815]), _1247815)))], (24340 ^ _784416) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1247811, _1247813), 24336 ^ [_1247811, _1247813, _1247815]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1247811, _1247813), _1247815)))], (24325 ^ _784416) ^ [_1247625, _1247627, _1247629] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1247625, _1247627), _1247629)), 24328 ^ _784416 : [(24329 ^ _784416) ^ [_1247710] : [hBOOL(hAPP(hAPP(_1247627, _1247710), _1247629)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1247625, _1247627), _1247710)))]]], (24344 ^ _784416) ^ [_1247997, _1247999] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1247997), _1247999) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1247997, _1247999)), _1247999))], (24346 ^ _784416) ^ [_1248040, _1248042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1248040), _1248042)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248040, _1248042) = _1248040)], (24352 ^ _784416) ^ [_1248135, _1248137, _1248139] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1248135), _1248137)), _1248139) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1248135), _1248139)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1248137), _1248139))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248135, _1248139)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248137, _1248139))), _1248139)))], (24354 ^ _784416) ^ [_1248218, _1248220] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248218, _1248220)), _1248218)))], (24356 ^ _784416) ^ [_1248252, _1248254, _1248256] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248252, _1248254)), _1248256) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248252), _1248256), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248254), _1248256)))], (24358 ^ _784416) ^ [_1248305, _1248307, _1248309] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248305), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248307, _1248309)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248305), _1248307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248305), _1248309)))], (24360 ^ _784416) ^ [_1248367, _1248369] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248367, _1248369)) = _1248369, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1248367), _1248369) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24366 ^ _784416) ^ [_1248466, _1248468] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248466, _1248468)) = _1248468), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1248466), _1248468) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248466, _1248468)))], (24372 ^ _784416) ^ [_1248525] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248525, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24374 ^ _784416) ^ [_1248552, _1248554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1248552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248554, _1248552)), _1248552)))], (24380 ^ _784416) ^ [_1248666, _1248668] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248666, _1248668) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1248666 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248668), 24383 ^ [_1248666, _1248668]))], (24387 ^ _784416) ^ [_1248771, _1248773] : [24388 ^ _784416 : [(24389 ^ _784416) ^ [_1248820] : [_1248771 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1248773), _1248820)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248771, _1248773) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24393 ^ _784416) ^ [_1248879, _1248881] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1248879), _1248881))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248879, _1248881) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1248879), _1248881), _1248881))], (24399 ^ _784416) ^ [_1248943, _1248945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1248943), _1248945)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1248943, _1248945) = _1248943)], (24405 ^ _784416) ^ [_1249032, _1249034] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1249032), _1249034))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1249032, _1249034) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1249032), _1249034), _1249034))], (24411 ^ _784416) ^ [_1249089, _1249091, _1249093] : [-(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), _1249089), _1249091)), _1249093), _1249091) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1249093, _1249091))], (24413 ^ _784416) ^ [_1249136, _1249138, _1249140] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1249136, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1249138), _1249140)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1249138), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1249136), _1249138), _1249140))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1249136, _1249138)))], (24415 ^ _784416) ^ [_1249199, _1249201, _1249203] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1249199), _1249201)), _1249203) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1249199), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1249201), _1249203))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1249199), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1249201, _1249203))), _1249203)))], (24417 ^ _784416) ^ [_1249272, _1249274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1249272), _1249274)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1249274, _1249272) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1249274), _1249272), _1249272))], (24423 ^ _784416) ^ [_1249387, _1249389] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1249387, _1249389) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1249387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1249387), _1249389)), _1249389)))], (24425 ^ _784416) ^ [_1249434, _1249436] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1249434), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1249436), _1249434)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1249436), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1249436, _1249434)))], (24427 ^ _784416) ^ [_1249481, _1249483] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1249481), _1249483)), _1249483) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1249481), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1249481, _1249483)))], (24429 ^ _784416) ^ [_1249528, _1249530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1249528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1249530, _1249528)), _1249528)))], (24435 ^ _784416) ^ [_1249627, _1249629, _1249631] : [-(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), _1249627), _1249629)), _1249631)), _1249629) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1249631), _1249629))], (24437 ^ _784416) ^ [_1249680] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1249680) = 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)))], (24439 ^ _784416) ^ [_1249706, _1249708, _1249710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1249706, tc_fun(_1249706, tc_HOL_Obool))), _1249708), _1249710)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1249706, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1249706, _1249710)), c_Wellfounded_Oaccp(_1249706, _1249708))))], (24445 ^ _784416) ^ [_1249843, _1249845, _1249847, _1249849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1249843)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1249845), _1249847)), -(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), _1249847), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1249849, _1249843))), _1249845)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1249847), _1249843))))], (24479 ^ _784416) ^ [_1250499, _1250501, _1250503] : [-(hBOOL(hAPP(_1250499, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1250501, _1250503)))), 24482 ^ _784416 : [(24483 ^ _784416) ^ [] : [-(_1250503 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24485 ^ _784416) ^ [] : [hBOOL(hAPP(_1250499, _1250501))]], 24486 ^ _784416 : [(24487 ^ _784416) ^ [] : [_1250503 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24491 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24489 ^ [_1250499, _1250501, _1250503]), _1250503)))], (24493 ^ _784416) ^ [] : [-(_1250501 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1250503), 24488 ^ [_1250499, _1250501, _1250503])), 24489 ^ [_1250499, _1250501, _1250503]))], (24495 ^ _784416) ^ [] : [hBOOL(hAPP(_1250499, 24489 ^ [_1250499, _1250501, _1250503]))]]], (24455 ^ _784416) ^ [_1250066, _1250068, _1250070] : [hBOOL(hAPP(_1250066, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1250068, _1250070))), 24458 ^ _784416 : [(24459 ^ _784416) ^ [] : [_1250070 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1250066, _1250068)))], (24465 ^ _784416) ^ [] : [-(_1250070 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24468 ^ _784416 : [(24469 ^ _784416) ^ [_1250314, _1250316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1250314), _1250070)), _1250068 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1250070), _1250316)), _1250314), -(hBOOL(hAPP(_1250066, _1250314)))]]]]], (24499 ^ _784416) ^ [_1250908, _1250910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1250908)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1250908), _1250910)), _1250908) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (24505 ^ _784416) ^ [_1251015, _1251017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251015), 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)), _1251017)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1251015, _1251017), c_Divides_OnegDivAlg(_1251015, _1251017))))], (24515 ^ _784416) ^ [_1251170, _1251172] : [-(_1251170 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1251172, _1251170), c_Divides_Odivmod__int(_1251172, _1251170))))], (24521 ^ _784416) ^ [_1251214, _1251216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251214)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251216)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1251214, _1251216), c_Divides_OposDivAlg(_1251214, _1251216))))], (24557 ^ _784416) ^ [_1251746, _1251748] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251746))), 24560 ^ _784416 : [(24561 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251748)), -(c_Divides_Odivmod__int(_1251746, _1251748) = c_Divides_OnegDivAlg(_1251746, _1251748))], (24567 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251748))), -(c_Divides_Odivmod__int(_1251746, _1251748) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1251746), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1251748))))]]], (24531 ^ _784416) ^ [_1251376, _1251378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251376)), 24534 ^ _784416 : [(24535 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251378)), -(c_Divides_Odivmod__int(_1251376, _1251378) = c_Divides_OposDivAlg(_1251376, _1251378))], (24541 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251378))), 24544 ^ _784416 : [(24545 ^ _784416) ^ [] : [_1251376 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1251376, _1251378) = 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)))], (24551 ^ _784416) ^ [] : [-(_1251376 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1251376, _1251378) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1251376), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1251378))))]]]]], (24573 ^ _784416) ^ [_1251974, _1251976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1251974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1251974), _1251976)), -(c_Divides_Odivmod__nat(_1251976, _1251974) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1251976), _1251974)), _1251974))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1251976), _1251974), _1251974)))], (24583 ^ _784416) ^ [_1252185, _1252187, _1252189] : [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), _1252185), _1252187))), -(hBOOL(hAPP(hAPP(_1252189, _1252185), _1252187))), 24590 ^ _784416 : [(24591 ^ _784416) ^ [] : [-(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), 24588 ^ [_1252185, _1252187, _1252189]), 24589 ^ [_1252185, _1252187, _1252189]))))], (24599 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1252189, 24588 ^ [_1252185, _1252187, _1252189]), 24589 ^ [_1252185, _1252187, _1252189]))], (24593 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24589 ^ [_1252185, _1252187, _1252189]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1252189, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 24588 ^ [_1252185, _1252187, _1252189])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 24589 ^ [_1252185, _1252187, _1252189]))))]]], (24603 ^ _784416) ^ [_1252658, _1252660, _1252662, _1252664, _1252666] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1252658, _1252660), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1252662), _1252664))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1252660)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1252666), _1252658), _1252660), 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), _1252666), _1252662)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1252666), _1252664)), _1252660))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1252666), _1252664), _1252660)))))], (24613 ^ _784416) ^ [_1252927, _1252929, _1252931, _1252933, _1252935] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1252927, _1252929), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1252931), _1252933))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1252929)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1252935)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1252927, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1252929), _1252935)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1252931), _1252935)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1252929), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1252931, _1252935))), _1252933)))))], (24627 ^ _784416) ^ [_1253234, _1253236, _1253238, _1253240] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1253234, _1253236), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1253238), _1253240))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1253234, _1253236) = _1253240)], (24633 ^ _784416) ^ [_1253345, _1253347] : [-(c_Divides_Odivmod__nat(_1253345, _1253347) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1253345, _1253347)))], (24635 ^ _784416) ^ [_1253379, _1253381] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1253379, _1253381), c_Divides_Odivmod__nat(_1253379, _1253381))))], (24637 ^ _784416) ^ [_1253412, _1253414, _1253416] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1253412, _1253414), _1253416)), -(c_Divides_Odivmod__nat(_1253412, _1253414) = _1253416)], (24643 ^ _784416) ^ [_1253507, _1253509, _1253511, _1253513] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1253507, _1253509), _1253511)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1253507, _1253509), _1253513)), -(_1253511 = _1253513)], (24653 ^ _784416) ^ [_1253664, _1253666] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1253664, _1253666), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1253664), _1253666)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1253664, _1253666)))))], (24655 ^ _784416) ^ [_1253710, _1253712, _1253714, _1253716] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1253710, _1253712), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1253714), _1253716))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1253710), _1253712) = _1253714)], (24661 ^ _784416) ^ [_1253825] : [-(c_Divides_Odivmod__nat(_1253825, 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)), _1253825))], (24663 ^ _784416) ^ [_1253854, _1253856] : [-(c_Divides_Odivmod__nat(_1253854, _1253856) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1253854), _1253856)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1253854, _1253856)))], (24665 ^ _784416) ^ [_1253898, _1253900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1253898), _1253900)), -(c_Divides_Odivmod__nat(_1253898, _1253900) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1253898))], (24671 ^ _784416) ^ [_1253997, _1253999] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1253997), _1253999)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1253997), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1253999)))], (24673 ^ _784416) ^ [_1254040, _1254042, _1254044] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1254040), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1254042)), _1254044)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1254040, _1254042), hAPP(c_Divides_OnegateSnd, _1254044))))], (24679 ^ _784416) ^ [_1254157, _1254159, _1254161, _1254163, _1254165, _1254167, _1254169] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1254157, _1254159), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1254161), _1254163))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1254165, _1254159), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1254167), _1254169))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1254159)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1254157), _1254165), _1254159), 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), _1254161), _1254167)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1254163), _1254169)), _1254159))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1254163), _1254169), _1254159)))))], (24693 ^ _784416) ^ [_1254518, _1254520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1254518), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1254520), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1254518, _1254520) = 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), _1254518), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1254520)))))], (24703 ^ _784416) ^ [_1254705, _1254707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1254705), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1254707), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1254705), _1254707) = 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), _1254705), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1254707)))))], (24713 ^ _784416) ^ [_1254905, _1254907] : [24714 ^ _784416 : [(24715 ^ _784416) ^ [] : [_1254905 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24717 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1254907), _1254905))]], -(c_Divides_Odivmod__nat(_1254907, _1254905) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1254907))], (24721 ^ _784416) ^ [_1255036, _1255038] : [-(c_Divides_Odivmod__nat(_1255038, _1255036) = 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), _1255038), _1255036), _1255036))), -(_1255036 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1255038), _1255036)))], (24731 ^ _784416) ^ [_1255101, _1255103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255101)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255103), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1255101, _1255103) = 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), _1255101), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1255103)))))], (24741 ^ _784416) ^ [_1255282, _1255284] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255284), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1255282), _1255284) = 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), _1255282), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1255284)))))], (24751 ^ _784416) ^ [_1255467, _1255469] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1255467), _1255469) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1255467, _1255469)))], (24753 ^ _784416) ^ [_1255504, _1255506] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1255504, _1255506) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1255504, _1255506)))], (24755 ^ _784416) ^ [_1255539, _1255541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255539), 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)), _1255541)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1255539), _1255541) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1255539, _1255541)))], (24765 ^ _784416) ^ [_1255706, _1255708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255706), 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)), _1255708)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1255706, _1255708) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1255706, _1255708)))], (24775 ^ _784416) ^ [_1255869, _1255871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255869)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255871)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1255869), _1255871) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1255869, _1255871)))], (24785 ^ _784416) ^ [_1256030, _1256032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256030)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256032)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1256030, _1256032) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1256030, _1256032)))], (24795 ^ _784416) ^ [_1256187, _1256189, _1256191, _1256193, _1256195, _1256197, _1256199] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1256187, _1256189)), hAPP(hAPP(c_Product__Type_OPair(_1256187, _1256189), _1256191), _1256193)), _1256195)), -(hBOOL(hAPP(hAPP(c_member(_1256197), hAPP(hAPP(_1256199, _1256191), _1256193)), hAPP(c_Set_Oimage(tc_prod(_1256187, _1256189), _1256197, hAPP(c_Product__Type_Oprod_Oprod__case(_1256187, _1256189, _1256197), _1256199)), _1256195))))], (24801 ^ _784416) ^ [_1256372, _1256374, _1256376, _1256378, _1256380] : [-(c_Product__Type_Oprod_Oprod__size(_1256372, _1256374, _1256376, _1256378, _1256380) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1256376, hAPP(c_Product__Type_Ofst(_1256372, _1256374), _1256380))), hAPP(_1256378, hAPP(c_Product__Type_Osnd(_1256372, _1256374), _1256380)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24803 ^ _784416) ^ [_1256439, _1256441, _1256443, _1256445, _1256447, _1256449, _1256451] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1256439, _1256441, _1256443), hAPP(c_Fun_Ocomp(_1256445, tc_fun(_1256441, _1256443), _1256439, _1256447), _1256449)), _1256451) = hAPP(hAPP(_1256447, hAPP(_1256449, hAPP(c_Product__Type_Ofst(_1256439, _1256441), _1256451))), hAPP(c_Product__Type_Osnd(_1256439, _1256441), _1256451)))], (24805 ^ _784416) ^ [_1256516, _1256518, _1256520, _1256522, _1256524] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1256516, _1256518, _1256520), _1256522), _1256524) = hAPP(hAPP(_1256522, hAPP(c_Product__Type_Ofst(_1256516, _1256518), _1256524)), hAPP(c_Product__Type_Osnd(_1256516, _1256518), _1256524)))], (24807 ^ _784416) ^ [_1256575, _1256577, _1256579, _1256581, _1256583, _1256585] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1256575, _1256577), _1256577, _1256579), hAPP(hAPP(c_COMBB(_1256581, tc_fun(_1256577, _1256579), tc_prod(_1256575, _1256577)), _1256583), hAPP(hAPP(c_COMBB(_1256575, _1256581, tc_prod(_1256575, _1256577)), _1256585), c_Product__Type_Ofst(_1256575, _1256577)))), c_Product__Type_Osnd(_1256575, _1256577)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1256575, _1256577, _1256579), hAPP(hAPP(c_COMBB(_1256581, tc_fun(_1256577, _1256579), _1256575), _1256583), _1256585)))], (24809 ^ _784416) ^ [_1256676, _1256678, _1256680, _1256682, _1256684] : [hBOOL(hAPP(hAPP(_1256676, _1256678), _1256680)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1256682, _1256684, tc_HOL_Obool), _1256676), hAPP(hAPP(c_Product__Type_OPair(_1256682, _1256684), _1256678), _1256680))))], (24815 ^ _784416) ^ [_1256805, _1256807, _1256809, _1256811, _1256813] : [hBOOL(hAPP(hAPP(_1256805, _1256807), _1256809)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1256811, _1256813, tc_HOL_Obool), _1256805), hAPP(hAPP(c_Product__Type_OPair(_1256811, _1256813), _1256807), _1256809))))], (24821 ^ _784416) ^ [_1256934, _1256936, _1256938, _1256940, _1256942, _1256944, _1256946] : [hBOOL(hAPP(hAPP(c_member(_1256934), _1256936), hAPP(hAPP(_1256938, _1256940), _1256942))), -(hBOOL(hAPP(hAPP(c_member(_1256934), _1256936), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1256944, _1256946, tc_fun(_1256934, tc_HOL_Obool)), _1256938), hAPP(hAPP(c_Product__Type_OPair(_1256944, _1256946), _1256940), _1256942)))))], (24827 ^ _784416) ^ [_1257105, _1257107, _1257109, _1257111, _1257113] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1257105, _1257107, tc_HOL_Obool), _1257109), hAPP(hAPP(c_Product__Type_OPair(_1257105, _1257107), _1257111), _1257113))), -(hBOOL(hAPP(hAPP(_1257109, _1257111), _1257113)))], (24833 ^ _784416) ^ [_1257234, _1257236, _1257238, _1257240, _1257242, _1257244, _1257246] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1257234, _1257236, tc_fun(_1257238, tc_HOL_Obool)), _1257240), hAPP(hAPP(c_Product__Type_OPair(_1257234, _1257236), _1257242), _1257244)), _1257246)), -(hBOOL(hAPP(hAPP(hAPP(_1257240, _1257242), _1257244), _1257246)))], (24839 ^ _784416) ^ [_1257385, _1257387] : [-(c_Relation_OId__on(_1257385, _1257387) = hAPP(c_Product__Type_Oprod_Oprod__case(_1257385, _1257385, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1257385, tc_HOL_Obool, tc_fun(_1257385, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1257385, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1257385, tc_HOL_Obool)), _1257385), c_COMBC(_1257385, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1257385, tc_HOL_Obool), tc_fun(_1257385, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1257385), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1257385), c_fconj)), c_fequal))), _1257387)))], (24841 ^ _784416) ^ [_1257479, _1257481, _1257483] : [-(c_HOL_OThe(tc_prod(_1257479, _1257481), _1257483) = c_HOL_OThe(tc_prod(_1257479, _1257481), hAPP(c_Product__Type_Oprod_Oprod__case(_1257479, _1257481, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1257481, tc_prod(_1257479, _1257481)), tc_fun(_1257481, tc_HOL_Obool), _1257479), hAPP(c_COMBB(tc_prod(_1257479, _1257481), tc_HOL_Obool, _1257481), _1257483)), c_Product__Type_OPair(_1257479, _1257481)))))], (24843 ^ _784416) ^ [_1257557, _1257559, _1257561, _1257563] : [-(c_HOL_OThe(tc_prod(_1257557, _1257559), hAPP(c_Product__Type_Oprod_Oprod__case(_1257557, _1257559, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1257557, tc_fun(_1257559, tc_HOL_Obool), tc_fun(_1257559, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1257559, tc_HOL_Obool), tc_fun(_1257559, tc_HOL_Obool)), _1257557), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1257559)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1257557), c_fconj), hAPP(c_fequal, _1257561)))), hAPP(c_fequal, _1257563)))) = hAPP(hAPP(c_Product__Type_OPair(_1257557, _1257559), _1257561), _1257563))], (24845 ^ _784416) ^ [_1257663, _1257665] : [-(c_Fun_Oinj__on(tc_fun(_1257663, _1257665), tc_fun(tc_prod(_1257663, _1257665), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1257663, _1257665), tc_HOL_Obool), tc_fun(tc_prod(_1257663, _1257665), tc_HOL_Obool), tc_fun(_1257663, _1257665)), c_Set_OCollect(tc_prod(_1257663, _1257665))), hAPP(hAPP(c_COMBB(tc_fun(_1257663, tc_fun(_1257665, tc_HOL_Obool)), tc_fun(tc_prod(_1257663, _1257665), tc_HOL_Obool), tc_fun(_1257663, _1257665)), c_Product__Type_Oprod_Oprod__case(_1257663, _1257665, tc_HOL_Obool)), hAPP(c_COMBB(_1257665, tc_fun(_1257665, tc_HOL_Obool), _1257663), hAPP(c_COMBC(_1257665, _1257665, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1257663, _1257665), tc_HOL_Obool))))], (24847 ^ _784416) ^ [_1257783, _1257785] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1257783), _1257785) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1257783, _1257785)))], (24849 ^ _784416) ^ [_1257820, _1257822] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1257820, _1257822) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1257820, _1257822)))], (24851 ^ _784416) ^ [_1257855, _1257857, _1257859] : [-(c_HOL_OThe(tc_prod(_1257855, _1257857), hAPP(c_Product__Type_Oprod_Oprod__case(_1257855, _1257857, tc_HOL_Obool), _1257859)) = c_HOL_OThe(tc_prod(_1257855, _1257857), hAPP(hAPP(c_COMBS(tc_prod(_1257855, _1257857), _1257857, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1257855, tc_fun(_1257857, tc_HOL_Obool), tc_prod(_1257855, _1257857)), _1257859), c_Product__Type_Ofst(_1257855, _1257857))), c_Product__Type_Osnd(_1257855, _1257857))))], (24885 ^ _784416) ^ [_1258490, _1258492, _1258494] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1258490, _1258492), _1258494))), _1258490 = 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), _1258494)), _1258492)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1258494)), 24892 ^ _784416 : [(24893 ^ _784416) ^ [] : [-(_1258492 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24895 ^ _784416) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1258494) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 24896 ^ _784416 : [(24897 ^ _784416) ^ [] : [_1258492 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24899 ^ _784416) ^ [] : [24900 ^ _784416 : [(24901 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258492)))], (24903 ^ _784416) ^ [] : [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), _1258494))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1258494)), _1258492))]], 24908 ^ _784416 : [(24909 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258492))], (24911 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1258492), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1258494))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1258494)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]]]], (24853 ^ _784416) ^ [_1257954, _1257956, _1257958] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1257954, _1257956), _1257958)), 24856 ^ _784416 : [(24857 ^ _784416) ^ [] : [-(_1257954 = 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), _1257958)), _1257956)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1257958)))], (24859 ^ _784416) ^ [] : [_1257956 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1257958) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24865 ^ _784416) ^ [] : [-(_1257956 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24868 ^ _784416 : [(24869 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1257956)), 24872 ^ _784416 : [(24873 ^ _784416) ^ [] : [-(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), _1257958))))], (24875 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1257958)), _1257956)))]]], (24877 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1257956))), 24880 ^ _784416 : [(24881 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1257956), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1257958))))], (24883 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1257958)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]]]]]], (24919 ^ _784416) ^ [_1259099, _1259101, _1259103, _1259105, _1259107, _1259109] : [hAPP(hAPP(c_Product__Type_OPair(_1259099, _1259101), _1259103), _1259105) = hAPP(hAPP(c_Product__Type_OPair(_1259099, _1259101), _1259107), _1259109), 24922 ^ _784416 : [(24923 ^ _784416) ^ [] : [-(_1259103 = _1259107)], (24925 ^ _784416) ^ [] : [-(_1259105 = _1259109)]]], (24927 ^ _784416) ^ [_1259277, _1259279, _1259281, _1259283, _1259285, _1259287] : [hAPP(hAPP(c_Product__Type_OPair(_1259277, _1259279), _1259281), _1259283) = hAPP(hAPP(c_Product__Type_OPair(_1259277, _1259279), _1259285), _1259287), 24930 ^ _784416 : [(24931 ^ _784416) ^ [] : [-(_1259281 = _1259285)], (24933 ^ _784416) ^ [] : [-(_1259283 = _1259287)]]], (24935 ^ _784416) ^ [_1259420, _1259422, _1259424, _1259426, _1259428, _1259430] : [-(hAPP(hAPP(c_Product__Type_OPair(_1259420, _1259422), _1259424), _1259426) = hAPP(hAPP(c_Product__Type_OPair(_1259420, _1259422), _1259428), _1259430)), _1259424 = _1259428, _1259426 = _1259430], (24945 ^ _784416) ^ [_1259621, _1259623, _1259625] : [hBOOL(hAPP(_1259621, 24946 ^ [_1259621, _1259623, _1259625])), 24949 ^ _784416 : [(24950 ^ _784416) ^ [_1259732, _1259734] : [-(hBOOL(hAPP(_1259621, hAPP(hAPP(c_Product__Type_OPair(_1259623, _1259625), _1259734), _1259732))))]]], (24952 ^ _784416) ^ [_1259768, _1259770, _1259772] : [hBOOL(hAPP(_1259768, hAPP(hAPP(c_Product__Type_OPair(_1259770, _1259772), 24953 ^ [_1259768, _1259770, _1259772]), 24954 ^ [_1259768, _1259770, _1259772]))), 24957 ^ _784416 : [(24958 ^ _784416) ^ [_1259915] : [-(hBOOL(hAPP(_1259768, _1259915)))]]], (24960 ^ _784416) ^ [_1259946, _1259948, _1259950, _1259952, _1259954, _1259956] : [_1259946 = _1259948, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1259950, _1259952, _1259954), _1259956), _1259946) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1259950, _1259952, _1259954), _1259956), _1259948))], (24966 ^ _784416) ^ [_1260071] : [-(c_Wellfounded_Ofinite__psubset(_1260071) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1260071, tc_HOL_Obool), tc_fun(_1260071, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1260071, tc_HOL_Obool), tc_fun(_1260071, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1260071, tc_HOL_Obool), tc_fun(tc_fun(_1260071, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1260071, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1260071, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1260071, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1260071, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1260071, tc_HOL_Obool)), c_COMBS(tc_fun(_1260071, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1260071, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1260071, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1260071, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1260071, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1260071, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1260071)))))], (24968 ^ _784416) ^ [_1260231, _1260233] : [-(c_Divides_Odivmod__int__rel(_1260231, _1260233) = 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, _1260231))), 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), _1260233)))))), 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)), _1260233))), 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)), _1260233))))), 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)), _1260233)))), 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), _1260233))), 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))))))))], (24970 ^ _784416) ^ [_1260346, _1260348, _1260350, _1260352, _1260354, _1260356] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1260346, _1260348, _1260350), _1260352), hAPP(hAPP(c_Product__Type_OPair(_1260346, _1260348), _1260354), _1260356)) = hAPP(hAPP(_1260352, _1260354), _1260356))], (24972 ^ _784416) ^ [_1260404, _1260406, _1260408, _1260410, _1260412, _1260414] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1260404, _1260406, _1260408), _1260410), hAPP(hAPP(c_Product__Type_OPair(_1260404, _1260406), _1260412), _1260414)) = hAPP(hAPP(_1260410, _1260412), _1260414))], (24974 ^ _784416) ^ [_1260462, _1260464, _1260466, _1260468, _1260470] : [hAPP(c_Product__Type_Ofst(_1260462, _1260464), hAPP(hAPP(c_Product__Type_OPair(_1260462, _1260464), _1260466), _1260468)) = _1260470, -(_1260466 = _1260470)], (24980 ^ _784416) ^ [_1260575, _1260577, _1260579, _1260581] : [-(hAPP(c_Product__Type_Ofst(_1260575, _1260577), hAPP(hAPP(c_Product__Type_OPair(_1260575, _1260577), _1260579), _1260581)) = _1260579)], (24982 ^ _784416) ^ [_1260619, _1260621, _1260623, _1260625, _1260627] : [hAPP(c_Product__Type_Osnd(_1260619, _1260621), hAPP(hAPP(c_Product__Type_OPair(_1260619, _1260621), _1260623), _1260625)) = _1260627, -(_1260625 = _1260627)], (24988 ^ _784416) ^ [_1260732, _1260734, _1260736, _1260738] : [-(hAPP(c_Product__Type_Osnd(_1260732, _1260734), hAPP(hAPP(c_Product__Type_OPair(_1260732, _1260734), _1260736), _1260738)) = _1260738)], (24990 ^ _784416) ^ [_1260776, _1260778, _1260780, _1260782] : [hAPP(c_Product__Type_Ofst(_1260776, _1260778), _1260780) = hAPP(c_Product__Type_Ofst(_1260776, _1260778), _1260782), hAPP(c_Product__Type_Osnd(_1260776, _1260778), _1260780) = hAPP(c_Product__Type_Osnd(_1260776, _1260778), _1260782), -(_1260780 = _1260782)], (25000 ^ _784416) ^ [_1260982, _1260984, _1260986, _1260988] : [_1260982 = _1260984, 25003 ^ _784416 : [(25004 ^ _784416) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1260986, _1260988), _1260982) = hAPP(c_Product__Type_Ofst(_1260986, _1260988), _1260984))], (25006 ^ _784416) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1260986, _1260988), _1260982) = hAPP(c_Product__Type_Osnd(_1260986, _1260988), _1260984))]]], (25008 ^ _784416) ^ [_1261133, _1261135, _1261137, _1261139] : [-(_1261133 = _1261135), hAPP(c_Product__Type_Ofst(_1261137, _1261139), _1261133) = hAPP(c_Product__Type_Ofst(_1261137, _1261139), _1261135), hAPP(c_Product__Type_Osnd(_1261137, _1261139), _1261133) = hAPP(c_Product__Type_Osnd(_1261137, _1261139), _1261135)], (25018 ^ _784416) ^ [_1261320, _1261322, _1261324, _1261326] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1261320, _1261322, _1261324), hAPP(hAPP(c_COMBB(tc_fun(_1261322, tc_prod(_1261320, _1261322)), tc_fun(_1261322, _1261324), _1261320), hAPP(c_COMBB(tc_prod(_1261320, _1261322), _1261324, _1261322), _1261326)), c_Product__Type_OPair(_1261320, _1261322))) = _1261326)], (25020 ^ _784416) ^ [_1261388, _1261390, _1261392] : [-(hAPP(c_Product__Type_Ofst(_1261388, _1261390), _1261392) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1261388, _1261390, _1261388), c_COMBK(_1261388, _1261390)), _1261392))], (25022 ^ _784416) ^ [_1261434, _1261436, _1261438] : [-(hAPP(c_Product__Type_Osnd(_1261434, _1261436), _1261438) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1261434, _1261436, _1261436), hAPP(c_COMBK(tc_fun(_1261436, _1261436), _1261434), c_COMBI(_1261436))), _1261438))], (25024 ^ _784416) ^ [_1261488, _1261490, _1261492] : [-(c_Fun_Oinj__on(tc_prod(_1261488, _1261490), tc_prod(_1261490, _1261488), hAPP(c_Product__Type_Oprod_Oprod__case(_1261488, _1261490, tc_prod(_1261490, _1261488)), hAPP(c_COMBC(_1261490, _1261488, tc_prod(_1261490, _1261488)), c_Product__Type_OPair(_1261490, _1261488))), _1261492))], (25026 ^ _784416) ^ [_1261546, _1261548, _1261550, _1261552, _1261554, _1261556, _1261558, _1261560] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1261546, _1261548, _1261550), _1261552), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1261554, _1261556, tc_prod(_1261546, _1261548)), _1261558), _1261560)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1261554, _1261556, _1261550), hAPP(hAPP(c_COMBB(tc_fun(_1261556, tc_prod(_1261546, _1261548)), tc_fun(_1261556, _1261550), _1261554), hAPP(c_COMBB(tc_prod(_1261546, _1261548), _1261550, _1261556), hAPP(c_Product__Type_Oprod_Oprod__case(_1261546, _1261548, _1261550), _1261552))), _1261558)), _1261560))], (25028 ^ _784416) ^ [_1261652, _1261654, _1261656] : [-(hAPP(hAPP(c_Product__Type_OPair(_1261652, _1261654), hAPP(c_Product__Type_Ofst(_1261652, _1261654), _1261656)), hAPP(c_Product__Type_Osnd(_1261652, _1261654), _1261656)) = _1261656)], (25030 ^ _784416) ^ [_1261700, _1261702, _1261704] : [-(_1261700 = hAPP(hAPP(c_Product__Type_OPair(_1261702, _1261704), hAPP(c_Product__Type_Ofst(_1261702, _1261704), _1261700)), hAPP(c_Product__Type_Osnd(_1261702, _1261704), _1261700)))], (25032 ^ _784416) ^ [_1261748, _1261750, _1261752, _1261754, _1261756] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1261748, _1261750, _1261752), _1261754), _1261756) = hAPP(hAPP(_1261754, hAPP(c_Product__Type_Ofst(_1261748, _1261750), _1261756)), hAPP(c_Product__Type_Osnd(_1261748, _1261750), _1261756)))], (25034 ^ _784416) ^ [_1261807, _1261809, _1261811, _1261813, _1261815] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1261807, _1261809, _1261811), _1261813), _1261815) = hAPP(hAPP(_1261813, hAPP(c_Product__Type_Ofst(_1261807, _1261809), _1261815)), hAPP(c_Product__Type_Osnd(_1261807, _1261809), _1261815)))], (25036 ^ _784416) ^ [] : [-(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)))))], (25038 ^ _784416) ^ [_1261884, _1261886, _1261888, _1261890, _1261892] : [hBOOL(hAPP(hAPP(_1261884, _1261886), _1261888)), -(hBOOL(hAPP(hAPP(_1261884, hAPP(c_Product__Type_Osnd(_1261890, _1261892), hAPP(hAPP(c_Product__Type_OPair(_1261890, _1261892), _1261888), _1261886))), hAPP(c_Product__Type_Ofst(_1261890, _1261892), hAPP(hAPP(c_Product__Type_OPair(_1261890, _1261892), _1261888), _1261886)))))], (25044 ^ _784416) ^ [_1262047, _1262049, _1262051, _1262053, _1262055, _1262057] : [hBOOL(hAPP(_1262047, _1262049)), hBOOL(hAPP(_1262051, _1262053)), 25051 ^ _784416 : [(25052 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1262047, hAPP(c_Product__Type_Ofst(_1262055, _1262057), hAPP(hAPP(c_Product__Type_OPair(_1262055, _1262057), _1262049), _1262053)))))], (25054 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1262051, hAPP(c_Product__Type_Osnd(_1262055, _1262057), hAPP(hAPP(c_Product__Type_OPair(_1262055, _1262057), _1262049), _1262053)))))]]], (25056 ^ _784416) ^ [_1262294] : [-(c_Int_Oint__ge__less__than2(_1262294) = 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), _1262294)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (25058 ^ _784416) ^ [_1262340] : [-(c_Int_Oint__ge__less__than(_1262340) = 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), _1262340)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (25060 ^ _784416) ^ [_1262386, _1262388, _1262390, _1262392] : [-(c_Nitpick_Oprod(_1262386, _1262388, _1262390, _1262392) = hAPP(c_Set_OCollect(tc_prod(_1262386, _1262388)), hAPP(c_Product__Type_Oprod_Oprod__case(_1262386, _1262388, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1262386, tc_fun(_1262388, tc_HOL_Obool), tc_fun(_1262388, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1262388, tc_HOL_Obool), tc_fun(_1262388, tc_HOL_Obool)), _1262386), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1262388)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1262386), c_fconj), hAPP(hAPP(c_COMBC(_1262386, tc_fun(_1262386, tc_HOL_Obool), tc_HOL_Obool), c_member(_1262386)), _1262390)))), hAPP(hAPP(c_COMBC(_1262388, tc_fun(_1262388, tc_HOL_Obool), tc_HOL_Obool), c_member(_1262388)), _1262392)))))], (25062 ^ _784416) ^ [_1262514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1262514)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1262514)) = 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), _1262514))))))], (25068 ^ _784416) ^ [_1262647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1262647)), 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), _1262647)) = 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), _1262647))))))], (25074 ^ _784416) ^ [_1262782, _1262784, _1262786, _1262788] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1262782, _1262784), _1262786), _1262788) = hAPP(c_Set_OCollect(tc_prod(_1262784, _1262784)), hAPP(c_Product__Type_Oprod_Oprod__case(_1262784, _1262784, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1262784, tc_fun(tc_prod(_1262782, _1262782), tc_HOL_Obool), tc_fun(_1262784, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1262784, tc_fun(tc_fun(tc_prod(_1262782, _1262782), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1262782, _1262782), tc_HOL_Obool), tc_fun(_1262784, tc_HOL_Obool)), _1262784), c_COMBC(_1262784, tc_fun(tc_prod(_1262782, _1262782), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1262784, tc_prod(_1262782, _1262782)), tc_fun(_1262784, tc_fun(tc_fun(tc_prod(_1262782, _1262782), tc_HOL_Obool), tc_HOL_Obool)), _1262784), hAPP(c_COMBB(tc_prod(_1262782, _1262782), tc_fun(tc_fun(tc_prod(_1262782, _1262782), tc_HOL_Obool), tc_HOL_Obool), _1262784), c_member(tc_prod(_1262782, _1262782)))), hAPP(hAPP(c_COMBC(_1262784, tc_fun(_1262784, _1262782), tc_fun(_1262784, tc_prod(_1262782, _1262782))), hAPP(hAPP(c_COMBB(tc_fun(_1262782, tc_prod(_1262782, _1262782)), tc_fun(tc_fun(_1262784, _1262782), tc_fun(_1262784, tc_prod(_1262782, _1262782))), _1262784), c_COMBB(_1262782, tc_prod(_1262782, _1262782), _1262784)), hAPP(hAPP(c_COMBB(_1262782, tc_fun(_1262782, tc_prod(_1262782, _1262782)), _1262784), c_Product__Type_OPair(_1262782, _1262782)), _1262788))), _1262788)))), _1262786))))], (25076 ^ _784416) ^ [_1263023, _1263025, _1263027, _1263029, _1263031, _1263033] : [-(c_Product__Type_Oprod_Oprod__rec(_1263023, _1263025, _1263027, _1263029, hAPP(hAPP(c_Product__Type_OPair(_1263023, _1263025), _1263031), _1263033)) = hAPP(hAPP(_1263029, _1263031), _1263033))], (25078 ^ _784416) ^ [_1263092, _1263094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1263092)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1263094))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1263092), _1263094)))], (25084 ^ _784416) ^ [_1263197, _1263199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1263197), _1263199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1263197)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1263199))))], (25090 ^ _784416) ^ [_1263323, _1263325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1263323)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1263325))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1263323), _1263325)))], (25096 ^ _784416) ^ [_1263428, _1263430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1263428), _1263430)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1263428)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1263430))))], (25102 ^ _784416) ^ [_1263539, _1263541] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1263539)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1263541)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1263539), _1263541)))], (25104 ^ _784416) ^ [_1263585] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1263585) = _1263585)], (25106 ^ _784416) ^ [_1263611, _1263613, _1263615] : [class_Int_Onumber(_1263611), 25109 ^ _784416 : [(25110 ^ _784416) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1263611), _1263613) = _1263615, -(_1263615 = hAPP(c_Int_Onumber__class_Onumber__of(_1263611), _1263613))], (25116 ^ _784416) ^ [] : [_1263615 = hAPP(c_Int_Onumber__class_Onumber__of(_1263611), _1263613), -(hAPP(c_Int_Onumber__class_Onumber__of(_1263611), _1263613) = _1263615)]]], (25122 ^ _784416) ^ [_1263852, _1263854, _1263856] : [class_Int_Onumber__ring(_1263852), class_Int_Oring__char__0(_1263852), 25129 ^ _784416 : [(25130 ^ _784416) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1263852), _1263854) = hAPP(c_Int_Onumber__class_Onumber__of(_1263852), _1263856), -(_1263854 = _1263856)], (25136 ^ _784416) ^ [] : [_1263854 = _1263856, -(hAPP(c_Int_Onumber__class_Onumber__of(_1263852), _1263854) = hAPP(c_Int_Onumber__class_Onumber__of(_1263852), _1263856))]]], (25142 ^ _784416) ^ [_1264147, _1264149] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1264147)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1264149)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1264147), _1264149)))], (25144 ^ _784416) ^ [_1264193] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1264193)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1264193)))], (25146 ^ _784416) ^ [_1264228, _1264230, _1264232] : [class_Int_Onumber(_1264228), class_Orderings_Olinorder(_1264228), 25153 ^ _784416 : [(25154 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264228), hAPP(c_Int_Onumber__class_Onumber__of(_1264228), _1264230)), hAPP(c_Int_Onumber__class_Onumber__of(_1264228), _1264232))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264228), hAPP(c_Int_Onumber__class_Onumber__of(_1264228), _1264232)), hAPP(c_Int_Onumber__class_Onumber__of(_1264228), _1264230)))], (25160 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264228), hAPP(c_Int_Onumber__class_Onumber__of(_1264228), _1264232)), hAPP(c_Int_Onumber__class_Onumber__of(_1264228), _1264230)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264228), hAPP(c_Int_Onumber__class_Onumber__of(_1264228), _1264230)), hAPP(c_Int_Onumber__class_Onumber__of(_1264228), _1264232))))]]], (25166 ^ _784416) ^ [_1264555, _1264557, _1264559, _1264561] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264555), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264555), _1264557), _1264559)), hAPP(c_Int_Onumber__class_Onumber__of(_1264555), _1264561)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264555), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264555), _1264557), hAPP(c_Int_Onumber__class_Onumber__of(_1264555), _1264561))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264555), _1264559), hAPP(c_Int_Onumber__class_Onumber__of(_1264555), _1264561)))), class_Int_Onumber(_1264555), class_Rings_Osemiring(_1264555)], (25176 ^ _784416) ^ [_1264798, _1264800, _1264802, _1264804] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264798), hAPP(c_Int_Onumber__class_Onumber__of(_1264798), _1264800)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264798), _1264802), _1264804)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264798), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264798), hAPP(c_Int_Onumber__class_Onumber__of(_1264798), _1264800)), _1264802)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264798), hAPP(c_Int_Onumber__class_Onumber__of(_1264798), _1264800)), _1264804))), class_Int_Onumber(_1264798), class_Rings_Osemiring(_1264798)], (25186 ^ _784416) ^ [_1265041, _1265043, _1265045, _1265047] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265041), hAPP(c_Int_Onumber__class_Onumber__of(_1265041), _1265043)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1265041), _1265045), _1265047)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1265041), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265041), hAPP(c_Int_Onumber__class_Onumber__of(_1265041), _1265043)), _1265045)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265041), hAPP(c_Int_Onumber__class_Onumber__of(_1265041), _1265043)), _1265047))), class_Int_Onumber(_1265041), class_Rings_Oring(_1265041)], (25196 ^ _784416) ^ [_1265284, _1265286, _1265288, _1265290] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265284), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1265284), _1265286), _1265288)), hAPP(c_Int_Onumber__class_Onumber__of(_1265284), _1265290)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1265284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265284), _1265286), hAPP(c_Int_Onumber__class_Onumber__of(_1265284), _1265290))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265284), _1265288), hAPP(c_Int_Onumber__class_Onumber__of(_1265284), _1265290)))), class_Int_Onumber(_1265284), class_Rings_Oring(_1265284)], (25206 ^ _784416) ^ [_1265527, _1265529, _1265531] : [class_Int_Onumber__ring(_1265527), class_Rings_Olinordered__idom(_1265527), 25213 ^ _784416 : [(25214 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265527), hAPP(c_Int_Onumber__class_Onumber__of(_1265527), _1265529)), hAPP(c_Int_Onumber__class_Onumber__of(_1265527), _1265531))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1265529), _1265531)))], (25220 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1265529), _1265531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265527), hAPP(c_Int_Onumber__class_Onumber__of(_1265527), _1265529)), hAPP(c_Int_Onumber__class_Onumber__of(_1265527), _1265531))))]]], (25226 ^ _784416) ^ [_1265858, _1265860, _1265862] : [class_Int_Onumber__ring(_1265858), class_Rings_Olinordered__idom(_1265858), 25233 ^ _784416 : [(25234 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265858), hAPP(c_Int_Onumber__class_Onumber__of(_1265858), _1265860)), hAPP(c_Int_Onumber__class_Onumber__of(_1265858), _1265862))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1265860), _1265862)))], (25240 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1265860), _1265862)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1265858), hAPP(c_Int_Onumber__class_Onumber__of(_1265858), _1265860)), hAPP(c_Int_Onumber__class_Onumber__of(_1265858), _1265862))))]]], (25246 ^ _784416) ^ [_1266189, _1266191, _1266193, _1266195] : [class_Int_Onumber__ring(_1266189), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1266189), hAPP(c_Int_Onumber__class_Onumber__of(_1266189), _1266191)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1266189), hAPP(c_Int_Onumber__class_Onumber__of(_1266189), _1266193)), _1266195)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1266189), hAPP(c_Int_Onumber__class_Onumber__of(_1266189), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1266191), _1266193))), _1266195))], (25252 ^ _784416) ^ [_1266358, _1266360, _1266362] : [class_Int_Onumber__ring(_1266358), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1266358), hAPP(c_Int_Onumber__class_Onumber__of(_1266358), _1266360)), hAPP(c_Int_Onumber__class_Onumber__of(_1266358), _1266362)) = hAPP(c_Int_Onumber__class_Onumber__of(_1266358), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1266360), _1266362)))], (25258 ^ _784416) ^ [_1266493, _1266495, _1266497] : [class_Int_Onumber__ring(_1266493), -(hAPP(c_Int_Onumber__class_Onumber__of(_1266493), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1266495), _1266497)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1266493), hAPP(c_Int_Onumber__class_Onumber__of(_1266493), _1266495)), hAPP(c_Int_Onumber__class_Onumber__of(_1266493), _1266497)))], (25264 ^ _784416) ^ [_1266628, _1266630, _1266632, _1266634] : [class_Int_Onumber__ring(_1266628), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266628), hAPP(c_Int_Onumber__class_Onumber__of(_1266628), _1266630)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266628), hAPP(c_Int_Onumber__class_Onumber__of(_1266628), _1266632)), _1266634)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266628), hAPP(c_Int_Onumber__class_Onumber__of(_1266628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1266630), _1266632))), _1266634))], (25270 ^ _784416) ^ [_1266797, _1266799, _1266801] : [class_Int_Onumber__ring(_1266797), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266797), hAPP(c_Int_Onumber__class_Onumber__of(_1266797), _1266799)), hAPP(c_Int_Onumber__class_Onumber__of(_1266797), _1266801)) = hAPP(c_Int_Onumber__class_Onumber__of(_1266797), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1266799), _1266801)))], (25276 ^ _784416) ^ [_1266932, _1266934, _1266936] : [class_Int_Onumber__ring(_1266932), -(hAPP(c_Int_Onumber__class_Onumber__of(_1266932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1266934), _1266936)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266932), hAPP(c_Int_Onumber__class_Onumber__of(_1266932), _1266934)), hAPP(c_Int_Onumber__class_Onumber__of(_1266932), _1266936)))], (25282 ^ _784416) ^ [_1267067, _1267069, _1267071] : [class_Int_Onumber__ring(_1267067), -(hAPP(c_Int_Onumber__class_Onumber__of(_1267067), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1267069), _1267071)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1267067), hAPP(c_Int_Onumber__class_Onumber__of(_1267067), _1267069)), hAPP(c_Int_Onumber__class_Onumber__of(_1267067), _1267071)))], (25288 ^ _784416) ^ [_1267202, _1267204] : [class_Int_Onumber__ring(_1267202), -(hAPP(c_Int_Onumber__class_Onumber__of(_1267202), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1267204)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1267202), hAPP(c_Int_Onumber__class_Onumber__of(_1267202), _1267204)))], (25294 ^ _784416) ^ [_1267313, _1267315] : [class_Int_Onumber__ring(_1267313), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1267313), hAPP(c_Int_Onumber__class_Onumber__of(_1267313), _1267315)) = hAPP(c_Int_Onumber__class_Onumber__of(_1267313), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1267315)))], (25300 ^ _784416) ^ [_1267424, _1267426] : [class_Int_Onumber__ring(_1267424), -(hBOOL(hAPP(hAPP(c_member(_1267424), hAPP(c_Int_Onumber__class_Onumber__of(_1267424), _1267426)), c_Int_Oring__1__class_OInts(_1267424))))], (25306 ^ _784416) ^ [_1267527, _1267529, _1267531, _1267533] : [class_Int_Onumber__ring(_1267527), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1267527), hAPP(c_Int_Onumber__class_Onumber__of(_1267527), _1267529)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1267527), hAPP(c_Int_Onumber__class_Onumber__of(_1267527), _1267531)), _1267533)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1267527), hAPP(c_Int_Onumber__class_Onumber__of(_1267527), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1267529), _1267531))), _1267533))], (25312 ^ _784416) ^ [_1267696, _1267698, _1267700] : [class_Int_Onumber__ring(_1267696), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267696), hAPP(c_Groups_Ouminus__class_Ouminus(_1267696), hAPP(c_Int_Onumber__class_Onumber__of(_1267696), _1267698))), _1267700) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267696), hAPP(c_Int_Onumber__class_Onumber__of(_1267696), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1267698))), _1267700))], (25318 ^ _784416) ^ [_1267841, _1267843, _1267845] : [class_Int_Onumber__ring(_1267841), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1267841), hAPP(c_Int_Onumber__class_Onumber__of(_1267841), _1267843)), hAPP(c_Int_Onumber__class_Onumber__of(_1267841), _1267845)) = hAPP(c_Int_Onumber__class_Onumber__of(_1267841), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1267843), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1267845))))], (25324 ^ _784416) ^ [_1267982, _1267984] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1267982)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1267984)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1267982), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1267984))))], (25326 ^ _784416) ^ [_1268058, _1268060, _1268062, _1268064, _1268066, _1268068] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1268058, _1268058)), hAPP(hAPP(c_Product__Type_OPair(_1268058, _1268058), _1268060), _1268062)), hAPP(hAPP(c_Relation_Oinv__image(_1268064, _1268058), _1268066), _1268068))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1268064, _1268064)), hAPP(hAPP(c_Product__Type_OPair(_1268064, _1268064), hAPP(_1268068, _1268060)), hAPP(_1268068, _1268062))), _1268066)))], (25332 ^ _784416) ^ [_1268245, _1268247, _1268249, _1268251, _1268253, _1268255] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1268251, _1268251)), hAPP(hAPP(c_Product__Type_OPair(_1268251, _1268251), hAPP(_1268255, _1268247)), hAPP(_1268255, _1268249))), _1268253)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1268245, _1268245)), hAPP(hAPP(c_Product__Type_OPair(_1268245, _1268245), _1268247), _1268249)), hAPP(hAPP(c_Relation_Oinv__image(_1268251, _1268245), _1268253), _1268255))))], (25338 ^ _784416) ^ [_1268438, _1268440, _1268442, _1268444] : [class_Int_Onumber__ring(_1268438), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1268438), hAPP(c_Int_Onumber__class_Onumber__of(_1268438), _1268440)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1268438), _1268442), hAPP(c_Int_Onumber__class_Onumber__of(_1268438), _1268444))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1268438), hAPP(c_Int_Onumber__class_Onumber__of(_1268438), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1268440), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1268444)))), _1268442))], (25344 ^ _784416) ^ [_1268613] : [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), _1268613))), -(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), _1268613)) = 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), _1268613))))], (25350 ^ _784416) ^ [_1268730] : [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), _1268730))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1268730)) = 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), _1268730))))], (25356 ^ _784416) ^ [_1268845, _1268847] : [-(c_FunDef_Orp__inv__image(_1268845, _1268847) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1268845, _1268845), tc_HOL_Obool), tc_fun(tc_prod(_1268845, _1268845), tc_HOL_Obool), tc_fun(tc_fun(_1268847, _1268845), tc_prod(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1268845, _1268845), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1268845, _1268845), tc_HOL_Obool), tc_fun(tc_fun(_1268847, _1268845), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1268845, _1268845), tc_HOL_Obool), tc_fun(tc_fun(_1268847, _1268845), tc_prod(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1268847, _1268845), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool)), tc_fun(tc_fun(_1268847, _1268845), tc_prod(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1268845, _1268845), tc_HOL_Obool), tc_fun(tc_fun(_1268847, _1268845), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1268845, _1268845), tc_HOL_Obool), tc_fun(tc_fun(_1268847, _1268845), tc_prod(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool))))), tc_fun(tc_prod(_1268845, _1268845), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1268847, _1268845), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool)), tc_fun(tc_fun(_1268847, _1268845), tc_prod(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool))), tc_fun(tc_prod(_1268845, _1268845), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1268847, _1268845), tc_fun(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1268847, _1268845), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool)), tc_fun(tc_fun(_1268847, _1268845), tc_prod(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool)))), tc_fun(tc_prod(_1268845, _1268845), tc_HOL_Obool)), c_COMBS(tc_fun(_1268847, _1268845), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1268847, _1268845), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool)), tc_fun(tc_fun(_1268847, _1268845), tc_fun(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool)))), tc_fun(tc_prod(_1268845, _1268845), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool))), tc_fun(_1268847, _1268845)), c_Product__Type_OPair(tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool), tc_fun(tc_prod(_1268847, _1268847), tc_HOL_Obool)))), c_Relation_Oinv__image(_1268845, _1268847))))), c_Relation_Oinv__image(_1268845, _1268847))))], (25358 ^ _784416) ^ [_1269358, _1269360, _1269362, _1269364, _1269366, _1269368] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1269358, _1269360)), hAPP(hAPP(c_Product__Type_OPair(_1269358, _1269360), _1269362), _1269364)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1269358, _1269360), tc_HOL_Obool), _1269366))), c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(_1269358, _1269360), tc_HOL_Obool), tc_fun(tc_prod(_1269358, _1269360), tc_HOL_Obool), _1269366), 25369 ^ _784416 : [(25370 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1269358, _1269360)), hAPP(hAPP(c_Product__Type_OPair(_1269358, _1269360), 25367 ^ [_1269358, _1269360, _1269362, _1269364, _1269366, _1269368]), 25368 ^ [_1269358, _1269360, _1269362, _1269364, _1269366, _1269368])), hAPP(_1269366, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1269358, _1269360), tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1269358, _1269360), tc_HOL_Obool), _1269366)), hAPP(c_Set_OCollect(tc_prod(_1269358, _1269360)), hAPP(c_Product__Type_Oprod_Oprod__case(_1269358, _1269360, tc_HOL_Obool), _1269368)))))))], (25372 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1269368, 25367 ^ [_1269358, _1269360, _1269362, _1269364, _1269366, _1269368]), 25368 ^ [_1269358, _1269360, _1269362, _1269364, _1269366, _1269368]))]], -(hBOOL(hAPP(hAPP(_1269368, _1269362), _1269364)))], (25376 ^ _784416) ^ [_1269933, _1269935, _1269937] : [class_Int_Onumber__ring(_1269933), 25379 ^ _784416 : [(25380 ^ _784416) ^ [] : [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), _1269935))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1269933), hAPP(c_Int_Onumber__class_Onumber__of(_1269933), _1269937)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1269935))) = hAPP(hAPP(c_HOL_OLet(_1269933, _1269933), hAPP(hAPP(c_Power_Opower__class_Opower(_1269933), hAPP(c_Int_Onumber__class_Onumber__of(_1269933), _1269937)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1269935))), hAPP(hAPP(c_COMBS(_1269933, _1269933, _1269933), hAPP(hAPP(c_COMBB(_1269933, tc_fun(_1269933, _1269933), _1269933), c_Groups_Otimes__class_Otimes(_1269933)), hAPP(c_Groups_Otimes__class_Otimes(_1269933), hAPP(c_Int_Onumber__class_Onumber__of(_1269933), _1269937)))), c_COMBI(_1269933))))], (25386 ^ _784416) ^ [] : [-(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), _1269935)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1269933), hAPP(c_Int_Onumber__class_Onumber__of(_1269933), _1269937)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1269935))) = c_Groups_Oone__class_Oone(_1269933))]]], (25392 ^ _784416) ^ [_1270331, _1270333, _1270335, _1270337, _1270339] : [class_Fields_Ofield(_1270331), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270333), _1270335)), -(hAPP(_1270337, _1270339) = c_Groups_Ozero__class_Ozero(_1270331)), 25403 ^ _784416 : [(25404 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1270333), _1270339), _1270335)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1270333, _1270331), _1270337), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1270333, tc_HOL_Obool)), _1270335), hAPP(hAPP(c_Set_Oinsert(_1270333), _1270339), c_Orderings_Obot__class_Obot(tc_fun(_1270333, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270331), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1270333, _1270331), _1270337), _1270335)), hAPP(_1270337, _1270339)))], (25410 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1270333), _1270339), _1270335))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1270333, _1270331), _1270337), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1270333, tc_HOL_Obool)), _1270335), hAPP(hAPP(c_Set_Oinsert(_1270333), _1270339), c_Orderings_Obot__class_Obot(tc_fun(_1270333, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1270333, _1270331), _1270337), _1270335))]]], (25416 ^ _784416) ^ [_1270872, _1270874, _1270876, _1270878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1270872), _1270874)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1270876), _1270878)), -(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), _1270872), _1270876)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1270874), _1270878))), c_FunDef_Opair__less)))], (25426 ^ _784416) ^ [_1271090, _1271092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1271090)), c_Int_OBit1(_1271092))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1271090), _1271092)))], (25432 ^ _784416) ^ [_1271191, _1271193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1271191), _1271193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1271191)), c_Int_OBit1(_1271193))))], (25438 ^ _784416) ^ [_1271313, _1271315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1271313)), c_Int_OBit1(_1271315))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1271313), _1271315)))], (25444 ^ _784416) ^ [_1271414, _1271416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1271414), _1271416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1271414)), c_Int_OBit1(_1271416))))], (25450 ^ _784416) ^ [_1271536, _1271538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1271536)), c_Int_OBit1(_1271538))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1271536), _1271538)))], (25456 ^ _784416) ^ [_1271637, _1271639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1271637), _1271639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1271637)), c_Int_OBit1(_1271639))))], (25462 ^ _784416) ^ [_1271759, _1271761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1271759)), c_Int_OBit1(_1271761))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1271759), _1271761)))], (25468 ^ _784416) ^ [_1271860, _1271862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1271860), _1271862)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1271860)), c_Int_OBit1(_1271862))))], (25474 ^ _784416) ^ [_1271967, _1271969] : [class_Rings_Odivision__ring(_1271967), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1271967), c_Groups_Ozero__class_Ozero(_1271967)), _1271969) = c_Groups_Ozero__class_Ozero(_1271967))], (25480 ^ _784416) ^ [_1272066, _1272068] : [class_Rings_Odivision__ring__inverse__zero(_1272066), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272066), _1272068), c_Groups_Ozero__class_Ozero(_1272066)) = c_Groups_Ozero__class_Ozero(_1272066))], (25486 ^ _784416) ^ [_1272165, _1272167, _1272169, _1272171] : [class_Rings_Odivision__ring(_1272165), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272165), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1272165), _1272167), _1272169)), _1272171) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1272165), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272165), _1272167), _1272171)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272165), _1272169), _1272171)))], (25492 ^ _784416) ^ [_1272324, _1272326, _1272328, _1272330] : [class_Rings_Odivision__ring(_1272324), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1272324), _1272326), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272324), _1272328), _1272330)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1272324), _1272326), _1272328)), _1272330))], (25498 ^ _784416) ^ [_1272482, _1272484] : [c_Int_OBit1(_1272482) = c_Int_OBit1(_1272484), -(_1272482 = _1272484)], (25504 ^ _784416) ^ [_1272563, _1272565] : [_1272563 = _1272565, -(c_Int_OBit1(_1272563) = c_Int_OBit1(_1272565))], (25510 ^ _784416) ^ [_1272650, _1272652, _1272654, _1272656] : [class_Fields_Ofield__inverse__zero(_1272650), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1272650), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272650), _1272652), _1272654)), _1272656) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272650), hAPP(hAPP(c_Power_Opower__class_Opower(_1272650), _1272652), _1272656)), hAPP(hAPP(c_Power_Opower__class_Opower(_1272650), _1272654), _1272656)))], (25516 ^ _784416) ^ [_1272809, _1272811, _1272813] : [class_Rings_Odivision__ring(_1272809), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1272809), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272809), _1272811), _1272813)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272809), hAPP(c_Groups_Ouminus__class_Ouminus(_1272809), _1272811)), _1272813))], (25522 ^ _784416) ^ [_1272938, _1272940] : [class_Rings_Odivision__ring(_1272938), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272938), _1272940), c_Groups_Oone__class_Oone(_1272938)) = _1272940)], (25528 ^ _784416) ^ [_1273033, _1273035, _1273037, _1273039] : [class_Rings_Odivision__ring(_1273033), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273033), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1273033), _1273035), _1273037)), _1273039) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1273033), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273033), _1273035), _1273039)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273033), _1273037), _1273039)))], (25534 ^ _784416) ^ [_1273192, _1273194, _1273196, _1273198] : [class_Rings_Odivision__ring(_1273192), -(_1273194 = c_Groups_Ozero__class_Ozero(_1273192)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273192), _1273196), _1273194) = _1273198, -(_1273196 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273192), _1273198), _1273194))], (25548 ^ _784416) ^ [_1273422, _1273424, _1273426, _1273428] : [class_Rings_Odivision__ring(_1273422), -(_1273424 = c_Groups_Ozero__class_Ozero(_1273422)), _1273426 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273422), _1273428), _1273424), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273422), _1273426), _1273424) = _1273428)], (25562 ^ _784416) ^ [_1273652, _1273654, _1273656, _1273658] : [class_Rings_Odivision__ring(_1273652), -(_1273654 = c_Groups_Ozero__class_Ozero(_1273652)), 25569 ^ _784416 : [(25570 ^ _784416) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273652), _1273656), _1273654) = _1273658, -(_1273656 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273652), _1273658), _1273654))], (25576 ^ _784416) ^ [] : [_1273656 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273652), _1273658), _1273654), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273652), _1273656), _1273654) = _1273658)]]], (25582 ^ _784416) ^ [_1273980, _1273982, _1273984, _1273986] : [class_Rings_Odivision__ring(_1273980), -(_1273982 = c_Groups_Ozero__class_Ozero(_1273980)), 25589 ^ _784416 : [(25590 ^ _784416) ^ [] : [_1273984 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273980), _1273986), _1273982), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273980), _1273984), _1273982) = _1273986)], (25596 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1273980), _1273984), _1273982) = _1273986, -(_1273984 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273980), _1273986), _1273982))]]], (25602 ^ _784416) ^ [_1274308, _1274310, _1274312] : [class_Rings_Odivision__ring(_1274308), -(_1274310 = c_Groups_Ozero__class_Ozero(_1274308)), 25609 ^ _784416 : [(25610 ^ _784416) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274308), _1274312), _1274310) = c_Groups_Oone__class_Oone(_1274308), -(_1274312 = _1274310)], (25616 ^ _784416) ^ [] : [_1274312 = _1274310, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274308), _1274312), _1274310) = c_Groups_Oone__class_Oone(_1274308))]]], (25622 ^ _784416) ^ [_1274610, _1274612] : [class_Rings_Odivision__ring(_1274610), -(_1274612 = c_Groups_Ozero__class_Ozero(_1274610)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274610), _1274612), _1274612) = c_Groups_Oone__class_Oone(_1274610))], (25632 ^ _784416) ^ [_1274724, _1274726] : [class_Rings_Odivision__ring__inverse__zero(_1274724), 25635 ^ _784416 : [(25636 ^ _784416) ^ [] : [_1274726 = c_Groups_Ozero__class_Ozero(_1274724), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274724), _1274726), _1274726) = c_Groups_Ozero__class_Ozero(_1274724))], (25642 ^ _784416) ^ [] : [-(_1274726 = c_Groups_Ozero__class_Ozero(_1274724)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274724), _1274726), _1274726) = c_Groups_Oone__class_Oone(_1274724))]]], (25648 ^ _784416) ^ [_1274946, _1274948, _1274950] : [class_Rings_Odivision__ring(_1274946), -(_1274948 = c_Groups_Ozero__class_Ozero(_1274946)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274946), hAPP(c_Groups_Ouminus__class_Ouminus(_1274946), _1274950)), hAPP(c_Groups_Ouminus__class_Ouminus(_1274946), _1274948)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274946), _1274950), _1274948))], (25658 ^ _784416) ^ [_1275094, _1275096, _1275098] : [class_Rings_Odivision__ring(_1275094), -(_1275096 = c_Groups_Ozero__class_Ozero(_1275094)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1275094), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275094), _1275098), _1275096)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275094), _1275098), hAPP(c_Groups_Ouminus__class_Ouminus(_1275094), _1275096)))], (25668 ^ _784416) ^ [_1275242, _1275244, _1275246, _1275248] : [class_Fields_Ofield(_1275242), -(_1275244 = c_Groups_Ozero__class_Ozero(_1275242)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1275242), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275242), _1275246), _1275244)), _1275248) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275242), hAPP(hAPP(c_Power_Opower__class_Opower(_1275242), _1275246), _1275248)), hAPP(hAPP(c_Power_Opower__class_Opower(_1275242), _1275244), _1275248)))], (25678 ^ _784416) ^ [_1275420, _1275422, _1275424] : [class_Fields_Ofield__inverse__zero(_1275420), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275420), c_Groups_Oone__class_Oone(_1275420)), hAPP(hAPP(c_Power_Opower__class_Opower(_1275420), _1275422), _1275424)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1275420), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275420), c_Groups_Oone__class_Oone(_1275420)), _1275422)), _1275424))], (25684 ^ _784416) ^ [_1275581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1275581)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275581), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25690 ^ _784416) ^ [_1275676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275676), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1275676)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25696 ^ _784416) ^ [_1275777] : [-(c_Int_OBit1(_1275777) = 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)), _1275777)), _1275777))], (25698 ^ _784416) ^ [_1275811, _1275813, _1275815, _1275817, _1275819] : [class_Fields_Ofield__inverse__zero(_1275811), hBOOL(hAPP(c_Finite__Set_Ofinite(_1275813), _1275815)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1275813, _1275811), hAPP(hAPP(c_COMBS(_1275813, _1275811, _1275811), hAPP(hAPP(c_COMBB(_1275811, tc_fun(_1275811, _1275811), _1275813), c_Rings_Oinverse__class_Odivide(_1275811)), _1275817)), _1275819)), _1275815) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275811), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1275813, _1275811), _1275817), _1275815)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1275813, _1275811), _1275819), _1275815)))], (25708 ^ _784416) ^ [_1276078, _1276080, _1276082, _1276084] : [class_Fields_Ofield__inverse__zero(_1276078), class_Int_Onumber(_1276078), 25715 ^ _784416 : [(25732 ^ _784416) ^ [] : [-(_1276080 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276078), _1276082), hAPP(c_Int_Onumber__class_Onumber__of(_1276078), _1276084))), 25735 ^ _784416 : [(25736 ^ _784416) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1276078), _1276084) = c_Groups_Ozero__class_Ozero(_1276078)], (25738 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276078), _1276080), hAPP(c_Int_Onumber__class_Onumber__of(_1276078), _1276084)) = _1276082]], 25739 ^ _784416 : [(25740 ^ _784416) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1276078), _1276084) = c_Groups_Ozero__class_Ozero(_1276078))], (25742 ^ _784416) ^ [] : [_1276080 = c_Groups_Ozero__class_Ozero(_1276078)]]], (25716 ^ _784416) ^ [] : [_1276080 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276078), _1276082), hAPP(c_Int_Onumber__class_Onumber__of(_1276078), _1276084)), 25719 ^ _784416 : [(25720 ^ _784416) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1276078), _1276084) = c_Groups_Ozero__class_Ozero(_1276078)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276078), _1276080), hAPP(c_Int_Onumber__class_Onumber__of(_1276078), _1276084)) = _1276082)], (25726 ^ _784416) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1276078), _1276084) = c_Groups_Ozero__class_Ozero(_1276078), -(_1276080 = c_Groups_Ozero__class_Ozero(_1276078))]]]]], (25746 ^ _784416) ^ [_1276688, _1276690, _1276692, _1276694] : [class_Fields_Ofield__inverse__zero(_1276688), class_Int_Onumber(_1276688), 25753 ^ _784416 : [(25770 ^ _784416) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1276688), _1276690) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276688), _1276692), _1276694)), 25773 ^ _784416 : [(25774 ^ _784416) ^ [] : [_1276694 = c_Groups_Ozero__class_Ozero(_1276688)], (25776 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276688), hAPP(c_Int_Onumber__class_Onumber__of(_1276688), _1276690)), _1276694) = _1276692]], 25777 ^ _784416 : [(25778 ^ _784416) ^ [] : [-(_1276694 = c_Groups_Ozero__class_Ozero(_1276688))], (25780 ^ _784416) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1276688), _1276690) = c_Groups_Ozero__class_Ozero(_1276688)]]], (25754 ^ _784416) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1276688), _1276690) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276688), _1276692), _1276694), 25757 ^ _784416 : [(25758 ^ _784416) ^ [] : [-(_1276694 = c_Groups_Ozero__class_Ozero(_1276688)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276688), hAPP(c_Int_Onumber__class_Onumber__of(_1276688), _1276690)), _1276694) = _1276692)], (25764 ^ _784416) ^ [] : [_1276694 = c_Groups_Ozero__class_Ozero(_1276688), -(hAPP(c_Int_Onumber__class_Onumber__of(_1276688), _1276690) = c_Groups_Ozero__class_Ozero(_1276688))]]]]], (25784 ^ _784416) ^ [_1277283, _1277285, _1277287, _1277289] : [class_Fields_Ofield__inverse__zero(_1277283), class_Int_Onumber(_1277283), 25791 ^ _784416 : [(25808 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277283), _1277285), _1277287) = hAPP(c_Int_Onumber__class_Onumber__of(_1277283), _1277289)), 25811 ^ _784416 : [(25812 ^ _784416) ^ [] : [_1277287 = c_Groups_Ozero__class_Ozero(_1277283)], (25814 ^ _784416) ^ [] : [_1277285 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277283), hAPP(c_Int_Onumber__class_Onumber__of(_1277283), _1277289)), _1277287)]], 25815 ^ _784416 : [(25816 ^ _784416) ^ [] : [-(_1277287 = c_Groups_Ozero__class_Ozero(_1277283))], (25818 ^ _784416) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1277283), _1277289) = c_Groups_Ozero__class_Ozero(_1277283)]]], (25792 ^ _784416) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277283), _1277285), _1277287) = hAPP(c_Int_Onumber__class_Onumber__of(_1277283), _1277289), 25795 ^ _784416 : [(25796 ^ _784416) ^ [] : [-(_1277287 = c_Groups_Ozero__class_Ozero(_1277283)), -(_1277285 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277283), hAPP(c_Int_Onumber__class_Onumber__of(_1277283), _1277289)), _1277287))], (25802 ^ _784416) ^ [] : [_1277287 = c_Groups_Ozero__class_Ozero(_1277283), -(hAPP(c_Int_Onumber__class_Onumber__of(_1277283), _1277289) = c_Groups_Ozero__class_Ozero(_1277283))]]]]], (25822 ^ _784416) ^ [_1277878, _1277880, _1277882, _1277884] : [class_Fields_Ofield__inverse__zero(_1277878), class_Int_Onumber(_1277878), 25829 ^ _784416 : [(25846 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277878), _1277880), hAPP(c_Int_Onumber__class_Onumber__of(_1277878), _1277882)) = _1277884), 25849 ^ _784416 : [(25850 ^ _784416) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1277878), _1277882) = c_Groups_Ozero__class_Ozero(_1277878)], (25852 ^ _784416) ^ [] : [_1277880 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277878), _1277884), hAPP(c_Int_Onumber__class_Onumber__of(_1277878), _1277882))]], 25853 ^ _784416 : [(25854 ^ _784416) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1277878), _1277882) = c_Groups_Ozero__class_Ozero(_1277878))], (25856 ^ _784416) ^ [] : [_1277884 = c_Groups_Ozero__class_Ozero(_1277878)]]], (25830 ^ _784416) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277878), _1277880), hAPP(c_Int_Onumber__class_Onumber__of(_1277878), _1277882)) = _1277884, 25833 ^ _784416 : [(25834 ^ _784416) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1277878), _1277882) = c_Groups_Ozero__class_Ozero(_1277878)), -(_1277880 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277878), _1277884), hAPP(c_Int_Onumber__class_Onumber__of(_1277878), _1277882)))], (25840 ^ _784416) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1277878), _1277882) = c_Groups_Ozero__class_Ozero(_1277878), -(_1277884 = c_Groups_Ozero__class_Ozero(_1277878))]]]]], (25860 ^ _784416) ^ [_1278488, _1278490] : [class_Int_Onumber__ring(_1278488), -(hAPP(c_Int_Onumber__class_Onumber__of(_1278488), c_Int_OBit1(_1278490)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1278488), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1278488), c_Groups_Oone__class_Oone(_1278488)), hAPP(c_Int_Onumber__class_Onumber__of(_1278488), _1278490))), hAPP(c_Int_Onumber__class_Onumber__of(_1278488), _1278490)))], (25866 ^ _784416) ^ [_1278633, _1278635, _1278637] : [class_Int_Onumber__ring(_1278633), 25869 ^ _784416 : [(25870 ^ _784416) ^ [] : [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), _1278635))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1278633), _1278637), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1278635))) = hAPP(hAPP(c_HOL_OLet(_1278633, _1278633), hAPP(hAPP(c_Power_Opower__class_Opower(_1278633), _1278637), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1278635))), hAPP(hAPP(c_COMBS(_1278633, _1278633, _1278633), hAPP(hAPP(c_COMBB(_1278633, tc_fun(_1278633, _1278633), _1278633), c_Groups_Otimes__class_Otimes(_1278633)), hAPP(c_Groups_Otimes__class_Otimes(_1278633), _1278637))), c_COMBI(_1278633))))], (25876 ^ _784416) ^ [] : [-(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), _1278635)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1278633), _1278637), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1278635))) = c_Groups_Oone__class_Oone(_1278633))]]], (25882 ^ _784416) ^ [_1279000, _1279002] : [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), _1279000))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1279002), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1279000))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1279002), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1279000))), 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), _1279002))), c_COMBI(tc_Int_Oint))))], (25888 ^ _784416) ^ [_1279157, _1279159] : [-(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), _1279157)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1279159), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1279157))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25894 ^ _784416) ^ [_1279211, _1279213, _1279215, _1279217] : [class_Fields_Olinordered__field__inverse__zero(_1279211), class_Int_Onumber(_1279211), 25901 ^ _784416 : [(25928 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279211), _1279213), hAPP(c_Int_Onumber__class_Onumber__of(_1279211), _1279215))), _1279217))), 25931 ^ _784416 : [(25932 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), c_Groups_Ozero__class_Ozero(_1279211)), hAPP(c_Int_Onumber__class_Onumber__of(_1279211), _1279215))))], (25934 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), _1279213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279211), _1279217), hAPP(c_Int_Onumber__class_Onumber__of(_1279211), _1279215))))]], 25935 ^ _784416 : [(25936 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), c_Groups_Ozero__class_Ozero(_1279211)), hAPP(c_Int_Onumber__class_Onumber__of(_1279211), _1279215)))], (25938 ^ _784416) ^ [] : [25939 ^ _784416 : [(25940 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), hAPP(c_Int_Onumber__class_Onumber__of(_1279211), _1279215)), c_Groups_Ozero__class_Ozero(_1279211))))], (25942 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279211), _1279217), hAPP(c_Int_Onumber__class_Onumber__of(_1279211), _1279215))), _1279213))]], 25943 ^ _784416 : [(25944 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), hAPP(c_Int_Onumber__class_Onumber__of(_1279211), _1279215)), c_Groups_Ozero__class_Ozero(_1279211)))], (25946 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), c_Groups_Ozero__class_Ozero(_1279211)), _1279217))]]]]], (25902 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279211), _1279213), hAPP(c_Int_Onumber__class_Onumber__of(_1279211), _1279215))), _1279217)), 25905 ^ _784416 : [(25906 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), c_Groups_Ozero__class_Ozero(_1279211)), hAPP(c_Int_Onumber__class_Onumber__of(_1279211), _1279215))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), _1279213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279211), _1279217), hAPP(c_Int_Onumber__class_Onumber__of(_1279211), _1279215)))))], (25912 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), c_Groups_Ozero__class_Ozero(_1279211)), hAPP(c_Int_Onumber__class_Onumber__of(_1279211), _1279215)))), 25915 ^ _784416 : [(25916 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), hAPP(c_Int_Onumber__class_Onumber__of(_1279211), _1279215)), c_Groups_Ozero__class_Ozero(_1279211))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279211), _1279217), hAPP(c_Int_Onumber__class_Onumber__of(_1279211), _1279215))), _1279213)))], (25922 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), hAPP(c_Int_Onumber__class_Onumber__of(_1279211), _1279215)), c_Groups_Ozero__class_Ozero(_1279211)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279211), c_Groups_Ozero__class_Ozero(_1279211)), _1279217)))]]]]]]], (25950 ^ _784416) ^ [_1280325, _1280327, _1280329, _1280331] : [class_Fields_Olinordered__field__inverse__zero(_1280325), class_Int_Onumber(_1280325), 25957 ^ _784416 : [(25984 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280325), _1280327), _1280329)), hAPP(c_Int_Onumber__class_Onumber__of(_1280325), _1280331)))), 25987 ^ _784416 : [(25988 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), c_Groups_Ozero__class_Ozero(_1280325)), _1280329)))], (25990 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), _1280327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1280325), hAPP(c_Int_Onumber__class_Onumber__of(_1280325), _1280331)), _1280329)))]], 25991 ^ _784416 : [(25992 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), c_Groups_Ozero__class_Ozero(_1280325)), _1280329))], (25994 ^ _784416) ^ [] : [25995 ^ _784416 : [(25996 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), _1280329), c_Groups_Ozero__class_Ozero(_1280325))))], (25998 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1280325), hAPP(c_Int_Onumber__class_Onumber__of(_1280325), _1280331)), _1280329)), _1280327))]], 25999 ^ _784416 : [(26000 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), _1280329), c_Groups_Ozero__class_Ozero(_1280325)))], (26002 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), c_Groups_Ozero__class_Ozero(_1280325)), hAPP(c_Int_Onumber__class_Onumber__of(_1280325), _1280331)))]]]]], (25958 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280325), _1280327), _1280329)), hAPP(c_Int_Onumber__class_Onumber__of(_1280325), _1280331))), 25961 ^ _784416 : [(25962 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), c_Groups_Ozero__class_Ozero(_1280325)), _1280329)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), _1280327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1280325), hAPP(c_Int_Onumber__class_Onumber__of(_1280325), _1280331)), _1280329))))], (25968 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), c_Groups_Ozero__class_Ozero(_1280325)), _1280329))), 25971 ^ _784416 : [(25972 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), _1280329), c_Groups_Ozero__class_Ozero(_1280325))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1280325), hAPP(c_Int_Onumber__class_Onumber__of(_1280325), _1280331)), _1280329)), _1280327)))], (25978 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), _1280329), c_Groups_Ozero__class_Ozero(_1280325)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280325), c_Groups_Ozero__class_Ozero(_1280325)), hAPP(c_Int_Onumber__class_Onumber__of(_1280325), _1280331))))]]]]]]], (26006 ^ _784416) ^ [_1281394, _1281396, _1281398, _1281400] : [class_Fields_Olinordered__field__inverse__zero(_1281394), class_Int_Onumber(_1281394), 26013 ^ _784416 : [(26040 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), hAPP(c_Int_Onumber__class_Onumber__of(_1281394), _1281396)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281394), _1281398), _1281400)))), 26043 ^ _784416 : [(26044 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), c_Groups_Ozero__class_Ozero(_1281394)), _1281400)))], (26046 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281394), hAPP(c_Int_Onumber__class_Onumber__of(_1281394), _1281396)), _1281400)), _1281398))]], 26047 ^ _784416 : [(26048 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), c_Groups_Ozero__class_Ozero(_1281394)), _1281400))], (26050 ^ _784416) ^ [] : [26051 ^ _784416 : [(26052 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), _1281400), c_Groups_Ozero__class_Ozero(_1281394))))], (26054 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), _1281398), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281394), hAPP(c_Int_Onumber__class_Onumber__of(_1281394), _1281396)), _1281400)))]], 26055 ^ _784416 : [(26056 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), _1281400), c_Groups_Ozero__class_Ozero(_1281394)))], (26058 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), hAPP(c_Int_Onumber__class_Onumber__of(_1281394), _1281396)), c_Groups_Ozero__class_Ozero(_1281394)))]]]]], (26014 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), hAPP(c_Int_Onumber__class_Onumber__of(_1281394), _1281396)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281394), _1281398), _1281400))), 26017 ^ _784416 : [(26018 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), c_Groups_Ozero__class_Ozero(_1281394)), _1281400)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281394), hAPP(c_Int_Onumber__class_Onumber__of(_1281394), _1281396)), _1281400)), _1281398)))], (26024 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), c_Groups_Ozero__class_Ozero(_1281394)), _1281400))), 26027 ^ _784416 : [(26028 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), _1281400), c_Groups_Ozero__class_Ozero(_1281394))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), _1281398), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281394), hAPP(c_Int_Onumber__class_Onumber__of(_1281394), _1281396)), _1281400))))], (26034 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), _1281400), c_Groups_Ozero__class_Ozero(_1281394)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281394), hAPP(c_Int_Onumber__class_Onumber__of(_1281394), _1281396)), c_Groups_Ozero__class_Ozero(_1281394))))]]]]]]], (26062 ^ _784416) ^ [_1282463, _1282465, _1282467, _1282469] : [class_Fields_Olinordered__field__inverse__zero(_1282463), class_Int_Onumber(_1282463), 26069 ^ _784416 : [(26096 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), _1282465), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1282463), _1282467), hAPP(c_Int_Onumber__class_Onumber__of(_1282463), _1282469))))), 26099 ^ _784416 : [(26100 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), c_Groups_Ozero__class_Ozero(_1282463)), hAPP(c_Int_Onumber__class_Onumber__of(_1282463), _1282469))))], (26102 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282463), _1282465), hAPP(c_Int_Onumber__class_Onumber__of(_1282463), _1282469))), _1282467))]], 26103 ^ _784416 : [(26104 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), c_Groups_Ozero__class_Ozero(_1282463)), hAPP(c_Int_Onumber__class_Onumber__of(_1282463), _1282469)))], (26106 ^ _784416) ^ [] : [26107 ^ _784416 : [(26108 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), hAPP(c_Int_Onumber__class_Onumber__of(_1282463), _1282469)), c_Groups_Ozero__class_Ozero(_1282463))))], (26110 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), _1282467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282463), _1282465), hAPP(c_Int_Onumber__class_Onumber__of(_1282463), _1282469))))]], 26111 ^ _784416 : [(26112 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), hAPP(c_Int_Onumber__class_Onumber__of(_1282463), _1282469)), c_Groups_Ozero__class_Ozero(_1282463)))], (26114 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), _1282465), c_Groups_Ozero__class_Ozero(_1282463)))]]]]], (26070 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), _1282465), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1282463), _1282467), hAPP(c_Int_Onumber__class_Onumber__of(_1282463), _1282469)))), 26073 ^ _784416 : [(26074 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), c_Groups_Ozero__class_Ozero(_1282463)), hAPP(c_Int_Onumber__class_Onumber__of(_1282463), _1282469))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282463), _1282465), hAPP(c_Int_Onumber__class_Onumber__of(_1282463), _1282469))), _1282467)))], (26080 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), c_Groups_Ozero__class_Ozero(_1282463)), hAPP(c_Int_Onumber__class_Onumber__of(_1282463), _1282469)))), 26083 ^ _784416 : [(26084 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), hAPP(c_Int_Onumber__class_Onumber__of(_1282463), _1282469)), c_Groups_Ozero__class_Ozero(_1282463))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), _1282467), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282463), _1282465), hAPP(c_Int_Onumber__class_Onumber__of(_1282463), _1282469)))))], (26090 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), hAPP(c_Int_Onumber__class_Onumber__of(_1282463), _1282469)), c_Groups_Ozero__class_Ozero(_1282463)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282463), _1282465), c_Groups_Ozero__class_Ozero(_1282463))))]]]]]]], (26118 ^ _784416) ^ [_1283577, _1283579, _1283581, _1283583] : [class_Fields_Ofield(_1283577), -(_1283579 = c_Groups_Ozero__class_Ozero(_1283577)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1283581), _1283583)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1283577), _1283579), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1283583), _1283581)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1283577), hAPP(hAPP(c_Power_Opower__class_Opower(_1283577), _1283579), _1283583)), hAPP(hAPP(c_Power_Opower__class_Opower(_1283577), _1283579), _1283581)))], (26132 ^ _784416) ^ [_1283861, _1283863, _1283865, _1283867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1283861), _1283863)), -(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), _1283861), _1283865)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1283863), _1283867))), c_FunDef_Opair__less)))], (26138 ^ _784416) ^ [_1283998, _1284000, _1284002, _1284004] : [class_Fields_Olinordered__field__inverse__zero(_1283998), class_Int_Onumber(_1283998), 26145 ^ _784416 : [(26172 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283998), _1284000), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1283998), _1284002), hAPP(c_Int_Onumber__class_Onumber__of(_1283998), _1284004))))), 26175 ^ _784416 : [(26176 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283998), c_Groups_Ozero__class_Ozero(_1283998)), hAPP(c_Int_Onumber__class_Onumber__of(_1283998), _1284004))))], (26178 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283998), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283998), _1284000), hAPP(c_Int_Onumber__class_Onumber__of(_1283998), _1284004))), _1284002))]], 26179 ^ _784416 : [(26180 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283998), c_Groups_Ozero__class_Ozero(_1283998)), hAPP(c_Int_Onumber__class_Onumber__of(_1283998), _1284004)))], (26182 ^ _784416) ^ [] : [26183 ^ _784416 : [(26184 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283998), hAPP(c_Int_Onumber__class_Onumber__of(_1283998), _1284004)), c_Groups_Ozero__class_Ozero(_1283998))))], (26186 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283998), _1284002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283998), _1284000), hAPP(c_Int_Onumber__class_Onumber__of(_1283998), _1284004))))]], 26187 ^ _784416 : [(26188 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283998), hAPP(c_Int_Onumber__class_Onumber__of(_1283998), _1284004)), c_Groups_Ozero__class_Ozero(_1283998)))], (26190 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283998), _1284000), c_Groups_Ozero__class_Ozero(_1283998)))]]]]], (26146 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283998), _1284000), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1283998), _1284002), hAPP(c_Int_Onumber__class_Onumber__of(_1283998), _1284004)))), 26149 ^ _784416 : [(26150 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283998), c_Groups_Ozero__class_Ozero(_1283998)), hAPP(c_Int_Onumber__class_Onumber__of(_1283998), _1284004))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283998), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283998), _1284000), hAPP(c_Int_Onumber__class_Onumber__of(_1283998), _1284004))), _1284002)))], (26156 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283998), c_Groups_Ozero__class_Ozero(_1283998)), hAPP(c_Int_Onumber__class_Onumber__of(_1283998), _1284004)))), 26159 ^ _784416 : [(26160 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283998), hAPP(c_Int_Onumber__class_Onumber__of(_1283998), _1284004)), c_Groups_Ozero__class_Ozero(_1283998))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283998), _1284002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283998), _1284000), hAPP(c_Int_Onumber__class_Onumber__of(_1283998), _1284004)))))], (26166 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283998), hAPP(c_Int_Onumber__class_Onumber__of(_1283998), _1284004)), c_Groups_Ozero__class_Ozero(_1283998)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283998), _1284000), c_Groups_Ozero__class_Ozero(_1283998))))]]]]]]], (26194 ^ _784416) ^ [_1285112, _1285114, _1285116, _1285118] : [class_Fields_Olinordered__field__inverse__zero(_1285112), class_Int_Onumber(_1285112), 26201 ^ _784416 : [(26228 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285112), hAPP(c_Int_Onumber__class_Onumber__of(_1285112), _1285114)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1285112), _1285116), _1285118)))), 26231 ^ _784416 : [(26232 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285112), c_Groups_Ozero__class_Ozero(_1285112)), _1285118)))], (26234 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1285112), hAPP(c_Int_Onumber__class_Onumber__of(_1285112), _1285114)), _1285118)), _1285116))]], 26235 ^ _784416 : [(26236 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285112), c_Groups_Ozero__class_Ozero(_1285112)), _1285118))], (26238 ^ _784416) ^ [] : [26239 ^ _784416 : [(26240 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285112), _1285118), c_Groups_Ozero__class_Ozero(_1285112))))], (26242 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285112), _1285116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1285112), hAPP(c_Int_Onumber__class_Onumber__of(_1285112), _1285114)), _1285118)))]], 26243 ^ _784416 : [(26244 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285112), _1285118), c_Groups_Ozero__class_Ozero(_1285112)))], (26246 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285112), hAPP(c_Int_Onumber__class_Onumber__of(_1285112), _1285114)), c_Groups_Ozero__class_Ozero(_1285112)))]]]]], (26202 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285112), hAPP(c_Int_Onumber__class_Onumber__of(_1285112), _1285114)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1285112), _1285116), _1285118))), 26205 ^ _784416 : [(26206 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285112), c_Groups_Ozero__class_Ozero(_1285112)), _1285118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1285112), hAPP(c_Int_Onumber__class_Onumber__of(_1285112), _1285114)), _1285118)), _1285116)))], (26212 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285112), c_Groups_Ozero__class_Ozero(_1285112)), _1285118))), 26215 ^ _784416 : [(26216 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285112), _1285118), c_Groups_Ozero__class_Ozero(_1285112))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285112), _1285116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1285112), hAPP(c_Int_Onumber__class_Onumber__of(_1285112), _1285114)), _1285118))))], (26222 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285112), _1285118), c_Groups_Ozero__class_Ozero(_1285112)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285112), hAPP(c_Int_Onumber__class_Onumber__of(_1285112), _1285114)), c_Groups_Ozero__class_Ozero(_1285112))))]]]]]]], (26250 ^ _784416) ^ [_1286181, _1286183, _1286185, _1286187] : [class_Fields_Olinordered__field__inverse__zero(_1286181), class_Int_Onumber(_1286181), 26257 ^ _784416 : [(26284 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286181), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1286181), _1286183), _1286185)), hAPP(c_Int_Onumber__class_Onumber__of(_1286181), _1286187)))), 26287 ^ _784416 : [(26288 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286181), c_Groups_Ozero__class_Ozero(_1286181)), _1286185)))], (26290 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286181), _1286183), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286181), hAPP(c_Int_Onumber__class_Onumber__of(_1286181), _1286187)), _1286185)))]], 26291 ^ _784416 : [(26292 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286181), c_Groups_Ozero__class_Ozero(_1286181)), _1286185))], (26294 ^ _784416) ^ [] : [26295 ^ _784416 : [(26296 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286181), _1286185), c_Groups_Ozero__class_Ozero(_1286181))))], (26298 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286181), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286181), hAPP(c_Int_Onumber__class_Onumber__of(_1286181), _1286187)), _1286185)), _1286183))]], 26299 ^ _784416 : [(26300 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286181), _1286185), c_Groups_Ozero__class_Ozero(_1286181)))], (26302 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286181), c_Groups_Ozero__class_Ozero(_1286181)), hAPP(c_Int_Onumber__class_Onumber__of(_1286181), _1286187)))]]]]], (26258 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286181), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1286181), _1286183), _1286185)), hAPP(c_Int_Onumber__class_Onumber__of(_1286181), _1286187))), 26261 ^ _784416 : [(26262 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286181), c_Groups_Ozero__class_Ozero(_1286181)), _1286185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286181), _1286183), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286181), hAPP(c_Int_Onumber__class_Onumber__of(_1286181), _1286187)), _1286185))))], (26268 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286181), c_Groups_Ozero__class_Ozero(_1286181)), _1286185))), 26271 ^ _784416 : [(26272 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286181), _1286185), c_Groups_Ozero__class_Ozero(_1286181))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286181), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286181), hAPP(c_Int_Onumber__class_Onumber__of(_1286181), _1286187)), _1286185)), _1286183)))], (26278 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286181), _1286185), c_Groups_Ozero__class_Ozero(_1286181)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286181), c_Groups_Ozero__class_Ozero(_1286181)), hAPP(c_Int_Onumber__class_Onumber__of(_1286181), _1286187))))]]]]]]], (26306 ^ _784416) ^ [_1287250, _1287252, _1287254, _1287256] : [class_Fields_Olinordered__field__inverse__zero(_1287250), class_Int_Onumber(_1287250), 26313 ^ _784416 : [(26340 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287250), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1287250), _1287252), hAPP(c_Int_Onumber__class_Onumber__of(_1287250), _1287254))), _1287256))), 26343 ^ _784416 : [(26344 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287250), c_Groups_Ozero__class_Ozero(_1287250)), hAPP(c_Int_Onumber__class_Onumber__of(_1287250), _1287254))))], (26346 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287250), _1287252), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287250), _1287256), hAPP(c_Int_Onumber__class_Onumber__of(_1287250), _1287254))))]], 26347 ^ _784416 : [(26348 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287250), c_Groups_Ozero__class_Ozero(_1287250)), hAPP(c_Int_Onumber__class_Onumber__of(_1287250), _1287254)))], (26350 ^ _784416) ^ [] : [26351 ^ _784416 : [(26352 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287250), hAPP(c_Int_Onumber__class_Onumber__of(_1287250), _1287254)), c_Groups_Ozero__class_Ozero(_1287250))))], (26354 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287250), _1287256), hAPP(c_Int_Onumber__class_Onumber__of(_1287250), _1287254))), _1287252))]], 26355 ^ _784416 : [(26356 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287250), hAPP(c_Int_Onumber__class_Onumber__of(_1287250), _1287254)), c_Groups_Ozero__class_Ozero(_1287250)))], (26358 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287250), c_Groups_Ozero__class_Ozero(_1287250)), _1287256))]]]]], (26314 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287250), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1287250), _1287252), hAPP(c_Int_Onumber__class_Onumber__of(_1287250), _1287254))), _1287256)), 26317 ^ _784416 : [(26318 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287250), c_Groups_Ozero__class_Ozero(_1287250)), hAPP(c_Int_Onumber__class_Onumber__of(_1287250), _1287254))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287250), _1287252), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287250), _1287256), hAPP(c_Int_Onumber__class_Onumber__of(_1287250), _1287254)))))], (26324 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287250), c_Groups_Ozero__class_Ozero(_1287250)), hAPP(c_Int_Onumber__class_Onumber__of(_1287250), _1287254)))), 26327 ^ _784416 : [(26328 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287250), hAPP(c_Int_Onumber__class_Onumber__of(_1287250), _1287254)), c_Groups_Ozero__class_Ozero(_1287250))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287250), _1287256), hAPP(c_Int_Onumber__class_Onumber__of(_1287250), _1287254))), _1287252)))], (26334 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287250), hAPP(c_Int_Onumber__class_Onumber__of(_1287250), _1287254)), c_Groups_Ozero__class_Ozero(_1287250)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287250), c_Groups_Ozero__class_Ozero(_1287250)), _1287256)))]]]]]]], (26362 ^ _784416) ^ [_1288364] : [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), _1288364))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1288364) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1288364)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (26368 ^ _784416) ^ [_1288479, _1288481, _1288483, _1288485] : [class_Fields_Olinordered__field__inverse__zero(_1288479), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288479), _1288481), _1288483)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288479), _1288485), c_Groups_Ozero__class_Ozero(_1288479))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288479), c_Groups_Ozero__class_Ozero(_1288479)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288479), _1288481), _1288483))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288479), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288479), _1288485), _1288481)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288479), _1288485), _1288483))))], (26386 ^ _784416) ^ [_1288838, _1288840, _1288842, _1288844] : [class_Fields_Olinordered__field(_1288838), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288838), _1288840), _1288842)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288838), c_Groups_Ozero__class_Ozero(_1288838)), _1288844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288838), c_Groups_Ozero__class_Ozero(_1288838)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288838), _1288842), _1288840))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288838), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288838), _1288844), _1288842)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288838), _1288844), _1288840))))], (26404 ^ _784416) ^ [_1289197, _1289199, _1289201, _1289203] : [class_Fields_Olinordered__field(_1289197), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289197), _1289199), c_Groups_Ozero__class_Ozero(_1289197))), 26411 ^ _784416 : [(26412 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289197), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289197), _1289201), _1289199)), _1289203)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289197), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289197), _1289203), _1289199)), _1289201)))], (26418 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289197), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289197), _1289203), _1289199)), _1289201)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289197), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289197), _1289201), _1289199)), _1289203)))]]], (26424 ^ _784416) ^ [_1289578, _1289580, _1289582, _1289584] : [class_Fields_Olinordered__field(_1289578), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289578), _1289580), c_Groups_Ozero__class_Ozero(_1289578))), 26431 ^ _784416 : [(26432 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289578), _1289582), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289578), _1289584), _1289580))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289578), _1289584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289578), _1289582), _1289580))))], (26438 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289578), _1289584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289578), _1289582), _1289580))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289578), _1289582), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289578), _1289584), _1289580))))]]], (26444 ^ _784416) ^ [_1289959, _1289961, _1289963, _1289965] : [class_Fields_Olinordered__field(_1289959), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289959), c_Groups_Ozero__class_Ozero(_1289959)), _1289961)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289959), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289959), _1289963), _1289961)), _1289965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289959), _1289963), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289959), _1289965), _1289961))))], (26458 ^ _784416) ^ [_1290228, _1290230, _1290232, _1290234, _1290236] : [class_Fields_Ofield__inverse__zero(_1290228), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290228), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290228), _1290230), _1290232)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290228), _1290234), _1290236)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290228), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290228), _1290230), _1290234)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290228), _1290232), _1290236)))], (26464 ^ _784416) ^ [_1290405, _1290407, _1290409] : [class_Fields_Ofield__inverse__zero(_1290405), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1290405), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290405), _1290407), _1290409)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290405), _1290407), hAPP(c_Groups_Ouminus__class_Ouminus(_1290405), _1290409)))], (26470 ^ _784416) ^ [_1290534, _1290536, _1290538] : [class_Fields_Ofield__inverse__zero(_1290534), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290534), hAPP(c_Groups_Ouminus__class_Ouminus(_1290534), _1290536)), hAPP(c_Groups_Ouminus__class_Ouminus(_1290534), _1290538)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290534), _1290536), _1290538))], (26476 ^ _784416) ^ [_1290663, _1290665, _1290667, _1290669] : [class_Fields_Olinordered__field__inverse__zero(_1290663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290663), _1290665), _1290667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290663), _1290669), c_Groups_Ozero__class_Ozero(_1290663))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290663), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290663), _1290667), _1290669)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290663), _1290665), _1290669))))], (26490 ^ _784416) ^ [_1290932, _1290934, _1290936, _1290938] : [class_Fields_Olinordered__field__inverse__zero(_1290932), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290932), _1290934), _1290936)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290932), c_Groups_Ozero__class_Ozero(_1290932)), _1290938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290932), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290932), _1290934), _1290938)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290932), _1290936), _1290938))))], (26504 ^ _784416) ^ [_1291201, _1291203, _1291205] : [class_Fields_Olinordered__field__inverse__zero(_1291201), 26507 ^ _784416 : [(26508 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291201), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291201), _1291203), _1291205)), c_Groups_Ozero__class_Ozero(_1291201))), 26513 ^ _784416 : [(26514 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291201), c_Groups_Ozero__class_Ozero(_1291201)), _1291203)))], (26516 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291201), _1291205), c_Groups_Ozero__class_Ozero(_1291201))))]], 26517 ^ _784416 : [(26518 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291201), _1291203), c_Groups_Ozero__class_Ozero(_1291201))))], (26520 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291201), c_Groups_Ozero__class_Ozero(_1291201)), _1291205)))]]], (26522 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291201), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291201), _1291203), _1291205)), c_Groups_Ozero__class_Ozero(_1291201)))), 26523 ^ _784416 : [(26524 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291201), c_Groups_Ozero__class_Ozero(_1291201)), _1291203)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291201), _1291205), c_Groups_Ozero__class_Ozero(_1291201)))], (26530 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291201), _1291203), c_Groups_Ozero__class_Ozero(_1291201))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291201), c_Groups_Ozero__class_Ozero(_1291201)), _1291205))]]]]], (26538 ^ _784416) ^ [_1291791, _1291793, _1291795] : [class_Fields_Olinordered__field__inverse__zero(_1291791), 26541 ^ _784416 : [(26542 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291791), c_Groups_Ozero__class_Ozero(_1291791)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291791), _1291793), _1291795))), 26547 ^ _784416 : [(26548 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291791), c_Groups_Ozero__class_Ozero(_1291791)), _1291793)))], (26550 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291791), c_Groups_Ozero__class_Ozero(_1291791)), _1291795)))]], 26551 ^ _784416 : [(26552 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291791), _1291793), c_Groups_Ozero__class_Ozero(_1291791))))], (26554 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291791), _1291795), c_Groups_Ozero__class_Ozero(_1291791))))]]], (26556 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291791), c_Groups_Ozero__class_Ozero(_1291791)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1291791), _1291793), _1291795)))), 26557 ^ _784416 : [(26558 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291791), c_Groups_Ozero__class_Ozero(_1291791)), _1291793)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291791), c_Groups_Ozero__class_Ozero(_1291791)), _1291795))], (26564 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291791), _1291793), c_Groups_Ozero__class_Ozero(_1291791))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291791), _1291795), c_Groups_Ozero__class_Ozero(_1291791)))]]]]], (26572 ^ _784416) ^ [_1292381, _1292383, _1292385] : [class_Fields_Olinordered__field__inverse__zero(_1292381), 26575 ^ _784416 : [(26576 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292381), c_Groups_Ozero__class_Ozero(_1292381)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292381), _1292383), _1292385))), 26581 ^ _784416 : [(26582 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292381), c_Groups_Ozero__class_Ozero(_1292381)), _1292383)))], (26584 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292381), c_Groups_Ozero__class_Ozero(_1292381)), _1292385)))]], 26585 ^ _784416 : [(26586 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292381), _1292383), c_Groups_Ozero__class_Ozero(_1292381))))], (26588 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292381), _1292385), c_Groups_Ozero__class_Ozero(_1292381))))]]], (26590 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292381), c_Groups_Ozero__class_Ozero(_1292381)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292381), _1292383), _1292385)))), 26591 ^ _784416 : [(26592 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292381), c_Groups_Ozero__class_Ozero(_1292381)), _1292383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292381), c_Groups_Ozero__class_Ozero(_1292381)), _1292385))], (26598 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292381), _1292383), c_Groups_Ozero__class_Ozero(_1292381))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292381), _1292385), c_Groups_Ozero__class_Ozero(_1292381)))]]]]], (26606 ^ _784416) ^ [_1292971, _1292973, _1292975] : [class_Fields_Olinordered__field__inverse__zero(_1292971), 26609 ^ _784416 : [(26610 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292971), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292971), _1292973), _1292975)), c_Groups_Ozero__class_Ozero(_1292971))), 26615 ^ _784416 : [(26616 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292971), c_Groups_Ozero__class_Ozero(_1292971)), _1292973)))], (26618 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292971), _1292975), c_Groups_Ozero__class_Ozero(_1292971))))]], 26619 ^ _784416 : [(26620 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292971), _1292973), c_Groups_Ozero__class_Ozero(_1292971))))], (26622 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292971), c_Groups_Ozero__class_Ozero(_1292971)), _1292975)))]]], (26624 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292971), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1292971), _1292973), _1292975)), c_Groups_Ozero__class_Ozero(_1292971)))), 26625 ^ _784416 : [(26626 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292971), c_Groups_Ozero__class_Ozero(_1292971)), _1292973)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292971), _1292975), c_Groups_Ozero__class_Ozero(_1292971)))], (26632 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292971), _1292973), c_Groups_Ozero__class_Ozero(_1292971))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292971), c_Groups_Ozero__class_Ozero(_1292971)), _1292975))]]]]], (26640 ^ _784416) ^ [_1293561, _1293563, _1293565] : [class_Fields_Olinordered__field(_1293561), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293561), c_Groups_Ozero__class_Ozero(_1293561)), _1293563)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293561), c_Groups_Ozero__class_Ozero(_1293561)), _1293565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293561), c_Groups_Ozero__class_Ozero(_1293561)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1293561), _1293563), _1293565))))], (26654 ^ _784416) ^ [_1293816, _1293818, _1293820] : [class_Fields_Olinordered__field(_1293816), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293816), c_Groups_Ozero__class_Ozero(_1293816)), _1293818)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293816), _1293820), c_Groups_Ozero__class_Ozero(_1293816))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1293816), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1293816), _1293818), _1293820)), c_Groups_Ozero__class_Ozero(_1293816))))], (26668 ^ _784416) ^ [_1294071, _1294073, _1294075] : [class_Fields_Olinordered__field(_1294071), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294071), _1294073), c_Groups_Ozero__class_Ozero(_1294071))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294071), c_Groups_Ozero__class_Ozero(_1294071)), _1294075)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294071), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294071), _1294073), _1294075)), c_Groups_Ozero__class_Ozero(_1294071))))], (26682 ^ _784416) ^ [_1294326, _1294328, _1294330] : [class_Fields_Olinordered__field(_1294326), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294326), _1294328), c_Groups_Ozero__class_Ozero(_1294326))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294326), _1294330), c_Groups_Ozero__class_Ozero(_1294326))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294326), c_Groups_Ozero__class_Ozero(_1294326)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294326), _1294328), _1294330))))], (26696 ^ _784416) ^ [_1294581, _1294583, _1294585, _1294587] : [class_Fields_Olinordered__field(_1294581), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294581), _1294583), _1294585)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294581), c_Groups_Ozero__class_Ozero(_1294581)), _1294587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294581), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294581), _1294583), _1294587)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294581), _1294585), _1294587))))], (26710 ^ _784416) ^ [_1294850, _1294852, _1294854, _1294856] : [class_Fields_Olinordered__field(_1294850), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294850), _1294852), _1294854)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294850), _1294856), c_Groups_Ozero__class_Ozero(_1294850))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294850), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294850), _1294854), _1294856)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1294850), _1294852), _1294856))))], (26724 ^ _784416) ^ [_1295119, _1295121, _1295123, _1295125, _1295127] : [class_Fields_Ofield(_1295119), -(_1295121 = c_Groups_Ozero__class_Ozero(_1295119)), -(_1295123 = c_Groups_Ozero__class_Ozero(_1295119)), 26735 ^ _784416 : [(26736 ^ _784416) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295119), _1295125), _1295121) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295119), _1295127), _1295123), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295119), _1295125), _1295123) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295119), _1295127), _1295121))], (26742 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295119), _1295125), _1295123) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295119), _1295127), _1295121), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295119), _1295125), _1295121) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295119), _1295127), _1295123))]]], (26748 ^ _784416) ^ [_1295568, _1295570, _1295572, _1295574] : [class_Fields_Ofield__inverse__zero(_1295568), -(_1295570 = c_Groups_Ozero__class_Ozero(_1295568)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295568), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295568), _1295570), _1295572)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295568), _1295570), _1295574)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295568), _1295572), _1295574))], (26758 ^ _784416) ^ [_1295730, _1295732, _1295734, _1295736] : [class_Fields_Ofield__inverse__zero(_1295730), -(_1295732 = c_Groups_Ozero__class_Ozero(_1295730)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295730), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295730), _1295734), _1295732)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295730), _1295736), _1295732)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295730), _1295734), _1295736))], (26768 ^ _784416) ^ [_1295892, _1295894, _1295896, _1295898] : [class_Fields_Ofield__inverse__zero(_1295892), 26771 ^ _784416 : [(26788 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295892), _1295894), _1295896) = _1295898), 26791 ^ _784416 : [(26792 ^ _784416) ^ [] : [_1295896 = c_Groups_Ozero__class_Ozero(_1295892)], (26794 ^ _784416) ^ [] : [_1295894 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295892), _1295898), _1295896)]], 26795 ^ _784416 : [(26796 ^ _784416) ^ [] : [-(_1295896 = c_Groups_Ozero__class_Ozero(_1295892))], (26798 ^ _784416) ^ [] : [_1295898 = c_Groups_Ozero__class_Ozero(_1295892)]]], (26772 ^ _784416) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1295892), _1295894), _1295896) = _1295898, 26775 ^ _784416 : [(26776 ^ _784416) ^ [] : [-(_1295896 = c_Groups_Ozero__class_Ozero(_1295892)), -(_1295894 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1295892), _1295898), _1295896))], (26782 ^ _784416) ^ [] : [_1295896 = c_Groups_Ozero__class_Ozero(_1295892), -(_1295898 = c_Groups_Ozero__class_Ozero(_1295892))]]]]], (26802 ^ _784416) ^ [_1296386, _1296388, _1296390, _1296392] : [class_Fields_Ofield__inverse__zero(_1296386), 26805 ^ _784416 : [(26822 ^ _784416) ^ [] : [-(_1296388 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1296386), _1296390), _1296392)), 26825 ^ _784416 : [(26826 ^ _784416) ^ [] : [_1296392 = c_Groups_Ozero__class_Ozero(_1296386)], (26828 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296386), _1296388), _1296392) = _1296390]], 26829 ^ _784416 : [(26830 ^ _784416) ^ [] : [-(_1296392 = c_Groups_Ozero__class_Ozero(_1296386))], (26832 ^ _784416) ^ [] : [_1296388 = c_Groups_Ozero__class_Ozero(_1296386)]]], (26806 ^ _784416) ^ [] : [_1296388 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1296386), _1296390), _1296392), 26809 ^ _784416 : [(26810 ^ _784416) ^ [] : [-(_1296392 = c_Groups_Ozero__class_Ozero(_1296386)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296386), _1296388), _1296392) = _1296390)], (26816 ^ _784416) ^ [] : [_1296392 = c_Groups_Ozero__class_Ozero(_1296386), -(_1296388 = c_Groups_Ozero__class_Ozero(_1296386))]]]]], (26836 ^ _784416) ^ [_1296880, _1296882, _1296884] : [class_Fields_Olinordered__field(_1296880), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296880), _1296882), c_Groups_Ozero__class_Ozero(_1296880))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296880), _1296884), c_Groups_Ozero__class_Ozero(_1296880))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296880), c_Groups_Ozero__class_Ozero(_1296880)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1296880), _1296882), _1296884))))], (26850 ^ _784416) ^ [_1297135, _1297137, _1297139] : [class_Fields_Olinordered__field(_1297135), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297135), _1297137), c_Groups_Ozero__class_Ozero(_1297135))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297135), c_Groups_Ozero__class_Ozero(_1297135)), _1297139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297135), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297135), _1297137), _1297139)), c_Groups_Ozero__class_Ozero(_1297135))))], (26864 ^ _784416) ^ [_1297390, _1297392, _1297394, _1297396, _1297398] : [class_Fields_Olinordered__field(_1297390), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297390), c_Groups_Ozero__class_Ozero(_1297390)), _1297392)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297390), _1297392), _1297394)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297390), c_Groups_Ozero__class_Ozero(_1297390)), _1297396)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297390), _1297396), _1297398)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297390), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297390), _1297392), _1297398)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297390), _1297394), _1297396))))], (26886 ^ _784416) ^ [_1297813, _1297815, _1297817, _1297819, _1297821] : [class_Fields_Olinordered__field(_1297813), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297813), c_Groups_Ozero__class_Ozero(_1297813)), _1297815)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297813), _1297815), _1297817)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297813), c_Groups_Ozero__class_Ozero(_1297813)), _1297819)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1297813), _1297819), _1297821)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1297813), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297813), _1297815), _1297821)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1297813), _1297817), _1297819))))], (26908 ^ _784416) ^ [_1298236, _1298238, _1298240, _1298242, _1298244] : [class_Fields_Olinordered__field(_1298236), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298236), c_Groups_Ozero__class_Ozero(_1298236)), _1298238)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298236), _1298238), _1298240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298236), c_Groups_Ozero__class_Ozero(_1298236)), _1298242)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298236), _1298242), _1298244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298236), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1298236), _1298238), _1298244)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1298236), _1298240), _1298242))))], (26930 ^ _784416) ^ [_1298659, _1298661, _1298663] : [class_Fields_Olinordered__field(_1298659), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298659), c_Groups_Ozero__class_Ozero(_1298659)), _1298661)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298659), _1298663), c_Groups_Ozero__class_Ozero(_1298659))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298659), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1298659), _1298661), _1298663)), c_Groups_Ozero__class_Ozero(_1298659))))], (26944 ^ _784416) ^ [_1298914, _1298916, _1298918] : [class_Fields_Olinordered__field(_1298914), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298914), c_Groups_Ozero__class_Ozero(_1298914)), _1298916)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1298914), c_Groups_Ozero__class_Ozero(_1298914)), _1298918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298914), c_Groups_Ozero__class_Ozero(_1298914)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1298914), _1298916), _1298918))))], (26958 ^ _784416) ^ [_1299169, _1299171, _1299173, _1299175] : [class_Fields_Olinordered__field__inverse__zero(_1299169), 26961 ^ _784416 : [(26988 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), _1299171), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1299169), _1299173), _1299175)))), 26991 ^ _784416 : [(26992 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), c_Groups_Ozero__class_Ozero(_1299169)), _1299175)))], (26994 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1299169), _1299171), _1299175)), _1299173))]], 26995 ^ _784416 : [(26996 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), c_Groups_Ozero__class_Ozero(_1299169)), _1299175))], (26998 ^ _784416) ^ [] : [26999 ^ _784416 : [(27000 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), _1299175), c_Groups_Ozero__class_Ozero(_1299169))))], (27002 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), _1299173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1299169), _1299171), _1299175)))]], 27003 ^ _784416 : [(27004 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), _1299175), c_Groups_Ozero__class_Ozero(_1299169)))], (27006 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), _1299171), c_Groups_Ozero__class_Ozero(_1299169)))]]]]], (26962 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), _1299171), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1299169), _1299173), _1299175))), 26965 ^ _784416 : [(26966 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), c_Groups_Ozero__class_Ozero(_1299169)), _1299175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1299169), _1299171), _1299175)), _1299173)))], (26972 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), c_Groups_Ozero__class_Ozero(_1299169)), _1299175))), 26975 ^ _784416 : [(26976 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), _1299175), c_Groups_Ozero__class_Ozero(_1299169))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), _1299173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1299169), _1299171), _1299175))))], (26982 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), _1299175), c_Groups_Ozero__class_Ozero(_1299169)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299169), _1299171), c_Groups_Ozero__class_Ozero(_1299169))))]]]]]]], (27010 ^ _784416) ^ [_1300122, _1300124, _1300126, _1300128] : [class_Fields_Olinordered__field__inverse__zero(_1300122), 27013 ^ _784416 : [(27040 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1300122), _1300124), _1300126)), _1300128))), 27043 ^ _784416 : [(27044 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), c_Groups_Ozero__class_Ozero(_1300122)), _1300126)))], (27046 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), _1300124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300122), _1300128), _1300126)))]], 27047 ^ _784416 : [(27048 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), c_Groups_Ozero__class_Ozero(_1300122)), _1300126))], (27050 ^ _784416) ^ [] : [27051 ^ _784416 : [(27052 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), _1300126), c_Groups_Ozero__class_Ozero(_1300122))))], (27054 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300122), _1300128), _1300126)), _1300124))]], 27055 ^ _784416 : [(27056 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), _1300126), c_Groups_Ozero__class_Ozero(_1300122)))], (27058 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), c_Groups_Ozero__class_Ozero(_1300122)), _1300128))]]]]], (27014 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1300122), _1300124), _1300126)), _1300128)), 27017 ^ _784416 : [(27018 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), c_Groups_Ozero__class_Ozero(_1300122)), _1300126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), _1300124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300122), _1300128), _1300126))))], (27024 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), c_Groups_Ozero__class_Ozero(_1300122)), _1300126))), 27027 ^ _784416 : [(27028 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), _1300126), c_Groups_Ozero__class_Ozero(_1300122))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1300122), _1300128), _1300126)), _1300124)))], (27034 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), _1300126), c_Groups_Ozero__class_Ozero(_1300122)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1300122), c_Groups_Ozero__class_Ozero(_1300122)), _1300128)))]]]]]]], (27062 ^ _784416) ^ [_1301075, _1301077, _1301079, _1301081] : [class_Fields_Olinordered__field(_1301075), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301075), c_Groups_Ozero__class_Ozero(_1301075)), _1301077)), 27069 ^ _784416 : [(27070 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301075), _1301079), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301075), _1301081), _1301077))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301075), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301075), _1301079), _1301077)), _1301081)))], (27076 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301075), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301075), _1301079), _1301077)), _1301081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301075), _1301079), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301075), _1301081), _1301077))))]]], (27082 ^ _784416) ^ [_1301456, _1301458, _1301460, _1301462] : [class_Fields_Olinordered__field(_1301456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301456), c_Groups_Ozero__class_Ozero(_1301456)), _1301458)), 27089 ^ _784416 : [(27090 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301456), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301456), _1301460), _1301458)), _1301462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301456), _1301460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301456), _1301462), _1301458))))], (27096 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301456), _1301460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301456), _1301462), _1301458))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301456), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301456), _1301460), _1301458)), _1301462)))]]], (27102 ^ _784416) ^ [_1301837, _1301839, _1301841, _1301843] : [class_Fields_Olinordered__field(_1301837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301837), c_Groups_Ozero__class_Ozero(_1301837)), _1301839)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301837), _1301841), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301837), _1301843), _1301839))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1301837), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1301837), _1301841), _1301839)), _1301843)))], (27116 ^ _784416) ^ [_1302106, _1302108, _1302110, _1302112] : [class_Fields_Olinordered__field(_1302106), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302106), c_Groups_Ozero__class_Ozero(_1302106)), _1302108)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302106), _1302110), _1302108)), _1302112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302106), _1302110), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302106), _1302112), _1302108))))], (27130 ^ _784416) ^ [_1302375, _1302377, _1302379, _1302381] : [class_Fields_Olinordered__field(_1302375), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302375), _1302377), c_Groups_Ozero__class_Ozero(_1302375))), 27137 ^ _784416 : [(27138 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302375), _1302379), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302375), _1302381), _1302377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302375), _1302381), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302375), _1302379), _1302377))))], (27144 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302375), _1302381), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302375), _1302379), _1302377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302375), _1302379), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302375), _1302381), _1302377))))]]], (27150 ^ _784416) ^ [_1302756, _1302758, _1302760, _1302762] : [class_Fields_Olinordered__field(_1302756), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302756), _1302758), c_Groups_Ozero__class_Ozero(_1302756))), 27157 ^ _784416 : [(27158 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302756), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302756), _1302760), _1302758)), _1302762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302756), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302756), _1302762), _1302758)), _1302760)))], (27164 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302756), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302756), _1302762), _1302758)), _1302760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302756), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1302756), _1302760), _1302758)), _1302762)))]]], (27170 ^ _784416) ^ [_1303137, _1303139, _1303141, _1303143] : [class_Fields_Olinordered__field(_1303137), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303137), _1303139), _1303141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303137), c_Groups_Ozero__class_Ozero(_1303137)), _1303143)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303137), c_Groups_Ozero__class_Ozero(_1303137)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303137), _1303141), _1303139))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303137), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303137), _1303143), _1303141)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303137), _1303143), _1303139))))], (27188 ^ _784416) ^ [_1303496, _1303498, _1303500, _1303502] : [class_Fields_Olinordered__field(_1303496), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303496), _1303498), _1303500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303496), _1303502), c_Groups_Ozero__class_Ozero(_1303496))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303496), c_Groups_Ozero__class_Ozero(_1303496)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303496), _1303498), _1303500))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303496), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303496), _1303502), _1303498)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303496), _1303502), _1303500))))], (27206 ^ _784416) ^ [_1303855, _1303857, _1303859, _1303861, _1303863] : [class_Fields_Ofield(_1303855), -(_1303857 = c_Groups_Ozero__class_Ozero(_1303855)), -(_1303859 = c_Groups_Ozero__class_Ozero(_1303855)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1303855), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303855), _1303861), _1303857)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303855), _1303863), _1303859)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1303855), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1303855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303855), _1303861), _1303859)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303855), _1303863), _1303857))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1303855), _1303857), _1303859)))], (27220 ^ _784416) ^ [_1304102, _1304104, _1304106, _1304108] : [class_Fields_Ofield(_1304102), -(_1304104 = c_Groups_Ozero__class_Ozero(_1304102)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1304102), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304102), _1304106), _1304104)), _1304108) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304102), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1304102), _1304106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1304102), _1304104), _1304108))), _1304104))], (27230 ^ _784416) ^ [_1304280, _1304282, _1304284, _1304286] : [class_Fields_Ofield__inverse__zero(_1304280), -(_1304282 = c_Groups_Ozero__class_Ozero(_1304280)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1304280), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304280), _1304284), _1304282)), _1304286) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304280), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1304280), _1304284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1304280), _1304286), _1304282))), _1304282))], (27240 ^ _784416) ^ [_1304458, _1304460, _1304462, _1304464] : [class_Fields_Ofield(_1304458), -(_1304460 = c_Groups_Ozero__class_Ozero(_1304458)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1304458), _1304462), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304458), _1304464), _1304460)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304458), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1304458), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1304458), _1304460), _1304462)), _1304464)), _1304460))], (27250 ^ _784416) ^ [_1304636, _1304638, _1304640, _1304642] : [class_Fields_Ofield__inverse__zero(_1304636), -(_1304638 = c_Groups_Ozero__class_Ozero(_1304636)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1304636), _1304640), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304636), _1304642), _1304638)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304636), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1304636), _1304642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1304636), _1304640), _1304638))), _1304638))], (27260 ^ _784416) ^ [_1304814, _1304816, _1304818, _1304820, _1304822] : [class_Fields_Ofield(_1304814), -(_1304816 = c_Groups_Ozero__class_Ozero(_1304814)), -(_1304818 = c_Groups_Ozero__class_Ozero(_1304814)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1304814), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304814), _1304820), _1304816)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304814), _1304822), _1304818)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1304814), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1304814), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1304814), _1304820), _1304818)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1304814), _1304822), _1304816))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1304814), _1304816), _1304818)))], (27274 ^ _784416) ^ [_1305061, _1305063, _1305065, _1305067] : [class_Fields_Ofield(_1305061), -(_1305063 = c_Groups_Ozero__class_Ozero(_1305061)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1305061), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1305061), _1305065), _1305063)), _1305067) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1305061), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1305061), _1305065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305061), _1305063), _1305067))), _1305063))], (27284 ^ _784416) ^ [_1305239, _1305241, _1305243, _1305245] : [class_Fields_Ofield(_1305239), -(_1305241 = c_Groups_Ozero__class_Ozero(_1305239)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1305239), _1305243), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1305239), _1305245), _1305241)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1305239), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1305239), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305239), _1305241), _1305243)), _1305245)), _1305241))], (27294 ^ _784416) ^ [_1305417, _1305419, _1305421] : [class_Fields_Olinordered__field(_1305417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305417), _1305419), _1305421)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305417), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1305417), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305417), _1305419), _1305421)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305417), c_Groups_Oone__class_Oone(_1305417)), c_Groups_Oone__class_Oone(_1305417)))), _1305421)))], (27304 ^ _784416) ^ [_1305632, _1305634, _1305636] : [class_Fields_Olinordered__field(_1305632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305632), _1305634), _1305636)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305632), _1305634), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1305632), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305632), _1305634), _1305636)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1305632), c_Groups_Oone__class_Oone(_1305632)), c_Groups_Oone__class_Oone(_1305632))))))], (27314 ^ _784416) ^ [_1305847, _1305849, _1305851, _1305853] : [class_Fields_Olinordered__field__inverse__zero(_1305847), 27317 ^ _784416 : [(27344 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305847), _1305849), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1305847), _1305851), _1305853)))), 27347 ^ _784416 : [(27348 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305847), c_Groups_Ozero__class_Ozero(_1305847)), _1305853)))], (27350 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305847), _1305849), _1305853)), _1305851))]], 27351 ^ _784416 : [(27352 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305847), c_Groups_Ozero__class_Ozero(_1305847)), _1305853))], (27354 ^ _784416) ^ [] : [27355 ^ _784416 : [(27356 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305847), _1305853), c_Groups_Ozero__class_Ozero(_1305847))))], (27358 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305847), _1305851), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305847), _1305849), _1305853)))]], 27359 ^ _784416 : [(27360 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305847), _1305853), c_Groups_Ozero__class_Ozero(_1305847)))], (27362 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305847), _1305849), c_Groups_Ozero__class_Ozero(_1305847)))]]]]], (27318 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305847), _1305849), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1305847), _1305851), _1305853))), 27321 ^ _784416 : [(27322 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305847), c_Groups_Ozero__class_Ozero(_1305847)), _1305853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305847), _1305849), _1305853)), _1305851)))], (27328 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305847), c_Groups_Ozero__class_Ozero(_1305847)), _1305853))), 27331 ^ _784416 : [(27332 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305847), _1305853), c_Groups_Ozero__class_Ozero(_1305847))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305847), _1305851), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1305847), _1305849), _1305853))))], (27338 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305847), _1305853), c_Groups_Ozero__class_Ozero(_1305847)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305847), _1305849), c_Groups_Ozero__class_Ozero(_1305847))))]]]]]]], (27366 ^ _784416) ^ [_1306800, _1306802, _1306804, _1306806] : [class_Fields_Olinordered__field__inverse__zero(_1306800), 27369 ^ _784416 : [(27396 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306800), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1306800), _1306802), _1306804)), _1306806))), 27399 ^ _784416 : [(27400 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306800), c_Groups_Ozero__class_Ozero(_1306800)), _1306804)))], (27402 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306800), _1306802), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306800), _1306806), _1306804)))]], 27403 ^ _784416 : [(27404 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306800), c_Groups_Ozero__class_Ozero(_1306800)), _1306804))], (27406 ^ _784416) ^ [] : [27407 ^ _784416 : [(27408 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306800), _1306804), c_Groups_Ozero__class_Ozero(_1306800))))], (27410 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306800), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306800), _1306806), _1306804)), _1306802))]], 27411 ^ _784416 : [(27412 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306800), _1306804), c_Groups_Ozero__class_Ozero(_1306800)))], (27414 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306800), c_Groups_Ozero__class_Ozero(_1306800)), _1306806))]]]]], (27370 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306800), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1306800), _1306802), _1306804)), _1306806)), 27373 ^ _784416 : [(27374 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306800), c_Groups_Ozero__class_Ozero(_1306800)), _1306804)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306800), _1306802), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306800), _1306806), _1306804))))], (27380 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306800), c_Groups_Ozero__class_Ozero(_1306800)), _1306804))), 27383 ^ _784416 : [(27384 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306800), _1306804), c_Groups_Ozero__class_Ozero(_1306800))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306800), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306800), _1306806), _1306804)), _1306802)))], (27390 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1306800), _1306804), c_Groups_Ozero__class_Ozero(_1306800)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306800), c_Groups_Ozero__class_Ozero(_1306800)), _1306806)))]]]]]]], (27418 ^ _784416) ^ [_1307753, _1307755, _1307757, _1307759] : [class_Fields_Olinordered__field(_1307753), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307753), c_Groups_Ozero__class_Ozero(_1307753)), _1307755)), 27425 ^ _784416 : [(27426 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307753), _1307757), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1307753), _1307759), _1307755))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307753), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307753), _1307757), _1307755)), _1307759)))], (27432 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307753), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307753), _1307757), _1307755)), _1307759)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307753), _1307757), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1307753), _1307759), _1307755))))]]], (27438 ^ _784416) ^ [_1308134, _1308136, _1308138, _1308140] : [class_Fields_Olinordered__field(_1308134), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308134), c_Groups_Ozero__class_Ozero(_1308134)), _1308136)), 27445 ^ _784416 : [(27446 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308134), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308134), _1308138), _1308136)), _1308140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308134), _1308138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308134), _1308140), _1308136))))], (27452 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308134), _1308138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308134), _1308140), _1308136))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308134), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308134), _1308138), _1308136)), _1308140)))]]], (27458 ^ _784416) ^ [_1308515, _1308517, _1308519, _1308521] : [class_Fields_Olinordered__field(_1308515), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308515), c_Groups_Ozero__class_Ozero(_1308515)), _1308517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308515), _1308519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308515), _1308521), _1308517))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308515), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1308515), _1308519), _1308517)), _1308521)))], (27472 ^ _784416) ^ [_1308784, _1308786, _1308788, _1308790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1308784), _1308786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1308788), _1308790)), -(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), _1308784), _1308788)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1308786), _1308790))), c_FunDef_Opair__leq)))], (27482 ^ _784416) ^ [_1308987, _1308989, _1308991, _1308993] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1308987), _1308989)), 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)), _1308987), _1308991)), 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)), _1308989), _1308993)), 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)), _1308989), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1308991), _1308993))), c_FunDef_Omin__strict)))], (27496 ^ _784416) ^ [_1309268, _1309270, _1309272, _1309274] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1309268), _1309270)), 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)), _1309272), _1309268)), 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)), _1309274), _1309270)), 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)), _1309272), _1309274)), _1309270)), c_FunDef_Omax__strict)))], (27510 ^ _784416) ^ [_1309549, _1309551, _1309553, _1309555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1309549), _1309551)), -(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), _1309549), _1309553)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1309551), _1309555))), c_FunDef_Opair__leq)))], (27516 ^ _784416) ^ [_1309686, _1309688, _1309690, _1309692, _1309694] : [class_Fields_Ofield(_1309686), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309688), _1309690)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309688), _1309692)), 27530 ^ _784416 : [(27531 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1309688), 27529 ^ [_1309686, _1309688, _1309690, _1309692, _1309694]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309688, tc_HOL_Obool)), _1309690), _1309692))))], (27533 ^ _784416) ^ [] : [-(hAPP(_1309694, 27529 ^ [_1309686, _1309688, _1309690, _1309692, _1309694]) = c_Groups_Ozero__class_Ozero(_1309686))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1309688, _1309686), _1309694), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309688, tc_HOL_Obool)), _1309690), _1309692)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1309686), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1309686), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1309688, _1309686), _1309694), _1309690)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1309688, _1309686), _1309694), _1309692))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1309688, _1309686), _1309694), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309688, tc_HOL_Obool)), _1309690), _1309692))))], (27537 ^ _784416) ^ [_1310182] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1310182)), -(_1310182 = 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))), _1310182)), c_FunDef_Omax__strict)))], (27547 ^ _784416) ^ [_1310288] : [-(_1310288 = 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)), _1310288), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (27553 ^ _784416) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (27555 ^ _784416) ^ [_1310351, _1310353, _1310355, _1310357] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1310351), _1310353)), 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)), _1310355), _1310351)), 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)), _1310357), _1310353)), 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)), _1310355), _1310357)), _1310353)), c_FunDef_Omax__weak)))], (27569 ^ _784416) ^ [_1310632, _1310634, _1310636, _1310638] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1310632), _1310634)), 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)), _1310632), _1310636)), 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)), _1310634), _1310638)), 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)), _1310634), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1310636), _1310638))), c_FunDef_Omin__weak)))], (27583 ^ _784416) ^ [] : [-(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)))))], (27585 ^ _784416) ^ [_1310937] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1310937))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1310937)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27591 ^ _784416) ^ [_1311026] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1311026)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1311026)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1311026)), 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)))))], (27597 ^ _784416) ^ [_1311081] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1311081)), -(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))), _1311081)), c_FunDef_Omax__weak)))], (27603 ^ _784416) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (27605 ^ _784416) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (27607 ^ _784416) ^ [_1311230] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1311230))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1311230)))], (27613 ^ _784416) ^ [_1311264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1311264)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1311264))], (27619 ^ _784416) ^ [_1311362] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1311362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1311362), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27625 ^ _784416) ^ [_1311447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1311447), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1311447)))], (27631 ^ _784416) ^ [_1311550] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1311550)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1311550))))], (27637 ^ _784416) ^ [_1311645] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1311645))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1311645)))))], (27643 ^ _784416) ^ [_1311746] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1311746))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1311746) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27675 ^ _784416) ^ [_1312237, _1312239] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1312237) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1312239)), 27678 ^ _784416 : [(27679 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1312237))))], (27681 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1312239)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 27682 ^ _784416 : [(27683 ^ _784416) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1312237)))], (27685 ^ _784416) ^ [] : [27686 ^ _784416 : [(27687 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1312239))))], (27689 ^ _784416) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1312237) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], 27690 ^ _784416 : [(27691 ^ _784416) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1312239)))], (27693 ^ _784416) ^ [] : [_1312237 = _1312239]]]]], (27649 ^ _784416) ^ [_1311852, _1311854] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1311852) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1311854), 27652 ^ _784416 : [(27653 ^ _784416) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1311852))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1311854)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27659 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1311852)))), 27662 ^ _784416 : [(27663 ^ _784416) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1311854))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1311852) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27669 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1311854)))), -(_1311852 = _1311854)]]]]], (27697 ^ _784416) ^ [_1312650, _1312652, _1312654] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1312650))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1312650)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1312652)), _1312654)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1312652)), _1312654))], (27703 ^ _784416) ^ [_1312788, _1312790, _1312792] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1312788)))), 27706 ^ _784416 : [(27707 ^ _784416) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1312790))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1312788)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1312790)), _1312792)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1312788)), _1312792))], (27713 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1312790)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1312788)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1312790)), _1312792)) = 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), _1312788), _1312790))), _1312792))]]], (27719 ^ _784416) ^ [_1313113] : [-(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)), _1313113), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (27721 ^ _784416) ^ [] : [-(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)))))], (27723 ^ _784416) ^ [_1313174, _1313176] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1313174))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1313174)), _1313176)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1313176))], (27729 ^ _784416) ^ [_1313285, _1313287] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1313285)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1313285)), _1313287)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1313285))), _1313287))], (27735 ^ _784416) ^ [_1313357] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1313357))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1313357)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (27741 ^ _784416) ^ [_1313448] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1313448)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1313448)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1313448)))], (27747 ^ _784416) ^ [_1313506] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1313506))), -(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), _1313506)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (27753 ^ _784416) ^ [_1313599] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1313599)))), -(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), _1313599)) = 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), _1313599))))], (27759 ^ _784416) ^ [] : [-(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)))], (27761 ^ _784416) ^ [] : [-(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))))], (27763 ^ _784416) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27765 ^ _784416) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (27767 ^ _784416) ^ [_1313729, _1313731] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1313729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1313731)), 27774 ^ _784416 : [(27775 ^ _784416) ^ [] : [hAPP(c_Int_Onat, _1313729) = hAPP(c_Int_Onat, _1313731), -(_1313729 = _1313731)], (27781 ^ _784416) ^ [] : [_1313729 = _1313731, -(hAPP(c_Int_Onat, _1313729) = hAPP(c_Int_Onat, _1313731))]]], (27787 ^ _784416) ^ [_1314014, _1314016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1314014)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1314016)), 27794 ^ _784416 : [(27795 ^ _784416) ^ [] : [hAPP(c_Int_Onat, _1314014) = hAPP(c_Int_Onat, _1314016), -(_1314014 = _1314016)], (27801 ^ _784416) ^ [] : [_1314014 = _1314016, -(hAPP(c_Int_Onat, _1314014) = hAPP(c_Int_Onat, _1314016))]]], (27818 ^ _784416) ^ [_1314496] : [27820 ^ _784416 : [(27821 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27819 ^ [_1314496])))], (27823 ^ _784416) ^ [] : [hBOOL(hAPP(_1314496, hAPP(c_Int_Onat, 27819 ^ [_1314496])))]], 27824 ^ _784416 : [(27825 ^ _784416) ^ [_1314629] : [-(hBOOL(hAPP(_1314496, _1314629)))]]], (27807 ^ _784416) ^ [_1314311] : [hBOOL(hAPP(_1314311, 27808 ^ [_1314311])), 27811 ^ _784416 : [(27812 ^ _784416) ^ [_1314405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1314405)), -(hBOOL(hAPP(_1314311, hAPP(c_Int_Onat, _1314405))))]]], (27827 ^ _784416) ^ [_1314674] : [27828 ^ _784416 : [(27829 ^ _784416) ^ [_1314731] : [hBOOL(hAPP(_1314674, _1314731))]], 27831 ^ _784416 : [(27832 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27830 ^ [_1314674])))], (27834 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1314674, hAPP(c_Int_Onat, 27830 ^ [_1314674]))))]]], (27836 ^ _784416) ^ [_1314817] : [-(hBOOL(hAPP(_1314817, 27843 ^ [_1314817]))), 27837 ^ _784416 : [(27838 ^ _784416) ^ [_1314869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1314869)), hBOOL(hAPP(_1314817, hAPP(c_Int_Onat, _1314869)))]]], (27847 ^ _784416) ^ [_1314996] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1314996) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1314996)))], (27849 ^ _784416) ^ [_1315028] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1315028)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1315028))], (27851 ^ _784416) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (27853 ^ _784416) ^ [_1315078] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1315078)), -(hAPP(c_Int_Onat, _1315078) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27859 ^ _784416) ^ [_1315163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1315163), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1315163) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27865 ^ _784416) ^ [_1315266] : [hAPP(c_Int_Onat, _1315266) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1315266), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (27871 ^ _784416) ^ [_1315353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1315353), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1315353) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27877 ^ _784416) ^ [_1315461, _1315463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1315461)), hAPP(c_Int_Onat, _1315463))), 27880 ^ _784416 : [(27881 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1315463)))], (27883 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1315461), _1315463)))]]], (27885 ^ _784416) ^ [_1315596, _1315598] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1315596)), hAPP(c_Int_Onat, _1315598)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1315598)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1315596), _1315598))], (27895 ^ _784416) ^ [_1315763, _1315765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1315763)), 27898 ^ _784416 : [(27899 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1315765)), hAPP(c_Int_Onat, _1315763))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1315765), _1315763)))], (27905 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1315765), _1315763)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1315765)), hAPP(c_Int_Onat, _1315763))))]]], (27911 ^ _784416) ^ [_1316022, _1316024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1316022)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1316024)), 27918 ^ _784416 : [(27919 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1316022)), hAPP(c_Int_Onat, _1316024))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1316022), _1316024)))], (27925 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1316022), _1316024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1316022)), hAPP(c_Int_Onat, _1316024))))]]], (27931 ^ _784416) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (27933 ^ _784416) ^ [_1316355] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1316355) = 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), _1316355), c_Int_Onat)))))], (27935 ^ _784416) ^ [_1316396] : [-(c_Int_Osucc(_1316396) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1316396), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (27937 ^ _784416) ^ [_1316439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1316439))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1316439)))], (27943 ^ _784416) ^ [_1316524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1316524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1316524))))], (27949 ^ _784416) ^ [_1316615, _1316617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1316615)), 27952 ^ _784416 : [(27953 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1316615)), hAPP(c_Int_Onat, _1316617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1316615), _1316617)))], (27959 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1316615), _1316617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1316615)), hAPP(c_Int_Onat, _1316617))))]]], (27965 ^ _784416) ^ [_1316874, _1316876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1316874)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1316876)), 27972 ^ _784416 : [(27973 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1316874)), hAPP(c_Int_Onat, _1316876))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1316874), _1316876)))], (27979 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1316874), _1316876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1316874)), hAPP(c_Int_Onat, _1316876))))]]], (27985 ^ _784416) ^ [_1317189, _1317191] : [27986 ^ _784416 : [(27987 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1317189))], (27989 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1317191))]], 27990 ^ _784416 : [(27991 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1317189)), hAPP(c_Int_Onat, _1317191))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1317189), _1317191)))], (27997 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1317189), _1317191)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1317189)), hAPP(c_Int_Onat, _1317191))))]]], (28003 ^ _784416) ^ [_1317490, _1317492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1317490)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1317492)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1317490), _1317492)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1317490)), hAPP(c_Int_Onat, _1317492)))], (28013 ^ _784416) ^ [_1317669, _1317671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1317669)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1317671)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1317669)), hAPP(c_Int_Onat, _1317671)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1317669), _1317671)))], (28023 ^ _784416) ^ [_1317848, _1317850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1317848)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1317848), _1317850)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1317848)), hAPP(c_Int_Onat, _1317850)))], (28029 ^ _784416) ^ [_1317971, _1317973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1317971)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1317973)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1317971)), hAPP(c_Int_Onat, _1317973)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1317971), _1317973)))], (28039 ^ _784416) ^ [_1318150, _1318152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1318150)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1318150), _1318152)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1318152), _1318150)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1318152)), hAPP(c_Int_Onat, _1318150)))], (28049 ^ _784416) ^ [_1318335, _1318337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1318335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1318337)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1318335, _1318337)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1318335), hAPP(c_Int_Onat, _1318337)))], (28059 ^ _784416) ^ [_1318506, _1318508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1318506)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1318508)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1318506), hAPP(c_Int_Onat, _1318508)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1318506, _1318508)))], (28069 ^ _784416) ^ [_1318677, _1318679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1318677)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1318677), _1318679)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1318677)), hAPP(c_Int_Onat, _1318679)))], (28075 ^ _784416) ^ [_1318800, _1318802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1318800)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1318802)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1318800)), hAPP(c_Int_Onat, _1318802)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1318800), _1318802)))], (28085 ^ _784416) ^ [_1318979, _1318981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1318979)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1318979)), _1318981) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1318979), _1318981)))], (28091 ^ _784416) ^ [_1319096, _1319098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1319096)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1319096), _1319098)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1319096)), _1319098))], (28097 ^ _784416) ^ [_1319213, _1319215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1319213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1319215)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1319213)), hAPP(c_Int_Onat, _1319215)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1319213, _1319215)))], (28107 ^ _784416) ^ [_1319395, _1319397] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1319395)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1319397)), hAPP(c_Int_Onat, _1319395)) = hAPP(c_Int_Onat, _1319397))], (28113 ^ _784416) ^ [_1319500, _1319502] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1319500))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1319502)), hAPP(c_Int_Onat, _1319500)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1319502), _1319500)), 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)))], (28119 ^ _784416) ^ [_1319576] : [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, _1319576))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1319576)))], (28125 ^ _784416) ^ [_1319661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1319661)), -(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, _1319661))))], (28131 ^ _784416) ^ [_1319752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1319752)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1319752)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1319752)))], (28137 ^ _784416) ^ [_1319855, _1319857] : [class_Int_Onumber__ring(_1319855), -(hAPP(c_Int_Onumber__class_Onumber__of(_1319855), c_Int_Osucc(_1319857)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1319855), c_Groups_Oone__class_Oone(_1319855)), hAPP(c_Int_Onumber__class_Onumber__of(_1319855), _1319857)))], (28143 ^ _784416) ^ [_1319974, _1319976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1319974), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1319974), _1319976)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1319974))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1319976))))], (28149 ^ _784416) ^ [_1320115, _1320117, _1320119, _1320121] : [c_FunDef_Oreduction__pair(_1320115, _1320117), -(c_FunDef_Oreduction__pair(_1320119, hAPP(hAPP(c_FunDef_Orp__inv__image(_1320115, _1320119), _1320117), _1320121)))], (28155 ^ _784416) ^ [_1320223, _1320225] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1320223))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320223), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320225)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28161 ^ _784416) ^ [_1320325, _1320327] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1320325)))), 28164 ^ _784416 : [(28165 ^ _784416) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1320327))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320325), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320327)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320325))], (28171 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1320327)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320325), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320327)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1320325), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1320327))))]]], (28177 ^ _784416) ^ [_1320607, _1320609] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1320607))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320607)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320609)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28183 ^ _784416) ^ [_1320712, _1320714] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1320712)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320712)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320714)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1320712)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1320714))))], (28189 ^ _784416) ^ [_1320791, _1320793] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1320791))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320791)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320793)) = 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), _1320793)))], (28195 ^ _784416) ^ [_1320908, _1320910] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1320908)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320908)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320910)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1320908)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320910))))], (28201 ^ _784416) ^ [_1320987, _1320989] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1320987))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1320987)), _1320989) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1320989))], (28207 ^ _784416) ^ [_1321092, _1321094] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1321092)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1321092)), _1321094) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1321092)), _1321094)))], (28213 ^ _784416) ^ [_1321156] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1321156)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1321156))))], (28215 ^ _784416) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (28217 ^ _784416) ^ [] : [-(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)))], (28219 ^ _784416) ^ [_1321230, _1321232] : [-(c_Int_Onat__aux(_1321230, _1321232) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1321230)), _1321232))], (28221 ^ _784416) ^ [_1321276, _1321278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1321276), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1321278)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1321276)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1321278))], (28227 ^ _784416) ^ [_1321387, _1321389] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1321387), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1321389)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1321387)) = 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), _1321389), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1321387)))), 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)))], (28233 ^ _784416) ^ [] : [-(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))))], (28235 ^ _784416) ^ [_1321493, _1321495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1321493)), hAPP(c_Nat_OSuc, _1321495))), -(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(_1321493))), 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)), _1321495)))))], (28241 ^ _784416) ^ [_1321620, _1321622] : [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(_1321620))), 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)), _1321622)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1321620)), hAPP(c_Nat_OSuc, _1321622))))], (28247 ^ _784416) ^ [_1321768, _1321770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1321768)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1321770))), -(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(_1321770))), 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), _1321768)), c_Int_Onat))))))], (28253 ^ _784416) ^ [_1321913, _1321915] : [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(_1321915))), 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), _1321913)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1321913)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1321915))))], (28259 ^ _784416) ^ [_1322064] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1322064), c_Int_OPls) = _1322064)], (28261 ^ _784416) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (28263 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (28265 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (28267 ^ _784416) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (28269 ^ _784416) ^ [_1322171] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1322171) = c_Int_OPls)], (28271 ^ _784416) ^ [_1322197] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1322197), c_Int_OPls) = _1322197)], (28273 ^ _784416) ^ [_1322226] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1322226) = _1322226)], (28275 ^ _784416) ^ [_1322261] : [c_Int_OBit1(_1322261) = c_Int_OPls], (28277 ^ _784416) ^ [_1322295] : [c_Int_OPls = c_Int_OBit1(_1322295)], (28279 ^ _784416) ^ [_1322320] : [-(c_Int_Osucc(c_Int_Opred(_1322320)) = _1322320)], (28281 ^ _784416) ^ [_1322347] : [class_Int_Onumber__ring(_1322347), -(c_Groups_Ozero__class_Ozero(_1322347) = hAPP(c_Int_Onumber__class_Onumber__of(_1322347), c_Int_OPls))], (28287 ^ _784416) ^ [_1322434] : [class_Int_Onumber__ring(_1322434), -(hAPP(c_Int_Onumber__class_Onumber__of(_1322434), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1322434))], (28293 ^ _784416) ^ [_1322521, _1322523] : [class_Int_Onumber__ring(_1322521), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1322521), hAPP(c_Int_Onumber__class_Onumber__of(_1322521), c_Int_OPls)), _1322523) = _1322523)], (28299 ^ _784416) ^ [_1322622, _1322624] : [class_Int_Onumber__ring(_1322622), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1322622), _1322624), hAPP(c_Int_Onumber__class_Onumber__of(_1322622), c_Int_OPls)) = _1322624)], (28305 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (28307 ^ _784416) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28309 ^ _784416) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (28311 ^ _784416) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (28313 ^ _784416) ^ [_1322813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1322813))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1322813)))], (28319 ^ _784416) ^ [_1322896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1322896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1322896))))], (28325 ^ _784416) ^ [_1322997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1322997)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1322997), c_Int_OPls)))], (28331 ^ _784416) ^ [_1323092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1323092), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1323092)), c_Int_OPls)))], (28337 ^ _784416) ^ [_1323193, _1323195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1323193)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1323195)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1323193)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1323195), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1323193))))], (28343 ^ _784416) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (28345 ^ _784416) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (28347 ^ _784416) ^ [_1323377, _1323379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1323377), _1323379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1323377)), _1323379)))], (28353 ^ _784416) ^ [_1323474, _1323476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1323474)), _1323476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1323474), _1323476)))], (28359 ^ _784416) ^ [_1323577] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1323577)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1323577))))], (28361 ^ _784416) ^ [_1323612] : [-(c_Int_Opred(_1323612) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1323612), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (28363 ^ _784416) ^ [_1323649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1323649), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1323649)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28369 ^ _784416) ^ [_1323746] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1323746), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1323746)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1323746)))], (28375 ^ _784416) ^ [_1323801, _1323803] : [class_Int_Onumber__ring(_1323801), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1323801), _1323803), hAPP(c_Int_Onumber__class_Onumber__of(_1323801), c_Int_OBit1(c_Int_OPls))) = _1323803)], (28381 ^ _784416) ^ [_1323902, _1323904] : [class_Int_Onumber__ring(_1323902), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1323902), hAPP(c_Int_Onumber__class_Onumber__of(_1323902), c_Int_OBit1(c_Int_OPls))), _1323904) = _1323904)], (28387 ^ _784416) ^ [_1324003, _1324005] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1324003), _1324005), hAPP(c_Int_Onumber__class_Onumber__of(_1324003), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1324003)), class_Fields_Ofield__inverse__zero(_1324003), class_Int_Onumber__ring(_1324003)], (28397 ^ _784416) ^ [_1324158] : [class_Int_Onumber__ring(_1324158), -(hAPP(c_Int_Onumber__class_Onumber__of(_1324158), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1324158))], (28403 ^ _784416) ^ [_1324245] : [class_Int_Onumber__ring(_1324245), -(c_Groups_Oone__class_Oone(_1324245) = hAPP(c_Int_Onumber__class_Onumber__of(_1324245), c_Int_OBit1(c_Int_OPls)))], (28409 ^ _784416) ^ [_1324344] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1324344), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1324344), c_Int_OPls)))], (28415 ^ _784416) ^ [_1324431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1324431), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1324431))], (28421 ^ _784416) ^ [_1324536] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1324536) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1324536), c_Int_OPls)))], (28427 ^ _784416) ^ [_1324623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1324623), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1324623) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28433 ^ _784416) ^ [_1324728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1324728)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1324728), c_Int_OPls)))], (28439 ^ _784416) ^ [_1324823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1324823), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1324823)), c_Int_OPls)))], (28445 ^ _784416) ^ [_1324936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1324936))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1324936)))], (28451 ^ _784416) ^ [_1325019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1325019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1325019))))], (28457 ^ _784416) ^ [_1325123, _1325125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1325123)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1325125))), 28460 ^ _784416 : [(28467 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1325123), _1325125)))], (28461 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1325123), _1325125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1325125)))]]], (28469 ^ _784416) ^ [_1325326, _1325328] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1325326)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1325328)))), 28472 ^ _784416 : [(28473 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1325326), _1325328)))], (28475 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1325328))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1325326), _1325328))], (28481 ^ _784416) ^ [_1325536, _1325538] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325536), _1325538), hAPP(c_Int_Onumber__class_Onumber__of(_1325536), c_Int_OBit1(c_Int_OPls))) = _1325538), class_Fields_Ofield(_1325536), class_Int_Onumber__ring(_1325536)], (28491 ^ _784416) ^ [_1325687, _1325689] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1325687), _1325689), hAPP(c_Int_Onumber__class_Onumber__of(_1325687), c_Int_OBit1(c_Int_OPls))) = _1325689), class_Fields_Ofield(_1325687), class_Int_Onumber__ring(_1325687)], (28511 ^ _784416) ^ [_1325983, _1325985] : [28512 ^ _784416 : [(28513 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1325983), _1325985))], (28515 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1325983), 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), _1325983)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1325985))))], (28501 ^ _784416) ^ [_1325853, _1325855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1325853)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1325855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1325853), _1325855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1325853), c_Int_OPls)))], (28519 ^ _784416) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (28521 ^ _784416) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (28523 ^ _784416) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (28525 ^ _784416) ^ [_1326198, _1326200] : [class_Int_Onumber__ring(_1326198), class_Rings_Olinordered__idom(_1326198), 28532 ^ _784416 : [(28533 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326198), c_Groups_Ozero__class_Ozero(_1326198)), hAPP(c_Int_Onumber__class_Onumber__of(_1326198), _1326200))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1326200)))], (28539 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1326200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326198), c_Groups_Ozero__class_Ozero(_1326198)), hAPP(c_Int_Onumber__class_Onumber__of(_1326198), _1326200))))]]], (28545 ^ _784416) ^ [_1326503, _1326505] : [class_Int_Onumber__ring(_1326503), class_Rings_Olinordered__idom(_1326503), 28552 ^ _784416 : [(28553 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326503), hAPP(c_Int_Onumber__class_Onumber__of(_1326503), _1326505)), c_Groups_Ozero__class_Ozero(_1326503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1326505), c_Int_OPls)))], (28559 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1326505), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326503), hAPP(c_Int_Onumber__class_Onumber__of(_1326503), _1326505)), c_Groups_Ozero__class_Ozero(_1326503))))]]], (28565 ^ _784416) ^ [_1326817, _1326819] : [class_Int_Onumber__ring(_1326817), class_Rings_Olinordered__idom(_1326817), 28572 ^ _784416 : [(28573 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1326817), c_Groups_Ozero__class_Ozero(_1326817)), hAPP(c_Int_Onumber__class_Onumber__of(_1326817), _1326819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1326819)))], (28579 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1326819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1326817), c_Groups_Ozero__class_Ozero(_1326817)), hAPP(c_Int_Onumber__class_Onumber__of(_1326817), _1326819))))]]], (28585 ^ _784416) ^ [_1327122, _1327124] : [class_Int_Onumber__ring(_1327122), class_Rings_Olinordered__idom(_1327122), 28592 ^ _784416 : [(28593 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327122), hAPP(c_Int_Onumber__class_Onumber__of(_1327122), _1327124)), c_Groups_Ozero__class_Ozero(_1327122))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1327124), c_Int_OPls)))], (28599 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1327124), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327122), hAPP(c_Int_Onumber__class_Onumber__of(_1327122), _1327124)), c_Groups_Ozero__class_Ozero(_1327122))))]]], (28605 ^ _784416) ^ [_1327448] : [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), _1327448))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1327448)))], (28611 ^ _784416) ^ [_1327533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1327533)), -(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), _1327533))))], (28617 ^ _784416) ^ [] : [-(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)))], (28619 ^ _784416) ^ [] : [-(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)))))], (28621 ^ _784416) ^ [_1327660, _1327662] : [class_Groups_Omonoid__mult(_1327660), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1327660), _1327662), 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(_1327660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1327660), _1327662), _1327662)), _1327662))], (28627 ^ _784416) ^ [] : [-(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))))))], (28629 ^ _784416) ^ [_1327801] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1327801))) = 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)))), _1327801))], (28631 ^ _784416) ^ [_1327845, _1327847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1327845), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1327845)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1327847)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1327847))], (28637 ^ _784416) ^ [_1327957, _1327959] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1327957), c_Int_OPls))), 28640 ^ _784416 : [(28641 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1327959), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1327957)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1327959)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1327957))], (28647 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1327959), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1327957)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1327959)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1327957), _1327959)))]]], (28653 ^ _784416) ^ [] : [-(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)))))], (28655 ^ _784416) ^ [_1328248, _1328250] : [class_Int_Onumber__ring(_1328248), -(hAPP(c_Int_Onumber__class_Onumber__of(_1328248), c_Int_Opred(_1328250)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328248), hAPP(c_Groups_Ouminus__class_Ouminus(_1328248), c_Groups_Oone__class_Oone(_1328248))), hAPP(c_Int_Onumber__class_Onumber__of(_1328248), _1328250)))], (28661 ^ _784416) ^ [_1328377, _1328379] : [class_Int_Onumber__ring(_1328377), class_Rings_Olinordered__idom(_1328377), 28668 ^ _784416 : [(28669 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328377), c_Groups_Oone__class_Oone(_1328377)), hAPP(c_Int_Onumber__class_Onumber__of(_1328377), _1328379))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1328379)))], (28675 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1328379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328377), c_Groups_Oone__class_Oone(_1328377)), hAPP(c_Int_Onumber__class_Onumber__of(_1328377), _1328379))))]]], (28681 ^ _784416) ^ [_1328682, _1328684] : [class_Int_Onumber__ring(_1328682), class_Rings_Olinordered__idom(_1328682), 28688 ^ _784416 : [(28689 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328682), hAPP(c_Int_Onumber__class_Onumber__of(_1328682), _1328684)), c_Groups_Oone__class_Oone(_1328682))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1328684), c_Int_OBit1(c_Int_OPls))))], (28695 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1328684), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328682), hAPP(c_Int_Onumber__class_Onumber__of(_1328682), _1328684)), c_Groups_Oone__class_Oone(_1328682))))]]], (28701 ^ _784416) ^ [_1328996, _1328998] : [class_Int_Onumber__ring(_1328996), class_Rings_Olinordered__idom(_1328996), 28708 ^ _784416 : [(28709 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328996), c_Groups_Oone__class_Oone(_1328996)), hAPP(c_Int_Onumber__class_Onumber__of(_1328996), _1328998))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1328998)))], (28715 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1328998)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328996), c_Groups_Oone__class_Oone(_1328996)), hAPP(c_Int_Onumber__class_Onumber__of(_1328996), _1328998))))]]], (28721 ^ _784416) ^ [_1329301, _1329303] : [class_Int_Onumber__ring(_1329301), class_Rings_Olinordered__idom(_1329301), 28728 ^ _784416 : [(28729 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329301), hAPP(c_Int_Onumber__class_Onumber__of(_1329301), _1329303)), c_Groups_Oone__class_Oone(_1329301))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1329303), c_Int_OBit1(c_Int_OPls))))], (28735 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1329303), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1329301), hAPP(c_Int_Onumber__class_Onumber__of(_1329301), _1329303)), c_Groups_Oone__class_Oone(_1329301))))]]], (28741 ^ _784416) ^ [_1329615, _1329617] : [class_Int_Onumber__ring(_1329615), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1329615), c_Groups_Oone__class_Oone(_1329615)), hAPP(c_Int_Onumber__class_Onumber__of(_1329615), _1329617)) = hAPP(c_Int_Onumber__class_Onumber__of(_1329615), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1329617)))], (28747 ^ _784416) ^ [_1329736, _1329738] : [class_Int_Onumber__ring(_1329736), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1329736), hAPP(c_Int_Onumber__class_Onumber__of(_1329736), _1329738)), c_Groups_Oone__class_Oone(_1329736)) = hAPP(c_Int_Onumber__class_Onumber__of(_1329736), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1329738), c_Int_OBit1(c_Int_OPls))))], (28753 ^ _784416) ^ [_1329863, _1329865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1329863)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1329865)), _1329863) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1329865), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1329863), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (28759 ^ _784416) ^ [_1329995, _1329997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1329995), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1329995)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1329997)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28765 ^ _784416) ^ [_1330100, _1330102] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330100), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1330100)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1330102)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1330100), _1330102)))], (28771 ^ _784416) ^ [_1330176, _1330178, _1330180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330176), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1330176)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1330178)), _1330180)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28777 ^ _784416) ^ [_1330295, _1330297, _1330299] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330295), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1330295)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1330297)), _1330299)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1330295), _1330297))), _1330299))], (28783 ^ _784416) ^ [_1330385] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1330385)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1330385) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28789 ^ _784416) ^ [_1330476] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1330476) = 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(_1330476)))))], (28795 ^ _784416) ^ [_1330573, _1330575] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1330573))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1330575)) = 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)))), _1330573), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1330575)))], (28797 ^ _784416) ^ [_1330624, _1330626] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1330624))), _1330626) = 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)))), _1330624), _1330626))], (28799 ^ _784416) ^ [_1330669, _1330671] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1330669, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1330671)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1330669, 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)))), _1330671)))], (28801 ^ _784416) ^ [_1330714, _1330716] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1330714)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1330716)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1330714)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1330716)))], (28803 ^ _784416) ^ [_1330769, _1330771] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1330769)))), _1330771) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1330769)), _1330771))], (28805 ^ _784416) ^ [_1330818, _1330820] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1330818), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1330820)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1330818), 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)))), _1330820)))], (28807 ^ _784416) ^ [_1330873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330873), 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), _1330873)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (28813 ^ _784416) ^ [_1330964] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330964), 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), _1330964)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1330964)))], (28819 ^ _784416) ^ [_1331022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331022), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1331022)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (28825 ^ _784416) ^ [_1331119] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331119), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1331119)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1331119)))], (28831 ^ _784416) ^ [_1331174, _1331176] : [class_Int_Onumber__ring(_1331174), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1331174), hAPP(c_Int_Onumber__class_Onumber__of(_1331174), _1331176)), c_Groups_Oone__class_Oone(_1331174)) = hAPP(c_Int_Onumber__class_Onumber__of(_1331174), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1331176), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (28837 ^ _784416) ^ [_1331301, _1331303] : [class_Int_Onumber__ring(_1331301), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1331301), c_Groups_Oone__class_Oone(_1331301)), hAPP(c_Int_Onumber__class_Onumber__of(_1331301), _1331303)) = hAPP(c_Int_Onumber__class_Onumber__of(_1331301), 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), _1331303))))], (28843 ^ _784416) ^ [_1331443, _1331445] : [hAPP(c_Nat_OSuc, _1331443) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1331445), -(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(_1331445))), 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)), _1331443))))))], (28849 ^ _784416) ^ [_1331566, _1331568] : [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(_1331568))), 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)), _1331566))))), -(hAPP(c_Nat_OSuc, _1331566) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1331568))], (28855 ^ _784416) ^ [_1331710, _1331712] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1331710) = hAPP(c_Nat_OSuc, _1331712), -(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(_1331710))), 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)), _1331712))))))], (28861 ^ _784416) ^ [_1331833, _1331835] : [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(_1331833))), 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)), _1331835))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1331833) = hAPP(c_Nat_OSuc, _1331835))], (28867 ^ _784416) ^ [_1331977, _1331979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1331977)), hAPP(c_Nat_OSuc, _1331979))), -(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(_1331977))), 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)), _1331979)))))], (28873 ^ _784416) ^ [_1332104, _1332106] : [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(_1332104))), 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)), _1332106)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1332104)), hAPP(c_Nat_OSuc, _1332106))))], (28879 ^ _784416) ^ [_1332252, _1332254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1332252)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1332254))), -(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(_1332254))), 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), _1332252)), c_Int_Onat))))))], (28885 ^ _784416) ^ [_1332397, _1332399] : [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(_1332399))), 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), _1332397)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1332397)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1332399))))], (28891 ^ _784416) ^ [] : [-(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))))], (28893 ^ _784416) ^ [_1332566, _1332568, _1332570, _1332572, _1332574] : [-(c_Nat_Onat_Onat__case(_1332566, _1332568, _1332570, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1332572)), _1332574)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1332566), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1332572))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1332566, _1332566), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1332566, tc_fun(_1332566, _1332566)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1332566, tc_fun(_1332566, _1332566)), tc_Int_Oint), c_If(_1332566)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1332566, _1332568, _1332570, _1332574))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1332566, tc_Int_Oint), _1332570), 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)), _1332574)))))], (28895 ^ _784416) ^ [_1332684, _1332686, _1332688, _1332690] : [-(c_Nat_Onat_Onat__case(_1332684, _1332686, _1332688, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1332690)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1332684), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1332690))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1332684, _1332684), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1332684, tc_fun(_1332684, _1332684)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1332684, tc_fun(_1332684, _1332684)), tc_Int_Oint), c_If(_1332684)), c_Nat__Numeral_Oneg)), _1332686)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1332684, tc_Int_Oint), _1332688), c_Int_Onat))))], (28897 ^ _784416) ^ [_1332786, _1332788, _1332790, _1332792, _1332794] : [-(hAPP(c_Nat_Onat_Onat__rec(_1332786, _1332788, _1332790), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1332792)), _1332794)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1332786), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1332792))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1332786, _1332786), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1332786, tc_fun(_1332786, _1332786)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1332786, tc_fun(_1332786, _1332786)), tc_Int_Oint), c_If(_1332786)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1332786, _1332788, _1332790), _1332794))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1332786, _1332786), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1332786, _1332786), tc_Int_Oint), _1332790), 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)), _1332794))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1332786, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1332786, _1332788, _1332790)), 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)), _1332794))))))], (28899 ^ _784416) ^ [_1332938, _1332940, _1332942] : [-(hAPP(c_Nat_Onat_Onat__rec(_1332938, _1332940, _1332942), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1332940)], (28901 ^ _784416) ^ [_1332972, _1332974, _1332976, _1332978] : [-(hAPP(c_Nat_Onat_Onat__rec(_1332972, _1332974, _1332976), hAPP(c_Nat_OSuc, _1332978)) = hAPP(hAPP(_1332976, _1332978), hAPP(c_Nat_Onat_Onat__rec(_1332972, _1332974, _1332976), _1332978)))], (28903 ^ _784416) ^ [_1333024, _1333026, _1333028] : [-(c_Nat_Onat_Onat__case(_1333024, _1333026, _1333028, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1333026)], (28905 ^ _784416) ^ [_1333056, _1333058, _1333060, _1333062] : [-(c_Nat_Onat_Onat__case(_1333056, _1333058, _1333060, hAPP(c_Nat_OSuc, _1333062)) = hAPP(_1333060, _1333062))], (28907 ^ _784416) ^ [_1333111, _1333113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1333111)), _1333113)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1333111), _1333113)))], (28913 ^ _784416) ^ [_1333214, _1333216] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1333214), _1333216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1333214)), _1333216)))], (28919 ^ _784416) ^ [_1333323, _1333325] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1333323), hAPP(c_Nat_OSuc, _1333325)) = 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), _1333323), _1333325)))], (28921 ^ _784416) ^ [_1333368, _1333370, _1333372, _1333374] : [-(hAPP(c_Nat_Onat_Onat__rec(_1333368, _1333370, _1333372), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1333374)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1333368), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1333374))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1333368, _1333368), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1333368, tc_fun(_1333368, _1333368)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1333368, tc_fun(_1333368, _1333368)), tc_Int_Oint), c_If(_1333368)), c_Nat__Numeral_Oneg)), _1333370)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1333368, _1333368), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1333368, _1333368), tc_Int_Oint), _1333372), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1333368, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1333368, _1333370, _1333372)), c_Int_Onat)))))], (28923 ^ _784416) ^ [_1333499, _1333501] : [class_Int_Onumber__ring(_1333499), 28926 ^ _784416 : [(28927 ^ _784416) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1333499), _1333501) = c_Groups_Oone__class_Oone(_1333499), -(c_Int_Oiszero(_1333499, hAPP(c_Int_Onumber__class_Onumber__of(_1333499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1333501), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))], (28933 ^ _784416) ^ [] : [c_Int_Oiszero(_1333499, hAPP(c_Int_Onumber__class_Onumber__of(_1333499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1333501), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1333499), _1333501) = c_Groups_Oone__class_Oone(_1333499))]]], (28939 ^ _784416) ^ [_1333758, _1333760] : [class_Int_Onumber__ring(_1333758), 28942 ^ _784416 : [(28943 ^ _784416) ^ [] : [c_Groups_Oone__class_Oone(_1333758) = hAPP(c_Int_Onumber__class_Onumber__of(_1333758), _1333760), -(c_Int_Oiszero(_1333758, hAPP(c_Int_Onumber__class_Onumber__of(_1333758), 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), _1333760)))))], (28949 ^ _784416) ^ [] : [c_Int_Oiszero(_1333758, hAPP(c_Int_Onumber__class_Onumber__of(_1333758), 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), _1333760)))), -(c_Groups_Oone__class_Oone(_1333758) = hAPP(c_Int_Onumber__class_Onumber__of(_1333758), _1333760))]]], (28955 ^ _784416) ^ [_1334017, _1334019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1334017), 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)))), _1334019)), 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)))), _1334017)) = 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), _1334019), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1334017))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (28961 ^ _784416) ^ [_1334177, _1334179] : [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), _1334177))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1334179)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1334177))) = 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), _1334179), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1334177)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (28967 ^ _784416) ^ [_1334324, _1334326] : [-(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), _1334324)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1334326)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1334324))) = 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), _1334326)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1334324)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (28973 ^ _784416) ^ [_1334406, _1334408] : [class_Int_Onumber__ring(_1334406), class_Int_Oring__char__0(_1334406), 28980 ^ _784416 : [(28981 ^ _784416) ^ [] : [c_Int_Oiszero(_1334406, hAPP(c_Int_Onumber__class_Onumber__of(_1334406), c_Int_OBit0(_1334408))), -(c_Int_Oiszero(_1334406, hAPP(c_Int_Onumber__class_Onumber__of(_1334406), _1334408)))], (28987 ^ _784416) ^ [] : [c_Int_Oiszero(_1334406, hAPP(c_Int_Onumber__class_Onumber__of(_1334406), _1334408)), -(c_Int_Oiszero(_1334406, hAPP(c_Int_Onumber__class_Onumber__of(_1334406), c_Int_OBit0(_1334408))))]]], (28993 ^ _784416) ^ [_1334711, _1334713] : [c_Int_OBit1(_1334711) = c_Int_OBit0(_1334713)], (28995 ^ _784416) ^ [_1334752, _1334754] : [c_Int_OBit0(_1334752) = c_Int_OBit1(_1334754)], (28997 ^ _784416) ^ [_1334781, _1334783] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1334781)), c_Int_OBit0(_1334783)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1334781), _1334783)))], (28999 ^ _784416) ^ [_1334824] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1334824)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1334824)))], (29001 ^ _784416) ^ [_1334857, _1334859] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1334857)), _1334859) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1334857), _1334859)))], (29003 ^ _784416) ^ [_1334913, _1334915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1334913)), c_Int_OBit0(_1334915))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1334913), _1334915)))], (29009 ^ _784416) ^ [_1335014, _1335016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335014), _1335016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1335014)), c_Int_OBit0(_1335016))))], (29015 ^ _784416) ^ [_1335136, _1335138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1335136)), c_Int_OBit0(_1335138))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335136), _1335138)))], (29021 ^ _784416) ^ [_1335237, _1335239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1335237), _1335239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1335237)), c_Int_OBit0(_1335239))))], (29027 ^ _784416) ^ [_1335359, _1335361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1335359)), c_Int_OBit0(_1335361))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1335359), _1335361)))], (29033 ^ _784416) ^ [_1335460, _1335462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1335460), _1335462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1335460)), c_Int_OBit0(_1335462))))], (29039 ^ _784416) ^ [_1335582, _1335584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1335582)), c_Int_OBit0(_1335584))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1335582), _1335584)))], (29045 ^ _784416) ^ [_1335683, _1335685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1335683), _1335685)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1335683)), c_Int_OBit0(_1335685))))], (29051 ^ _784416) ^ [_1335805, _1335807] : [c_Int_OBit0(_1335805) = c_Int_OBit0(_1335807), -(_1335805 = _1335807)], (29057 ^ _784416) ^ [_1335886, _1335888] : [_1335886 = _1335888, -(c_Int_OBit0(_1335886) = c_Int_OBit0(_1335888))], (29063 ^ _784416) ^ [_1335973, _1335975] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1335973)), c_Int_OBit0(_1335975)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1335973), _1335975)))], (29065 ^ _784416) ^ [_1336016] : [-(c_Int_OBit0(_1336016) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1336016), _1336016))], (29067 ^ _784416) ^ [_1336059] : [c_Int_OBit0(_1336059) = c_Int_OPls, -(_1336059 = c_Int_OPls)], (29073 ^ _784416) ^ [_1336134] : [_1336134 = c_Int_OPls, -(c_Int_OBit0(_1336134) = c_Int_OPls)], (29079 ^ _784416) ^ [_1336227] : [c_Int_OPls = c_Int_OBit0(_1336227), -(c_Int_OPls = _1336227)], (29085 ^ _784416) ^ [_1336302] : [c_Int_OPls = _1336302, -(c_Int_OPls = c_Int_OBit0(_1336302))], (29091 ^ _784416) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (29093 ^ _784416) ^ [_1336401, _1336403] : [class_Rings_Osemiring__1(_1336401), 29096 ^ _784416 : [(29097 ^ _784416) ^ [] : [c_Int_Oiszero(_1336401, _1336403), -(_1336403 = c_Groups_Ozero__class_Ozero(_1336401))], (29103 ^ _784416) ^ [] : [_1336403 = c_Groups_Ozero__class_Ozero(_1336401), -(c_Int_Oiszero(_1336401, _1336403))]]], (29109 ^ _784416) ^ [_1336612] : [class_Rings_Osemiring__1(_1336612), -(c_Int_Oiszero(_1336612, c_Groups_Ozero__class_Ozero(_1336612)))], (29115 ^ _784416) ^ [_1336689] : [class_Rings_Osemiring__1(_1336689), c_Int_Oiszero(_1336689, c_Groups_Oone__class_Oone(_1336689))], (29121 ^ _784416) ^ [_1336779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1336779)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1336779), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29127 ^ _784416) ^ [_1336874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1336874), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1336874)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29133 ^ _784416) ^ [_1336987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1336987)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1336987), c_Int_OPls)))], (29139 ^ _784416) ^ [_1337082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1337082), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1337082)), c_Int_OPls)))], (29145 ^ _784416) ^ [_1337195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1337195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1337195)))], (29151 ^ _784416) ^ [_1337278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1337278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1337278))))], (29157 ^ _784416) ^ [_1337382, _1337384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1337382)), c_Int_OBit1(_1337384))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1337382), _1337384)))], (29163 ^ _784416) ^ [_1337483, _1337485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1337483), _1337485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1337483)), c_Int_OBit1(_1337485))))], (29169 ^ _784416) ^ [_1337605, _1337607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1337605)), c_Int_OBit1(_1337607))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1337605), _1337607)))], (29175 ^ _784416) ^ [_1337706, _1337708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1337706), _1337708)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1337706)), c_Int_OBit1(_1337708))))], (29181 ^ _784416) ^ [_1337825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1337825))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1337825)))], (29187 ^ _784416) ^ [_1337908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1337908)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1337908))))], (29193 ^ _784416) ^ [_1338009] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1338009)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1338009), c_Int_OPls)))], (29199 ^ _784416) ^ [_1338104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1338104), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1338104)), c_Int_OPls)))], (29205 ^ _784416) ^ [_1338220, _1338222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1338220)), c_Int_OBit0(_1338222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1338220), _1338222)))], (29211 ^ _784416) ^ [_1338321, _1338323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1338321), _1338323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1338321)), c_Int_OBit0(_1338323))))], (29217 ^ _784416) ^ [_1338443, _1338445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1338443)), c_Int_OBit0(_1338445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1338443), _1338445)))], (29223 ^ _784416) ^ [_1338544, _1338546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1338544), _1338546)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1338544)), c_Int_OBit0(_1338546))))], (29229 ^ _784416) ^ [_1338651, _1338653] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1338651)), c_Int_OBit0(_1338653)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1338651), _1338653)))], (29231 ^ _784416) ^ [_1338694, _1338696] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1338694)), c_Int_OBit1(_1338696)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1338694), _1338696)))], (29233 ^ _784416) ^ [_1338737] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1338737)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1338737)))], (29235 ^ _784416) ^ [_1338770, _1338772] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1338770)), c_Int_OBit1(_1338772)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1338770), _1338772)))], (29237 ^ _784416) ^ [_1338813, _1338815] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1338813)), c_Int_OBit0(_1338815)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1338813), _1338815)))], (29239 ^ _784416) ^ [_1338856, _1338858] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1338856))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1338858))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1338856)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1338858)))], (29241 ^ _784416) ^ [_1338921] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1338921)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1338921))))], (29247 ^ _784416) ^ [_1339016] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1339016))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1339016)))))], (29253 ^ _784416) ^ [_1339117] : [-(c_Int_Opred(c_Int_OBit0(_1339117)) = c_Int_OBit1(c_Int_Opred(_1339117)))], (29255 ^ _784416) ^ [_1339148] : [-(c_Int_Opred(c_Int_OBit1(_1339148)) = c_Int_OBit0(_1339148))], (29257 ^ _784416) ^ [_1339177] : [-(c_Int_Osucc(c_Int_OBit1(_1339177)) = c_Int_OBit0(c_Int_Osucc(_1339177)))], (29259 ^ _784416) ^ [_1339208] : [-(c_Int_Osucc(c_Int_OBit0(_1339208)) = c_Int_OBit1(_1339208))], (29261 ^ _784416) ^ [_1339237] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1339237)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1339237)), 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))))], (29263 ^ _784416) ^ [_1339274, _1339276] : [class_Int_Onumber__ring(_1339274), -(hAPP(c_Int_Onumber__class_Onumber__of(_1339274), c_Int_OBit0(_1339276)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1339274), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1339274), c_Groups_Ozero__class_Ozero(_1339274)), hAPP(c_Int_Onumber__class_Onumber__of(_1339274), _1339276))), hAPP(c_Int_Onumber__class_Onumber__of(_1339274), _1339276)))], (29269 ^ _784416) ^ [_1339434, _1339436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1339434)), c_Int_OBit0(_1339436))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1339434), _1339436)))], (29275 ^ _784416) ^ [_1339535, _1339537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1339535), _1339537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1339535)), c_Int_OBit0(_1339537))))], (29281 ^ _784416) ^ [_1339657, _1339659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1339657)), c_Int_OBit0(_1339659))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1339657), _1339659)))], (29287 ^ _784416) ^ [_1339758, _1339760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1339758), _1339760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1339758)), c_Int_OBit0(_1339760))))], (29293 ^ _784416) ^ [_1339880, _1339882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1339880)), c_Int_OBit1(_1339882))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1339880), _1339882)))], (29299 ^ _784416) ^ [_1339981, _1339983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1339981), _1339983)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1339981)), c_Int_OBit1(_1339983))))], (29305 ^ _784416) ^ [_1340103, _1340105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1340103)), c_Int_OBit1(_1340105))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1340103), _1340105)))], (29311 ^ _784416) ^ [_1340204, _1340206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1340204), _1340206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1340204)), c_Int_OBit1(_1340206))))], (29317 ^ _784416) ^ [] : [-(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))))], (29319 ^ _784416) ^ [_1340329, _1340331] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1340329)), _1340331) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1340329), _1340331))), _1340331))], (29321 ^ _784416) ^ [_1340376, _1340378] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1340376)), c_Int_OBit1(_1340378)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1340376)), _1340378)))], (29323 ^ _784416) ^ [_1340421, _1340423] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1340421)), c_Int_OBit1(_1340423)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1340421), c_Int_Osucc(_1340423))))], (29325 ^ _784416) ^ [_1340466, _1340468, _1340470] : [class_Int_Onumber__ring(_1340466), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1340466), _1340468), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1340470))) = hAPP(hAPP(c_HOL_OLet(_1340466, _1340466), hAPP(hAPP(c_Power_Opower__class_Opower(_1340466), _1340468), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1340470))), hAPP(hAPP(c_COMBS(_1340466, _1340466, _1340466), c_Groups_Otimes__class_Otimes(_1340466)), c_COMBI(_1340466))))], (29331 ^ _784416) ^ [_1340637, _1340639] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1340637), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1340639))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1340637), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1340639))), 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))))], (29333 ^ _784416) ^ [_1340688] : [class_Int_Onumber__ring(_1340688), -(c_Int_Oiszero(_1340688, hAPP(c_Int_Onumber__class_Onumber__of(_1340688), c_Int_OPls)))], (29339 ^ _784416) ^ [_1340771, _1340773] : [c_Int_Oiszero(_1340771, hAPP(c_Int_Onumber__class_Onumber__of(_1340771), c_Int_OBit1(_1340773))), class_Int_Onumber__ring(_1340771), class_Int_Oring__char__0(_1340771)], (29349 ^ _784416) ^ [_1340911, _1340913] : [class_Int_Onumber__ring(_1340911), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1340911), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1340911), c_Groups_Oone__class_Oone(_1340911)), c_Groups_Oone__class_Oone(_1340911))), hAPP(c_Int_Onumber__class_Onumber__of(_1340911), _1340913)) = hAPP(c_Int_Onumber__class_Onumber__of(_1340911), c_Int_OBit0(_1340913)))], (29355 ^ _784416) ^ [_1341050] : [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), _1341050))), 29358 ^ _784416 : [(29359 ^ _784416) ^ [] : [-(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(_1341050)))))], (29361 ^ _784416) ^ [] : [-(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(_1341050)))))]]], (29363 ^ _784416) ^ [_1341189, _1341191, _1341193] : [class_Int_Onumber__ring(_1341189), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1341189), hAPP(c_Int_Onumber__class_Onumber__of(_1341189), _1341191)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1341193))) = hAPP(hAPP(c_HOL_OLet(_1341189, _1341189), hAPP(hAPP(c_Power_Opower__class_Opower(_1341189), hAPP(c_Int_Onumber__class_Onumber__of(_1341189), _1341191)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1341193))), hAPP(hAPP(c_COMBS(_1341189, _1341189, _1341189), c_Groups_Otimes__class_Otimes(_1341189)), c_COMBI(_1341189))))], (29369 ^ _784416) ^ [_1341380, _1341382] : [class_Int_Onumber__ring(_1341380), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341380), hAPP(c_Int_Onumber__class_Onumber__of(_1341380), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1341382) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1341380), _1341382), _1341382))], (29375 ^ _784416) ^ [_1341497, _1341499] : [class_Int_Onumber__ring(_1341497), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341497), _1341499), hAPP(c_Int_Onumber__class_Onumber__of(_1341497), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1341497), _1341499), _1341499))], (29381 ^ _784416) ^ [_1341614] : [class_Int_Onumber__ring(_1341614), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1341614), c_Groups_Oone__class_Oone(_1341614)), c_Groups_Oone__class_Oone(_1341614)) = hAPP(c_Int_Onumber__class_Onumber__of(_1341614), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (29387 ^ _784416) ^ [_1341721, _1341723] : [class_Rings_Oring__1__no__zero__divisors(_1341721), 29390 ^ _784416 : [(29391 ^ _784416) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1341721), _1341723), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1341721), -(_1341723 = c_Groups_Ozero__class_Ozero(_1341721))], (29397 ^ _784416) ^ [] : [_1341723 = c_Groups_Ozero__class_Ozero(_1341721), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1341721), _1341723), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1341721))]]], (29403 ^ _784416) ^ [_1341962] : [class_Rings_Osemiring__1(_1341962), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1341962), c_Groups_Ozero__class_Ozero(_1341962)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1341962))], (29409 ^ _784416) ^ [] : [-(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))))], (29411 ^ _784416) ^ [] : [-(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))))], (29413 ^ _784416) ^ [_1342095, _1342097] : [class_Rings_Ocomm__semiring__1(_1342095), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342095), _1342097), _1342097) = hAPP(hAPP(c_Power_Opower__class_Opower(_1342095), _1342097), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (29419 ^ _784416) ^ [_1342202, _1342204] : [class_Groups_Omonoid__mult(_1342202), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1342202), _1342204), 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(_1342202), _1342204), _1342204))], (29425 ^ _784416) ^ [] : [-(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))))))], (29427 ^ _784416) ^ [_1342327] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1342327), 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, _1342327)))], (29429 ^ _784416) ^ [_1342362] : [-(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)))), _1342362) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1342362)))], (29431 ^ _784416) ^ [_1342394] : [class_Rings_Osemiring__1(_1342394), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1342394), c_Groups_Oone__class_Oone(_1342394)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1342394))], (29437 ^ _784416) ^ [_1342491, _1342493] : [class_Rings_Oring__1(_1342491), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1342491), hAPP(c_Groups_Ouminus__class_Ouminus(_1342491), _1342493)), 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(_1342491), _1342493), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (29443 ^ _784416) ^ [_1342608] : [-(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)))), _1342608) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1342608), _1342608))], (29445 ^ _784416) ^ [_1342640] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1342640), 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), _1342640), _1342640))], (29447 ^ _784416) ^ [_1342675, _1342677, _1342679] : [class_Groups_Omonoid__mult(_1342675), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1342675), _1342677), 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)))), _1342679)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1342675), hAPP(hAPP(c_Power_Opower__class_Opower(_1342675), _1342677), _1342679)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (29453 ^ _784416) ^ [] : [-(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)))))], (29455 ^ _784416) ^ [] : [-(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))))], (29457 ^ _784416) ^ [_1342842] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1342842)), 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, _1342842, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (29459 ^ _784416) ^ [_1342879] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1342879))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1342879), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (29461 ^ _784416) ^ [_1342923, _1342925] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1342923)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1342925))) = 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), _1342923), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1342925))))], (29463 ^ _784416) ^ [_1342975] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1342975), _1342975)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1342975)], (29465 ^ _784416) ^ [_1343010] : [class_Int_Onumber__ring(_1343010), c_Int_Oiszero(_1343010, hAPP(c_Int_Onumber__class_Onumber__of(_1343010), c_Int_OBit1(c_Int_OPls)))], (29471 ^ _784416) ^ [_1343094, _1343096, _1343098] : [class_Int_Onumber__ring(_1343094), 29474 ^ _784416 : [(29475 ^ _784416) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1343094), _1343096) = hAPP(c_Int_Onumber__class_Onumber__of(_1343094), _1343098), -(c_Int_Oiszero(_1343094, hAPP(c_Int_Onumber__class_Onumber__of(_1343094), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1343096), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1343098)))))], (29481 ^ _784416) ^ [] : [c_Int_Oiszero(_1343094, hAPP(c_Int_Onumber__class_Onumber__of(_1343094), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1343096), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1343098)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1343094), _1343096) = hAPP(c_Int_Onumber__class_Onumber__of(_1343094), _1343098))]]], (29487 ^ _784416) ^ [_1343377, _1343379] : [class_Fields_Olinordered__field__inverse__zero(_1343377), class_Int_Onumber__ring(_1343377), 29494 ^ _784416 : [(29495 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343377), c_Groups_Ozero__class_Ozero(_1343377)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1343377), _1343379), hAPP(c_Int_Onumber__class_Onumber__of(_1343377), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343377), c_Groups_Ozero__class_Ozero(_1343377)), _1343379)))], (29501 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343377), c_Groups_Ozero__class_Ozero(_1343377)), _1343379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343377), c_Groups_Ozero__class_Ozero(_1343377)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1343377), _1343379), hAPP(c_Int_Onumber__class_Onumber__of(_1343377), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (29507 ^ _784416) ^ [_1343727, _1343729] : [class_Fields_Olinordered__field__inverse__zero(_1343727), class_Int_Onumber__ring(_1343727), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343727), c_Groups_Ozero__class_Ozero(_1343727)), _1343729)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343727), c_Groups_Ozero__class_Ozero(_1343727)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1343727), _1343729), hAPP(c_Int_Onumber__class_Onumber__of(_1343727), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (29521 ^ _784416) ^ [_1343968, _1343970] : [class_Rings_Olinordered__idom(_1343968), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343968), c_Groups_Ozero__class_Ozero(_1343968)), hAPP(hAPP(c_Power_Opower__class_Opower(_1343968), _1343970), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (29527 ^ _784416) ^ [_1344077, _1344079, _1344081] : [class_Rings_Olinordered__semidom(_1344077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344077), hAPP(hAPP(c_Power_Opower__class_Opower(_1344077), _1344079), 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(_1344077), _1344081), 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(_1344077), c_Groups_Ozero__class_Ozero(_1344077)), _1344081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344077), _1344079), _1344081)))], (29541 ^ _784416) ^ [_1344340, _1344342, _1344344] : [class_Rings_Olinordered__semidom(_1344340), hAPP(hAPP(c_Power_Opower__class_Opower(_1344340), _1344342), 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(_1344340), _1344344), 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(_1344340), c_Groups_Ozero__class_Ozero(_1344340)), _1344342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344340), c_Groups_Ozero__class_Ozero(_1344340)), _1344344)), -(_1344342 = _1344344)], (29559 ^ _784416) ^ [_1344647, _1344649] : [class_Rings_Olinordered__idom(_1344647), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344647), hAPP(hAPP(c_Power_Opower__class_Opower(_1344647), _1344649), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1344647)))], (29565 ^ _784416) ^ [_1344757, _1344759] : [class_Rings_Olinordered__idom(_1344757), 29568 ^ _784416 : [(29569 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344757), c_Groups_Ozero__class_Ozero(_1344757)), hAPP(hAPP(c_Power_Opower__class_Opower(_1344757), _1344759), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1344759 = c_Groups_Ozero__class_Ozero(_1344757)], (29575 ^ _784416) ^ [] : [-(_1344759 = c_Groups_Ozero__class_Ozero(_1344757)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344757), c_Groups_Ozero__class_Ozero(_1344757)), hAPP(hAPP(c_Power_Opower__class_Opower(_1344757), _1344759), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (29581 ^ _784416) ^ [_1344981, _1344983, _1344985] : [class_Rings_Olinordered__idom(_1344981), 29584 ^ _784416 : [(29585 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344981), hAPP(hAPP(c_Power_Opower__class_Opower(_1344981), _1344983), 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(_1344981), _1344985), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1344981), 29588 ^ _784416 : [(29589 ^ _784416) ^ [] : [-(_1344983 = c_Groups_Ozero__class_Ozero(_1344981))], (29591 ^ _784416) ^ [] : [-(_1344985 = c_Groups_Ozero__class_Ozero(_1344981))]]], (29593 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344981), hAPP(hAPP(c_Power_Opower__class_Opower(_1344981), _1344983), 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(_1344981), _1344985), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1344981)), _1344983 = c_Groups_Ozero__class_Ozero(_1344981), _1344985 = c_Groups_Ozero__class_Ozero(_1344981)]]], (29603 ^ _784416) ^ [_1345356, _1345358] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1345356), hAPP(c_Int_Onumber__class_Onumber__of(_1345356), _1345358)), 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(_1345356), hAPP(c_Int_Onumber__class_Onumber__of(_1345356), _1345358)), hAPP(c_Int_Onumber__class_Onumber__of(_1345356), _1345358))), class_Groups_Omonoid__mult(_1345356), class_Int_Onumber(_1345356)], (29613 ^ _784416) ^ [_1345543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1345543), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1345543 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1345543 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29623 ^ _784416) ^ [] : [-(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))))], (29625 ^ _784416) ^ [_1345659, _1345661] : [class_Rings_Oring__1__no__zero__divisors(_1345659), 29628 ^ _784416 : [(29639 ^ _784416) ^ [] : [29640 ^ _784416 : [(29641 ^ _784416) ^ [] : [_1345661 = c_Groups_Oone__class_Oone(_1345659)], (29643 ^ _784416) ^ [] : [_1345661 = hAPP(c_Groups_Ouminus__class_Ouminus(_1345659), c_Groups_Oone__class_Oone(_1345659))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1345659), _1345661), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1345659))], (29629 ^ _784416) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1345659), _1345661), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1345659), -(_1345661 = c_Groups_Oone__class_Oone(_1345659)), -(_1345661 = hAPP(c_Groups_Ouminus__class_Ouminus(_1345659), c_Groups_Oone__class_Oone(_1345659)))]]], (29647 ^ _784416) ^ [_1345966, _1345968, _1345970] : [class_Rings_Ocomm__semiring__1(_1345966), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1345966), _1345968), 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)))), _1345970)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345966), hAPP(hAPP(c_Power_Opower__class_Opower(_1345966), _1345968), _1345970)), hAPP(hAPP(c_Power_Opower__class_Opower(_1345966), _1345968), _1345970)))], (29653 ^ _784416) ^ [_1346113, _1346115, _1346117] : [class_Rings_Oring__1(_1346113), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1346113), hAPP(c_Groups_Ouminus__class_Ouminus(_1346113), _1346115)), 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)))), _1346117)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1346113), _1346115), 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)))), _1346117)))], (29659 ^ _784416) ^ [_1346244, _1346246, _1346248] : [class_Rings_Olinordered__semidom(_1346244), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346244), hAPP(hAPP(c_Power_Opower__class_Opower(_1346244), _1346246), 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(_1346244), _1346248), 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(_1346244), c_Groups_Ozero__class_Ozero(_1346244)), _1346248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346244), _1346246), _1346248)))], (29673 ^ _784416) ^ [_1346507, _1346509, _1346511] : [class_Rings_Olinordered__idom(_1346507), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346507), c_Groups_Ozero__class_Ozero(_1346507)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346507), hAPP(hAPP(c_Power_Opower__class_Opower(_1346507), _1346509), 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(_1346507), _1346511), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (29679 ^ _784416) ^ [_1346650, _1346652, _1346654] : [class_Rings_Olinordered__idom(_1346650), 29682 ^ _784416 : [(29683 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346650), hAPP(hAPP(c_Power_Opower__class_Opower(_1346650), _1346652), 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(_1346650), _1346654), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1346650))), 29686 ^ _784416 : [(29687 ^ _784416) ^ [] : [-(_1346652 = c_Groups_Ozero__class_Ozero(_1346650))], (29689 ^ _784416) ^ [] : [-(_1346654 = c_Groups_Ozero__class_Ozero(_1346650))]]], (29691 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346650), hAPP(hAPP(c_Power_Opower__class_Opower(_1346650), _1346652), 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(_1346650), _1346654), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1346650)))), _1346652 = c_Groups_Ozero__class_Ozero(_1346650), _1346654 = c_Groups_Ozero__class_Ozero(_1346650)]]], (29701 ^ _784416) ^ [_1347046, _1347048, _1347050] : [class_Rings_Olinordered__idom(_1347046), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347046), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347046), hAPP(hAPP(c_Power_Opower__class_Opower(_1347046), _1347048), 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(_1347046), _1347050), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1347046)))], (29707 ^ _784416) ^ [_1347190, _1347192, _1347194] : [class_Rings_Olinordered__idom(_1347190), 29710 ^ _784416 : [(29721 ^ _784416) ^ [] : [29722 ^ _784416 : [(29723 ^ _784416) ^ [] : [-(_1347192 = c_Groups_Ozero__class_Ozero(_1347190))], (29725 ^ _784416) ^ [] : [-(_1347194 = c_Groups_Ozero__class_Ozero(_1347190))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347190), c_Groups_Ozero__class_Ozero(_1347190)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347190), hAPP(hAPP(c_Power_Opower__class_Opower(_1347190), _1347192), 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(_1347190), _1347194), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (29711 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347190), c_Groups_Ozero__class_Ozero(_1347190)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347190), hAPP(hAPP(c_Power_Opower__class_Opower(_1347190), _1347192), 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(_1347190), _1347194), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1347192 = c_Groups_Ozero__class_Ozero(_1347190), _1347194 = c_Groups_Ozero__class_Ozero(_1347190)]]], (29729 ^ _784416) ^ [_1347565, _1347567, _1347569] : [class_Int_Onumber__ring(_1347565), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1347565), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347565), _1347567), _1347569)), 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(_1347565), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347565), hAPP(hAPP(c_Power_Opower__class_Opower(_1347565), _1347567), 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(_1347565), _1347569), 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(_1347565), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347565), hAPP(c_Int_Onumber__class_Onumber__of(_1347565), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1347567)), _1347569)))], (29735 ^ _784416) ^ [_1347780, _1347782, _1347784] : [class_Rings_Olinordered__idom(_1347780), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347780), c_Groups_Ozero__class_Ozero(_1347780)), hAPP(hAPP(c_Power_Opower__class_Opower(_1347780), _1347782), 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)))), _1347784)))))], (29741 ^ _784416) ^ [_1347897, _1347899, _1347901] : [class_Rings_Ocomm__semiring__1(_1347897), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1347897), _1347899), 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)))), _1347901))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347897), _1347899), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347897), hAPP(hAPP(c_Power_Opower__class_Opower(_1347897), _1347899), _1347901)), hAPP(hAPP(c_Power_Opower__class_Opower(_1347897), _1347899), _1347901))))], (29747 ^ _784416) ^ [_1348066, _1348068, _1348070] : [class_Groups_Omonoid__mult(_1348066), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1348066), _1348068), 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)))), _1348070))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348066), _1348068), hAPP(hAPP(c_Power_Opower__class_Opower(_1348066), hAPP(hAPP(c_Power_Opower__class_Opower(_1348066), _1348068), _1348070)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (29753 ^ _784416) ^ [_1348219, _1348221] : [class_Rings_Oring__1(_1348219), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1348219), hAPP(c_Groups_Ouminus__class_Ouminus(_1348219), c_Groups_Oone__class_Oone(_1348219))), 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)))), _1348221)) = c_Groups_Oone__class_Oone(_1348219))], (29759 ^ _784416) ^ [_1348343, _1348345] : [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), _1348343))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1348345))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1348343))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1348345)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1348343)))], (29765 ^ _784416) ^ [_1348480, _1348482] : [-(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), _1348480)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1348482))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1348480))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1348482)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1348480)))], (29771 ^ _784416) ^ [_1348569] : [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, _1348569, 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, _1348569, 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))], (29777 ^ _784416) ^ [_1348660] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1348660, 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, _1348660, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (29783 ^ _784416) ^ [_1348757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1348757)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1348757), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (29789 ^ _784416) ^ [_1348852, _1348854, _1348856] : [class_Int_Onumber__ring(_1348852), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1348852), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1348852), _1348854), _1348856)), 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(_1348852), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1348852), hAPP(hAPP(c_Power_Opower__class_Opower(_1348852), _1348854), 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(_1348852), _1348856), 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(_1348852), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348852), hAPP(c_Int_Onumber__class_Onumber__of(_1348852), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1348854)), _1348856)))], (29795 ^ _784416) ^ [_1349067, _1349069, _1349071] : [class_Rings_Olinordered__idom(_1349067), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349067), c_Groups_Ozero__class_Ozero(_1349067)), hAPP(hAPP(c_Power_Opower__class_Opower(_1349067), _1349069), 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)))), _1349071))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349067), c_Groups_Ozero__class_Ozero(_1349067)), _1349069)))], (29805 ^ _784416) ^ [_1349262, _1349264, _1349266] : [class_Rings_Olinordered__idom(_1349262), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1349262), _1349264), c_Groups_Ozero__class_Ozero(_1349262))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1349262), hAPP(hAPP(c_Power_Opower__class_Opower(_1349262), _1349264), 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)))), _1349266)))), c_Groups_Ozero__class_Ozero(_1349262))))], (29815 ^ _784416) ^ [_1349457, _1349459] : [class_Rings_Oring__1(_1349457), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1349457), hAPP(c_Groups_Ouminus__class_Ouminus(_1349457), c_Groups_Oone__class_Oone(_1349457))), 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)))), _1349459))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1349457), c_Groups_Oone__class_Oone(_1349457)))], (29821 ^ _784416) ^ [_1349588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1349588)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1349588), 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)))))))], (29827 ^ _784416) ^ [_1349695, _1349697] : [class_Int_Onumber__ring(_1349695), 29830 ^ _784416 : [(29831 ^ _784416) ^ [] : [c_Groups_Ozero__class_Ozero(_1349695) = hAPP(c_Int_Onumber__class_Onumber__of(_1349695), _1349697), -(c_Int_Oiszero(_1349695, hAPP(c_Int_Onumber__class_Onumber__of(_1349695), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1349697)))))], (29837 ^ _784416) ^ [] : [c_Int_Oiszero(_1349695, hAPP(c_Int_Onumber__class_Onumber__of(_1349695), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1349697)))), -(c_Groups_Ozero__class_Ozero(_1349695) = hAPP(c_Int_Onumber__class_Onumber__of(_1349695), _1349697))]]], (29843 ^ _784416) ^ [_1349954, _1349956] : [class_Int_Onumber__ring(_1349954), 29846 ^ _784416 : [(29847 ^ _784416) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1349954), _1349956) = c_Groups_Ozero__class_Ozero(_1349954), -(c_Int_Oiszero(_1349954, hAPP(c_Int_Onumber__class_Onumber__of(_1349954), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1349956), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))], (29853 ^ _784416) ^ [] : [c_Int_Oiszero(_1349954, hAPP(c_Int_Onumber__class_Onumber__of(_1349954), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1349956), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1349954), _1349956) = c_Groups_Ozero__class_Ozero(_1349954))]]], (29859 ^ _784416) ^ [_1350213, _1350215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1350213)), -(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)))), _1350215)), 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)))), _1350213)) = 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, _1350215, _1350213))))], (29865 ^ _784416) ^ [_1350340, _1350342] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1350340), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1350342))), 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)))), _1350340)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1350342), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1350340))], (29871 ^ _784416) ^ [_1350481, _1350483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1350481)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1350483))), 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)))), _1350481)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1350483), _1350481))], (29877 ^ _784416) ^ [_1350604] : [-(c_Divides_Oadjust(_1350604) = 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)), _1350604))))), 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)), _1350604))))), 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))))))))], (29879 ^ _784416) ^ [_1350665, _1350667, _1350669] : [-(hAPP(c_Divides_Oadjust(_1350665), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1350667), _1350669)) = 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), _1350669), _1350665)), 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)))), _1350667)), 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)))), _1350667)), _1350669))))], (29881 ^ _784416) ^ [_1350745] : [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), _1350745))), 29884 ^ _784416 : [(29885 ^ _784416) ^ [] : [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), _1350745))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1350745)) = 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)))], (29891 ^ _784416) ^ [] : [-(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), _1350745)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1350745)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1350745)), 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), _1350745)))))]]], (29897 ^ _784416) ^ [_1351014, _1351016] : [29898 ^ _784416 : [(29899 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1351014), _1351016))], (29901 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1351016), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1351014, _1351016) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1351014))], (29905 ^ _784416) ^ [_1351155, _1351157] : [-(c_Divides_OposDivAlg(_1351155, _1351157) = hAPP(c_Divides_Oadjust(_1351157), c_Divides_OposDivAlg(_1351155, 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)))), _1351157)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1351155), _1351157))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1351157), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29915 ^ _784416) ^ [_1351224, _1351226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1351224)), 29918 ^ _784416 : [(29919 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1351226), _1351224)), -(c_Divides_OposDivAlg(_1351226, _1351224) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1351226))], (29925 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1351226), _1351224))), -(c_Divides_OposDivAlg(_1351226, _1351224) = hAPP(c_Divides_Oadjust(_1351224), c_Divides_OposDivAlg(_1351226, 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)))), _1351224))))]]], (29931 ^ _784416) ^ [_1351464, _1351466] : [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), _1351464))), 29934 ^ _784416 : [(29935 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1351466)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1351464))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1351466), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1351464)) = 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), _1351466)))], (29941 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1351466)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1351464)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1351466), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1351464)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1351464)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1351466), 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), _1351464)))))]]], (29947 ^ _784416) ^ [_1351782, _1351784] : [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), _1351782), _1351784))), 29950 ^ _784416 : [(29951 ^ _784416) ^ [] : [29952 ^ _784416 : [(29953 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1351782), _1351784))], (29955 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1351784), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1351782, _1351784) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1351782))], (29959 ^ _784416) ^ [] : [-(c_Divides_OposDivAlg(_1351782, _1351784) = hAPP(c_Divides_Oadjust(_1351784), c_Divides_OposDivAlg(_1351782, 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)))), _1351784)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1351782), _1351784))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1351784), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (29969 ^ _784416) ^ [_1352105, _1352107] : [class_Rings_Oring__1(_1352105), 29972 ^ _784416 : [(29973 ^ _784416) ^ [] : [_1352107 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1352105), _1352107) = c_Groups_Ozero__class_Ozero(_1352105))], (29979 ^ _784416) ^ [] : [-(_1352107 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29982 ^ _784416 : [(29983 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1352107), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1352105), _1352107) = hAPP(c_Groups_Ouminus__class_Ouminus(_1352105), hAPP(c_Int_Oring__1__class_Oof__int(_1352105), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1352107))))], (29989 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1352107), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1352105), _1352107) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1352105), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1352105, _1352105)), tc_fun(tc_Int_Oint, _1352105)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1352105, _1352105), _1352105), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1352105, _1352105)), tc_fun(tc_Int_Oint, _1352105)), tc_Int_Oint), c_COMBB(tc_fun(_1352105, _1352105), _1352105, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1352105, tc_fun(tc_fun(_1352105, _1352105), _1352105), tc_Int_Oint), c_HOL_OLet(_1352105, _1352105)), c_Int_Oring__1__class_Oof__int(_1352105)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1352105, _1352105), tc_fun(_1352105, _1352105)), hAPP(hAPP(c_COMBB(tc_fun(_1352105, tc_fun(_1352105, _1352105)), tc_fun(tc_fun(_1352105, _1352105), tc_fun(_1352105, _1352105)), tc_Int_Oint), c_COMBS(_1352105, _1352105, _1352105)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1352105, _1352105), tc_fun(_1352105, tc_fun(_1352105, _1352105))), hAPP(hAPP(c_COMBB(tc_fun(_1352105, tc_fun(_1352105, _1352105)), tc_fun(tc_fun(_1352105, _1352105), tc_fun(_1352105, tc_fun(_1352105, _1352105))), tc_Int_Oint), c_COMBB(_1352105, tc_fun(_1352105, _1352105), _1352105)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1352105, tc_fun(_1352105, _1352105)), tc_Int_Oint), c_If(_1352105)), 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(_1352105, _1352105, _1352105), c_Groups_Oplus__class_Oplus(_1352105)), c_COMBI(_1352105))))), hAPP(hAPP(c_COMBC(_1352105, _1352105, _1352105), hAPP(hAPP(c_COMBB(_1352105, tc_fun(_1352105, _1352105), _1352105), c_Groups_Oplus__class_Oplus(_1352105)), hAPP(hAPP(c_COMBS(_1352105, _1352105, _1352105), c_Groups_Oplus__class_Oplus(_1352105)), c_COMBI(_1352105)))), c_Groups_Oone__class_Oone(_1352105))))), c_Divides_Odivmod__int(_1352107, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))]]]]], (29995 ^ _784416) ^ [_1353018] : [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), _1353018))), 29998 ^ _784416 : [(29999 ^ _784416) ^ [] : [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), _1353018)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1353018)) = 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), _1353018))))], (30005 ^ _784416) ^ [] : [-(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), _1353018))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1353018)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1353018)), 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), _1353018)))))]]], (30011 ^ _784416) ^ [_1353308, _1353310] : [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), _1353308))), 30014 ^ _784416 : [(30015 ^ _784416) ^ [] : [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), _1353310)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1353308)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1353310), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1353308)) = 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), _1353310)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1353308))))], (30021 ^ _784416) ^ [] : [-(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), _1353310)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1353308))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1353310), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1353308)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1353308)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1353310), 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), _1353308)))))]]], (30027 ^ _784416) ^ [_1353656] : [class_Int_Onumber__ring(_1353656), -(hAPP(c_Int_Oring__1__class_Oof__int(_1353656), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1353656), c_Int_OMin))], (30033 ^ _784416) ^ [_1353761] : [c_Int_OBit1(_1353761) = c_Int_OMin, -(_1353761 = c_Int_OMin)], (30039 ^ _784416) ^ [_1353836] : [_1353836 = c_Int_OMin, -(c_Int_OBit1(_1353836) = c_Int_OMin)], (30045 ^ _784416) ^ [_1353929] : [c_Int_OMin = c_Int_OBit1(_1353929), -(c_Int_OMin = _1353929)], (30051 ^ _784416) ^ [_1354004] : [c_Int_OMin = _1354004, -(c_Int_OMin = c_Int_OBit1(_1354004))], (30057 ^ _784416) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (30059 ^ _784416) ^ [_1354103, _1354105, _1354107] : [class_Int_Oring__char__0(_1354103), 30062 ^ _784416 : [(30063 ^ _784416) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1354103), _1354105) = hAPP(c_Int_Oring__1__class_Oof__int(_1354103), _1354107), -(_1354105 = _1354107)], (30069 ^ _784416) ^ [] : [_1354105 = _1354107, -(hAPP(c_Int_Oring__1__class_Oof__int(_1354103), _1354105) = hAPP(c_Int_Oring__1__class_Oof__int(_1354103), _1354107))]]], (30075 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (30077 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (30079 ^ _784416) ^ [_1354386] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1354386) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1354386))], (30081 ^ _784416) ^ [_1354415, _1354417] : [class_Int_Onumber__ring(_1354415), -(hAPP(c_Int_Onumber__class_Onumber__of(_1354415), _1354417) = hAPP(c_Int_Oring__1__class_Oof__int(_1354415), _1354417))], (30087 ^ _784416) ^ [] : [c_Int_OPls = c_Int_OMin], (30089 ^ _784416) ^ [] : [c_Int_OMin = c_Int_OPls], (30091 ^ _784416) ^ [_1354567] : [c_Int_OBit0(_1354567) = c_Int_OMin], (30093 ^ _784416) ^ [_1354601] : [c_Int_OMin = c_Int_OBit0(_1354601)], (30095 ^ _784416) ^ [_1354626, _1354628, _1354630, _1354632] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1354626), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1354628, tc_Int_Oint), _1354630), _1354632)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1354628, _1354626), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1354626, _1354628), c_Int_Oring__1__class_Oof__int(_1354626)), _1354630)), _1354632)), class_Groups_Ocomm__monoid__mult(_1354626), class_Rings_Oring__1(_1354626)], (30105 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30107 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (30109 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (30111 ^ _784416) ^ [_1354901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1354901)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1354901), c_Int_OMin)))], (30117 ^ _784416) ^ [_1354996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1354996), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1354996)), c_Int_OMin)))], (30123 ^ _784416) ^ [_1355109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1355109))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1355109)))], (30129 ^ _784416) ^ [_1355192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1355192)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1355192))))], (30135 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (30137 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (30139 ^ _784416) ^ [_1355335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1355335))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1355335)))], (30145 ^ _784416) ^ [_1355418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1355418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1355418))))], (30151 ^ _784416) ^ [_1355519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1355519)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1355519), c_Int_OMin)))], (30157 ^ _784416) ^ [_1355614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1355614), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1355614)), c_Int_OMin)))], (30163 ^ _784416) ^ [_1355727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1355727)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1355727), c_Int_OMin)))], (30169 ^ _784416) ^ [_1355822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1355822), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1355822)), c_Int_OMin)))], (30175 ^ _784416) ^ [_1355935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1355935))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1355935)))], (30181 ^ _784416) ^ [_1356018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1356018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1356018))))], (30187 ^ _784416) ^ [] : [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)], (30189 ^ _784416) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30191 ^ _784416) ^ [_1356149] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1356149) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1356149))], (30193 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (30195 ^ _784416) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (30197 ^ _784416) ^ [_1356214] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1356214), c_Int_OMin) = c_Int_Opred(_1356214))], (30199 ^ _784416) ^ [_1356245] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1356245) = c_Int_Opred(_1356245))], (30201 ^ _784416) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (30203 ^ _784416) ^ [_1356291] : [class_Rings_Oring__1(_1356291), -(hAPP(c_Int_Oring__1__class_Oof__int(_1356291), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1356291))], (30209 ^ _784416) ^ [_1356378, _1356380] : [class_Int_Oring__char__0(_1356378), 30212 ^ _784416 : [(30213 ^ _784416) ^ [] : [c_Groups_Ozero__class_Ozero(_1356378) = hAPP(c_Int_Oring__1__class_Oof__int(_1356378), _1356380), -(_1356380 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30219 ^ _784416) ^ [] : [_1356380 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1356378) = hAPP(c_Int_Oring__1__class_Oof__int(_1356378), _1356380))]]], (30225 ^ _784416) ^ [_1356604, _1356606] : [class_Int_Oring__char__0(_1356604), 30228 ^ _784416 : [(30229 ^ _784416) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1356604), _1356606) = c_Groups_Ozero__class_Ozero(_1356604), -(_1356606 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30235 ^ _784416) ^ [] : [_1356606 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1356604), _1356606) = c_Groups_Ozero__class_Ozero(_1356604))]]], (30241 ^ _784416) ^ [_1356830, _1356832, _1356834] : [class_Rings_Olinordered__idom(_1356830), 30244 ^ _784416 : [(30245 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356830), hAPP(c_Int_Oring__1__class_Oof__int(_1356830), _1356832)), hAPP(c_Int_Oring__1__class_Oof__int(_1356830), _1356834))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1356832), _1356834)))], (30251 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1356832), _1356834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356830), hAPP(c_Int_Oring__1__class_Oof__int(_1356830), _1356832)), hAPP(c_Int_Oring__1__class_Oof__int(_1356830), _1356834))))]]], (30257 ^ _784416) ^ [_1357107, _1357109, _1357111] : [class_Rings_Olinordered__idom(_1357107), 30260 ^ _784416 : [(30261 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357107), hAPP(c_Int_Oring__1__class_Oof__int(_1357107), _1357109)), hAPP(c_Int_Oring__1__class_Oof__int(_1357107), _1357111))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1357109), _1357111)))], (30267 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1357109), _1357111)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357107), hAPP(c_Int_Oring__1__class_Oof__int(_1357107), _1357109)), hAPP(c_Int_Oring__1__class_Oof__int(_1357107), _1357111))))]]], (30273 ^ _784416) ^ [_1357384] : [class_Int_Onumber__ring(_1357384), c_Int_Oiszero(_1357384, hAPP(c_Int_Onumber__class_Onumber__of(_1357384), c_Int_OMin))], (30279 ^ _784416) ^ [_1357468, _1357470, _1357472] : [class_Rings_Oring__1(_1357468), -(hAPP(c_Int_Oring__1__class_Oof__int(_1357468), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1357470), _1357472)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1357468), hAPP(c_Int_Oring__1__class_Oof__int(_1357468), _1357470)), hAPP(c_Int_Oring__1__class_Oof__int(_1357468), _1357472)))], (30285 ^ _784416) ^ [_1357603, _1357605] : [class_Int_Onumber__ring(_1357603), -(hAPP(c_Int_Oring__1__class_Oof__int(_1357603), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1357605)) = hAPP(c_Int_Onumber__class_Onumber__of(_1357603), _1357605))], (30291 ^ _784416) ^ [_1357704, _1357706, _1357708] : [class_Rings_Oring__1(_1357704), -(hAPP(c_Int_Oring__1__class_Oof__int(_1357704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1357706), _1357708)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357704), hAPP(c_Int_Oring__1__class_Oof__int(_1357704), _1357706)), hAPP(c_Int_Oring__1__class_Oof__int(_1357704), _1357708)))], (30297 ^ _784416) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (30299 ^ _784416) ^ [_1357857] : [class_Rings_Oring__1(_1357857), -(hAPP(c_Int_Oring__1__class_Oof__int(_1357857), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1357857))], (30305 ^ _784416) ^ [_1357944, _1357946, _1357948] : [class_Rings_Oring__1(_1357944), -(hAPP(c_Int_Oring__1__class_Oof__int(_1357944), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1357946), _1357948)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1357944), hAPP(c_Int_Oring__1__class_Oof__int(_1357944), _1357946)), hAPP(c_Int_Oring__1__class_Oof__int(_1357944), _1357948)))], (30311 ^ _784416) ^ [_1358079] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1358079), c_Int_OMin) = c_Int_Osucc(_1358079))], (30313 ^ _784416) ^ [_1358110, _1358112] : [class_Rings_Oring__1(_1358110), -(hAPP(c_Int_Oring__1__class_Oof__int(_1358110), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1358112)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1358110), hAPP(c_Int_Oring__1__class_Oof__int(_1358110), _1358112)))], (30319 ^ _784416) ^ [_1358221, _1358223] : [class_Rings_Oring__1(_1358221), -(hBOOL(hAPP(hAPP(c_member(_1358221), hAPP(c_Int_Oring__1__class_Oof__int(_1358221), _1358223)), c_Int_Oring__1__class_OInts(_1358221))))], (30325 ^ _784416) ^ [_1358324, _1358326, _1358328] : [class_Rings_Oring__1(_1358324), -(hAPP(c_Int_Oring__1__class_Oof__int(_1358324), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1358326), _1358328)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1358324), hAPP(c_Int_Oring__1__class_Oof__int(_1358324), _1358326)), _1358328))], (30331 ^ _784416) ^ [_1358449, _1358451] : [class_Int_Onumber__ring(_1358449), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358449), hAPP(c_Int_Onumber__class_Onumber__of(_1358449), c_Int_OMin)), _1358451) = hAPP(c_Groups_Ouminus__class_Ouminus(_1358449), _1358451))], (30337 ^ _784416) ^ [_1358560, _1358562] : [class_Int_Onumber__ring(_1358560), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358560), _1358562), hAPP(c_Int_Onumber__class_Onumber__of(_1358560), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1358560), _1358562))], (30343 ^ _784416) ^ [_1358671] : [class_Int_Onumber__ring(_1358671), -(hAPP(c_Int_Onumber__class_Onumber__of(_1358671), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1358671), c_Groups_Oone__class_Oone(_1358671)))], (30349 ^ _784416) ^ [_1358768] : [class_Int_Onumber__ring(_1358768), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1358768), c_Groups_Oone__class_Oone(_1358768)) = hAPP(c_Int_Onumber__class_Onumber__of(_1358768), c_Int_OMin))], (30355 ^ _784416) ^ [_1358865, _1358867] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358865), _1358867), hAPP(c_Int_Onumber__class_Onumber__of(_1358865), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1358865), _1358867)), class_Fields_Ofield__inverse__zero(_1358865), class_Int_Onumber__ring(_1358865)], (30365 ^ _784416) ^ [_1359038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1359038)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1359038), c_Int_OMin)))], (30371 ^ _784416) ^ [_1359133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1359133), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1359133)), c_Int_OMin)))], (30377 ^ _784416) ^ [_1359246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1359246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1359246)))], (30383 ^ _784416) ^ [_1359329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1359329)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1359329))))], (30389 ^ _784416) ^ [_1359418] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1359418, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30391 ^ _784416) ^ [_1359445] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1359445)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1359445)))], (30393 ^ _784416) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (30395 ^ _784416) ^ [_1359511, _1359513] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1359511), _1359513) = c_Groups_Oone__class_Oone(tc_Int_Oint), 30400 ^ _784416 : [(30401 ^ _784416) ^ [] : [-(_1359511 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (30403 ^ _784416) ^ [] : [-(_1359513 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 30404 ^ _784416 : [(30405 ^ _784416) ^ [] : [-(_1359511 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (30407 ^ _784416) ^ [] : [-(_1359513 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (30409 ^ _784416) ^ [_1359695, _1359697] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1359695), _1359697) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 30410 ^ _784416 : [(30411 ^ _784416) ^ [] : [_1359695 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1359697 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (30417 ^ _784416) ^ [] : [_1359695 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1359697 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)]]], (30425 ^ _784416) ^ [_1359921, _1359923] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1359921), _1359923) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1359921 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1359921 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (30435 ^ _784416) ^ [_1360023] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1360023)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1360023)))], (30437 ^ _784416) ^ [_1360056] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1360056)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1360056)))], (30439 ^ _784416) ^ [_1360089] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1360089), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1360089))], (30441 ^ _784416) ^ [_1360121, _1360123] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360121), hAPP(c_Int_Onumber__class_Onumber__of(_1360121), c_Int_OMin)), _1360123) = hAPP(c_Groups_Ouminus__class_Ouminus(_1360121), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360121), c_Groups_Oone__class_Oone(_1360121)), _1360123))), class_Fields_Ofield__inverse__zero(_1360121), class_Int_Onumber__ring(_1360121)], (30451 ^ _784416) ^ [_1360302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1360302)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1360302) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (30457 ^ _784416) ^ [_1360387, _1360389] : [class_Rings_Olinordered__idom(_1360387), 30460 ^ _784416 : [(30461 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360387), hAPP(c_Int_Oring__1__class_Oof__int(_1360387), _1360389)), c_Groups_Ozero__class_Ozero(_1360387))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1360389), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30467 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1360389), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360387), hAPP(c_Int_Oring__1__class_Oof__int(_1360387), _1360389)), c_Groups_Ozero__class_Ozero(_1360387))))]]], (30473 ^ _784416) ^ [_1360649, _1360651] : [class_Rings_Olinordered__idom(_1360649), 30476 ^ _784416 : [(30477 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360649), c_Groups_Ozero__class_Ozero(_1360649)), hAPP(c_Int_Oring__1__class_Oof__int(_1360649), _1360651))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1360651)))], (30483 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1360651)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1360649), c_Groups_Ozero__class_Ozero(_1360649)), hAPP(c_Int_Oring__1__class_Oof__int(_1360649), _1360651))))]]], (30489 ^ _784416) ^ [_1360902, _1360904] : [class_Rings_Olinordered__idom(_1360902), 30492 ^ _784416 : [(30493 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360902), c_Groups_Ozero__class_Ozero(_1360902)), hAPP(c_Int_Oring__1__class_Oof__int(_1360902), _1360904))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1360904)))], (30499 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1360904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360902), c_Groups_Ozero__class_Ozero(_1360902)), hAPP(c_Int_Oring__1__class_Oof__int(_1360902), _1360904))))]]], (30505 ^ _784416) ^ [_1361155, _1361157] : [class_Rings_Olinordered__idom(_1361155), 30508 ^ _784416 : [(30509 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361155), hAPP(c_Int_Oring__1__class_Oof__int(_1361155), _1361157)), c_Groups_Ozero__class_Ozero(_1361155))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1361157), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30515 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1361157), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361155), hAPP(c_Int_Oring__1__class_Oof__int(_1361155), _1361157)), c_Groups_Ozero__class_Ozero(_1361155))))]]], (30521 ^ _784416) ^ [_1361417] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1361417) = 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), _1361417), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (30523 ^ _784416) ^ [_1361452, _1361454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1361452)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1361452), _1361454)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1361452), _1361454) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (30533 ^ _784416) ^ [_1361619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1361619)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1361619) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1361619), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30539 ^ _784416) ^ [_1361718, _1361720] : [class_Int_Onumber__ring(_1361718), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1361718), hAPP(c_Int_Onumber__class_Onumber__of(_1361718), 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)))), _1361720)) = c_Groups_Oone__class_Oone(_1361718))], (30545 ^ _784416) ^ [_1361829, _1361831] : [class_Int_Onumber__ring(_1361829), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1361829), hAPP(c_Int_Onumber__class_Onumber__of(_1361829), 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)))), _1361831))) = hAPP(c_Int_Onumber__class_Onumber__of(_1361829), c_Int_OMin))], (30551 ^ _784416) ^ [_1361961, _1361963] : [30552 ^ _784416 : [(30553 ^ _784416) ^ [] : [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), _1361961), _1361963)))], (30555 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1361963), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1361961, _1361963) = 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), _1361961), _1361963)))], (30559 ^ _784416) ^ [_1362120, _1362122] : [-(c_Divides_OnegDivAlg(_1362120, _1362122) = hAPP(c_Divides_Oadjust(_1362122), c_Divides_OnegDivAlg(_1362120, 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)))), _1362122)))), -(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), _1362120), _1362122)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1362122), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30569 ^ _784416) ^ [_1362192, _1362194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1362192)), 30572 ^ _784416 : [(30573 ^ _784416) ^ [] : [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), _1362194), _1362192))), -(c_Divides_OnegDivAlg(_1362194, _1362192) = 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), _1362194), _1362192)))], (30579 ^ _784416) ^ [] : [-(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), _1362194), _1362192)))), -(c_Divides_OnegDivAlg(_1362194, _1362192) = hAPP(c_Divides_Oadjust(_1362192), c_Divides_OnegDivAlg(_1362194, 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)))), _1362192))))]]], (30585 ^ _784416) ^ [_1362456, _1362458] : [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), _1362456), _1362458))), 30588 ^ _784416 : [(30589 ^ _784416) ^ [] : [30590 ^ _784416 : [(30591 ^ _784416) ^ [] : [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), _1362456), _1362458)))], (30593 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1362458), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1362456, _1362458) = 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), _1362456), _1362458)))], (30597 ^ _784416) ^ [] : [-(c_Divides_OnegDivAlg(_1362456, _1362458) = hAPP(c_Divides_Oadjust(_1362458), c_Divides_OnegDivAlg(_1362456, 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)))), _1362458)))), -(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), _1362456), _1362458)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1362458), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (30607 ^ _784416) ^ [_1362803, _1362805, _1362807] : [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), _1362803), _1362805))), -(hBOOL(hAPP(hAPP(_1362807, _1362803), _1362805))), 30614 ^ _784416 : [(30615 ^ _784416) ^ [] : [-(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), 30612 ^ [_1362803, _1362805, _1362807]), 30613 ^ [_1362803, _1362805, _1362807]))))], (30627 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1362807, 30612 ^ [_1362803, _1362805, _1362807]), 30613 ^ [_1362803, _1362805, _1362807]))], (30617 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1362807, 30612 ^ [_1362803, _1362805, _1362807]), 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)))), 30613 ^ [_1362803, _1362805, _1362807])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 30612 ^ [_1362803, _1362805, _1362807]), 30613 ^ [_1362803, _1362805, _1362807]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 30613 ^ [_1362803, _1362805, _1362807]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (30631 ^ _784416) ^ [_1363295] : [_1363295 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1363295) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30637 ^ _784416) ^ [_1363371] : [-(_1363371 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 30640 ^ _784416 : [(30641 ^ _784416) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1363371, 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, _1363371) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(c_Code__Numeral_Oint__of, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1363371), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (30647 ^ _784416) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1363371, 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, _1363371) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(c_Code__Numeral_Oint__of, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1363371), 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)))]]], (30653 ^ _784416) ^ [_1363631, _1363633] : [class_Rings_Osemiring__1(_1363631), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1363633)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1363631), 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)))), _1363633))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363631), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1363631), hAPP(c_Int_Onat, _1363633))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1363631), hAPP(c_Int_Onat, _1363633))))], (30663 ^ _784416) ^ [_1363832, _1363834] : [-(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), _1363832))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1363834))))], (30665 ^ _784416) ^ [_1363871, _1363873] : [-(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, _1363871)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1363873))))], (30667 ^ _784416) ^ [_1363913, _1363915] : [class_Rings_Oring__1(_1363913), -(hAPP(c_Int_Oring__1__class_Oof__int(_1363913), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1363915)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1363913), _1363915))], (30673 ^ _784416) ^ [_1364014] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1364014)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1364014))], (30675 ^ _784416) ^ [_1364061, _1364063] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1364061), _1364063)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1364061)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1364063))))], (30681 ^ _784416) ^ [_1364166, _1364168] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1364166)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1364168))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1364166), _1364168)))], (30687 ^ _784416) ^ [_1364286] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1364286)))], (30689 ^ _784416) ^ [] : [-(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))], (30691 ^ _784416) ^ [_1364332, _1364334, _1364336] : [class_Nat_Osemiring__char__0(_1364332), 30694 ^ _784416 : [(30695 ^ _784416) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1364332), _1364334) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1364332), _1364336), -(_1364334 = _1364336)], (30701 ^ _784416) ^ [] : [_1364334 = _1364336, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1364332), _1364334) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1364332), _1364336))]]], (30707 ^ _784416) ^ [_1364573] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1364573)) = _1364573)], (30709 ^ _784416) ^ [_1364614] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1364614)), -(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)), _1364614))))], (30715 ^ _784416) ^ [_1364699] : [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)), _1364699))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1364699)))], (30721 ^ _784416) ^ [_1364790] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1364790) = 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)), _1364790)))], (30723 ^ _784416) ^ [] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (30725 ^ _784416) ^ [_1364840, _1364842, _1364844] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1364840), _1364842), _1364844) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1364840), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1364840, tc_Int_Oint), _1364842), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1364844))), class_Groups_Ocomm__monoid__add(_1364840), class_Groups_Ocomm__monoid__mult(_1364840)], (30735 ^ _784416) ^ [_1365031, _1365033, _1365035] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1365031, tc_Nat_Onat), _1365033), _1365035)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1365031, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1365031), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1365033)), _1365035))], (30737 ^ _784416) ^ [_1365101] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1365101) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1365101 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30743 ^ _784416) ^ [_1365178] : [_1365178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1365178) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30749 ^ _784416) ^ [] : [-(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))], (30751 ^ _784416) ^ [] : [-(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)))], (30753 ^ _784416) ^ [_1365297] : [-(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), _1365297))))], (30755 ^ _784416) ^ [_1365337] : [30757 ^ _784416 : [(30758 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30756 ^ [_1365337])))], (30760 ^ _784416) ^ [] : [hBOOL(hAPP(_1365337, 30756 ^ [_1365337]))]], 30761 ^ _784416 : [(30762 ^ _784416) ^ [_1365464] : [-(hBOOL(hAPP(_1365337, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1365464))))]]], (30764 ^ _784416) ^ [_1365494] : [hBOOL(hAPP(_1365494, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 30765 ^ [_1365494]))), 30768 ^ _784416 : [(30769 ^ _784416) ^ [_1365594] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1365594)), -(hBOOL(hAPP(_1365494, _1365594)))]]], (30786 ^ _784416) ^ [_1365867] : [30787 ^ _784416 : [(30788 ^ _784416) ^ [_1365924] : [hBOOL(hAPP(_1365867, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1365924)))]], 30790 ^ _784416 : [(30791 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30789 ^ [_1365867])))], (30793 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1365867, 30789 ^ [_1365867])))]]], (30775 ^ _784416) ^ [_1365697] : [-(hBOOL(hAPP(_1365697, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 30782 ^ [_1365697])))), 30776 ^ _784416 : [(30777 ^ _784416) ^ [_1365749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1365749)), hBOOL(hAPP(_1365697, _1365749))]]], (30795 ^ _784416) ^ [_1366016] : [-(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), _1366016))))], (30797 ^ _784416) ^ [_1366053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366053)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (30799 ^ _784416) ^ [_1366099, _1366101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366099)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1366099), _1366101)))], (30805 ^ _784416) ^ [_1366204, _1366206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1366204), _1366206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366204)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366206))))], (30811 ^ _784416) ^ [_1366330, _1366332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366330)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366332))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1366330), _1366332)))], (30817 ^ _784416) ^ [_1366435, _1366437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1366435), _1366437)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366435)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366437))))], (30823 ^ _784416) ^ [_1366561, _1366563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366561)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366563))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1366561), _1366563)))], (30829 ^ _784416) ^ [_1366666, _1366668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1366666), _1366668)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366666)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366668))))], (30835 ^ _784416) ^ [_1366792, _1366794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366792)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366794))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1366792), _1366794)))], (30841 ^ _784416) ^ [_1366897, _1366899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1366897), _1366899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366897)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1366899))))], (30847 ^ _784416) ^ [_1367008, _1367010] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1367008)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1367010)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1367008), _1367010)))], (30849 ^ _784416) ^ [_1367054, _1367056, _1367058] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1367054)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1367056)), _1367058)) = 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), _1367054), _1367056))), _1367058))], (30851 ^ _784416) ^ [_1367114, _1367116] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1367114)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1367116)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1367114), _1367116)))], (30853 ^ _784416) ^ [_1367175, _1367177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1367175), _1367177)), -(_1367177 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1367175), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 30856 ^ [_1367175, _1367177])))], (30860 ^ _784416) ^ [_1367288, _1367290] : [30861 ^ _784416 : [(30862 ^ _784416) ^ [_1367341] : [_1367290 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1367288), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1367341))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1367288), _1367290)))], (30866 ^ _784416) ^ [_1367408, _1367410] : [class_Rings_Olinordered__semidom(_1367408), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367408), c_Groups_Ozero__class_Ozero(_1367408)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1367408), _1367410))))], (30872 ^ _784416) ^ [_1367511, _1367513] : [class_Rings_Olinordered__semidom(_1367511), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367511), c_Groups_Ozero__class_Ozero(_1367511)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1367511), _1367513))))], (30878 ^ _784416) ^ [_1367629, _1367631] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1367629)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1367631), 30881 ^ _784416 : [(30882 ^ _784416) ^ [] : [-(_1367629 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30884 ^ _784416) ^ [] : [-(_1367631 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (30886 ^ _784416) ^ [_1367746, _1367748] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1367746)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1367748)), _1367746 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1367748 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (30896 ^ _784416) ^ [_1367895, _1367897] : [class_Rings_Olinordered__semidom(_1367895), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1367895), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1367895), _1367897)), c_Groups_Ozero__class_Ozero(_1367895)))], (30902 ^ _784416) ^ [_1368011, _1368013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1368011)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1368013))))], (30904 ^ _784416) ^ [_1368050, _1368052] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1368050), _1368052)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1368050)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1368052)))], (30906 ^ _784416) ^ [_1368096, _1368098] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1368096)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1368098)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1368096), _1368098)))], (30908 ^ _784416) ^ [_1368142, _1368144] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1368142)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1368144)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1368142), _1368144)))], (30910 ^ _784416) ^ [_1368188] : [class_Rings_Osemiring__1(_1368188), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368188), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1368188))], (30916 ^ _784416) ^ [_1368275, _1368277, _1368279] : [class_Rings_Olinordered__semidom(_1368275), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368275), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368275), _1368277)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368275), _1368279))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1368277), _1368279)))], (30926 ^ _784416) ^ [_1368450, _1368452, _1368454] : [class_Rings_Olinordered__semidom(_1368450), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1368452), _1368454)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368450), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368450), _1368452)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368450), _1368454))))], (30936 ^ _784416) ^ [_1368625, _1368627, _1368629] : [class_Rings_Olinordered__semidom(_1368625), 30939 ^ _784416 : [(30940 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368625), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368625), _1368627)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368625), _1368629))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1368627), _1368629)))], (30946 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1368627), _1368629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368625), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368625), _1368627)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368625), _1368629))))]]], (30952 ^ _784416) ^ [] : [-(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))], (30954 ^ _784416) ^ [] : [-(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)))], (30956 ^ _784416) ^ [_1368938, _1368940, _1368942] : [class_Rings_Olinordered__semidom(_1368938), 30959 ^ _784416 : [(30960 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368938), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368938), _1368940)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368938), _1368942))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1368940), _1368942)))], (30966 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1368940), _1368942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368938), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368938), _1368940)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368938), _1368942))))]]], (30972 ^ _784416) ^ [_1369215, _1369217, _1369219] : [class_Rings_Osemiring__1(_1369215), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1369215), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1369217), _1369219)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1369215), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1369215), _1369217)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1369215), _1369219)))], (30978 ^ _784416) ^ [_1369350, _1369352, _1369354] : [class_Rings_Osemiring__1(_1369350), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1369350), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1369352), _1369354)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369350), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1369350), _1369352)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1369350), _1369354)))], (30984 ^ _784416) ^ [_1369485, _1369487] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1369485, _1369487)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1369485), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1369487)))], (30986 ^ _784416) ^ [_1369527, _1369529] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1369527), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1369529)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1369527, _1369529)))], (30988 ^ _784416) ^ [_1369565] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1369565))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1369565)) = _1369565)], (30994 ^ _784416) ^ [_1369607, _1369609] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1369607), _1369609)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1369607)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1369609)))], (30996 ^ _784416) ^ [_1369653, _1369655] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1369653)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1369655)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1369653), _1369655)))], (30998 ^ _784416) ^ [_1369699] : [class_Rings_Osemiring__1(_1369699), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1369699), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1369699))], (31004 ^ _784416) ^ [_1369786] : [-(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)), _1369786)) = _1369786)], (31006 ^ _784416) ^ [_1369815, _1369817] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1369815), _1369817) = 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)), _1369815)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1369817))))], (31008 ^ _784416) ^ [_1369861, _1369863] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1369861), _1369863) = 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)), _1369861)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1369863))))], (31010 ^ _784416) ^ [_1369907, _1369909] : [class_Rings_Oring__1(_1369907), -(hBOOL(hAPP(hAPP(c_member(_1369907), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1369907), _1369909)), c_Int_Oring__1__class_OInts(_1369907))))], (31016 ^ _784416) ^ [_1370010, _1370012, _1370014] : [class_Rings_Osemiring__1(_1370010), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1370010), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1370012), _1370014)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1370010), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1370010), _1370012)), _1370014))], (31022 ^ _784416) ^ [_1370135, _1370137] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1370135)), _1370137) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1370135), _1370137)))], (31024 ^ _784416) ^ [_1370178, _1370180] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1370178), _1370180)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1370178)), _1370180))], (31026 ^ _784416) ^ [_1370221, _1370223] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1370221)), _1370223) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1370221), _1370223)))], (31028 ^ _784416) ^ [_1370264, _1370266] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1370264), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1370266)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1370264), _1370266)))], (31030 ^ _784416) ^ [_1370307] : [class_Nat_Osemiring__char__0(_1370307), -(c_Fun_Oinj__on(tc_Nat_Onat, _1370307, c_Nat_Osemiring__1__class_Oof__nat(_1370307), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (31036 ^ _784416) ^ [] : [-(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))))], (31038 ^ _784416) ^ [_1370406, _1370408, _1370410] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1370406, tc_Nat_Onat), _1370408), _1370410) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1370406, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1370406), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1370408)), _1370410)))], (31040 ^ _784416) ^ [_1370476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1370476)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1370476 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31046 ^ _784416) ^ [_1370563] : [_1370563 = 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), _1370563)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31052 ^ _784416) ^ [] : [-(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))], (31054 ^ _784416) ^ [_1370689, _1370691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1370689), _1370691)), -(_1370691 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1370689), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 31057 ^ [_1370689, _1370691]))))], (31061 ^ _784416) ^ [_1370808, _1370810] : [31062 ^ _784416 : [(31063 ^ _784416) ^ [_1370864] : [_1370810 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1370808), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1370864)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1370808), _1370810)))], (31067 ^ _784416) ^ [_1370940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370940)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1370940)) = _1370940)], (31073 ^ _784416) ^ [_1371025] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371025))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1371025)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31079 ^ _784416) ^ [_1371084, _1371086] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1371084) = _1371086, 31082 ^ _784416 : [(31083 ^ _784416) ^ [] : [-(_1371084 = hAPP(c_Int_Onat, _1371086))], (31085 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371086)))]]], (31087 ^ _784416) ^ [_1371199, _1371201] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1371199) = _1371201), _1371199 = hAPP(c_Int_Onat, _1371201), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371201))], (31097 ^ _784416) ^ [_1371346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371346)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1371346)) = _1371346)], (31103 ^ _784416) ^ [_1371452, _1371454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1371452), hAPP(c_Int_Onat, _1371454))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1371452)), _1371454)))], (31109 ^ _784416) ^ [_1371557, _1371559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1371557)), _1371559)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1371557), hAPP(c_Int_Onat, _1371559))))], (31115 ^ _784416) ^ [_1371683, _1371685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1371683)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1371685)))), 31118 ^ _784416 : [(31119 ^ _784416) ^ [] : [-(_1371683 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31121 ^ _784416) ^ [] : [-(_1371685 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (31123 ^ _784416) ^ [_1371810, _1371812] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1371810)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1371812))))), _1371810 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1371812 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31133 ^ _784416) ^ [_1371969] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1371969)) = 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), _1371969)))], (31135 ^ _784416) ^ [_1372004] : [-(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), _1372004))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31137 ^ _784416) ^ [_1372038] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1372038))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31139 ^ _784416) ^ [_1372070, _1372072, _1372074, _1372076] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1372070), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1372072, tc_Nat_Onat), _1372074), _1372076)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1372072, _1372070), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1372070, _1372072), c_Nat_Osemiring__1__class_Oof__nat(_1372070)), _1372074)), _1372076)), class_Groups_Ocomm__monoid__mult(_1372070), class_Rings_Osemiring__1(_1372070)], (31149 ^ _784416) ^ [_1372273, _1372275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1372273), _1372275)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1372275)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1372273)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1372275), _1372273)))], (31155 ^ _784416) ^ [_1372402, _1372404] : [class_Rings_Osemiring__1(_1372402), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1372402), hAPP(c_Nat_OSuc, _1372404)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1372402), c_Groups_Oone__class_Oone(_1372402)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1372402), _1372404)))], (31161 ^ _784416) ^ [_1372523] : [-(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, _1372523))))))], (31163 ^ _784416) ^ [_1372557, _1372559, _1372561] : [class_Rings_Oring__1(_1372557), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1372559), _1372561)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1372557), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1372561), _1372559)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1372557), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1372557), _1372561)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1372557), _1372559)))], (31173 ^ _784416) ^ [] : [-(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))], (31175 ^ _784416) ^ [_1372786] : [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), _1372786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1372786)))], (31181 ^ _784416) ^ [_1372871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1372871)), -(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), _1372871))))], (31203 ^ _784416) ^ [_1373169, _1373171] : [-(hAPP(c_Int_Onat, _1373169) = _1373171), 31206 ^ _784416 : [(31207 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1373169)))], (31209 ^ _784416) ^ [] : [_1373169 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1373171)]], 31210 ^ _784416 : [(31211 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1373169))], (31213 ^ _784416) ^ [] : [_1373171 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (31187 ^ _784416) ^ [_1372977, _1372979] : [hAPP(c_Int_Onat, _1372977) = _1372979, 31190 ^ _784416 : [(31191 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1372977)), -(_1372977 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1372979))], (31197 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1372977))), -(_1372979 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (31233 ^ _784416) ^ [_1373600, _1373602] : [-(_1373600 = hAPP(c_Int_Onat, _1373602)), 31236 ^ _784416 : [(31237 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1373602)))], (31239 ^ _784416) ^ [] : [_1373602 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1373600)]], 31240 ^ _784416 : [(31241 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1373602))], (31243 ^ _784416) ^ [] : [_1373600 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (31217 ^ _784416) ^ [_1373408, _1373410] : [_1373408 = hAPP(c_Int_Onat, _1373410), 31220 ^ _784416 : [(31221 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1373410)), -(_1373410 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1373408))], (31227 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1373410))), -(_1373408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (31263 ^ _784416) ^ [_1374102, _1374104] : [-(hBOOL(hAPP(_1374102, hAPP(c_Int_Onat, _1374104)))), 31267 ^ _784416 : [(31268 ^ _784416) ^ [] : [-(_1374104 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 31266 ^ [_1374102, _1374104]))], (31270 ^ _784416) ^ [] : [hBOOL(hAPP(_1374102, 31266 ^ [_1374102, _1374104]))]], 31271 ^ _784416 : [(31272 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374104), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31274 ^ _784416) ^ [] : [hBOOL(hAPP(_1374102, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (31247 ^ _784416) ^ [_1373839, _1373841] : [hBOOL(hAPP(_1373839, hAPP(c_Int_Onat, _1373841))), 31250 ^ _784416 : [(31251 ^ _784416) ^ [_1373939] : [_1373841 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1373939), -(hBOOL(hAPP(_1373839, _1373939)))], (31257 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1373841), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1373839, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (31278 ^ _784416) ^ [_1374365, _1374367, _1374369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374365), _1374367)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1374369)), -(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), _1374369)), _1374365)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1374369)), _1374367))))], (31288 ^ _784416) ^ [_1374567] : [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, _1374567)))))], (31290 ^ _784416) ^ [_1374601] : [-(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, _1374601)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31292 ^ _784416) ^ [_1374653, _1374655] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1374653) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1374655), 31295 ^ _784416 : [(31296 ^ _784416) ^ [] : [-(_1374653 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1374655)))], (31298 ^ _784416) ^ [] : [-(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), _1374655))))]]], (31300 ^ _784416) ^ [_1374786, _1374788] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1374786) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1374788)), _1374786 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1374788)), 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), _1374788)))], (31310 ^ _784416) ^ [] : [-(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)))))], (31312 ^ _784416) ^ [_1374969, _1374971] : [class_Rings_Olinordered__semidom(_1374969), 31315 ^ _784416 : [(31316 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1374969), c_Groups_Ozero__class_Ozero(_1374969)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1374969), _1374971))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1374971)))], (31322 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1374971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1374969), c_Groups_Ozero__class_Ozero(_1374969)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1374969), _1374971))))]]], (31328 ^ _784416) ^ [_1375228] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375228))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1375228)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31334 ^ _784416) ^ [_1375319] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375319)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1375319)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1375319))], (31340 ^ _784416) ^ [_1375369, _1375371] : [class_Rings_Oring__1(_1375369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1375371)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1375369), hAPP(c_Int_Onat, _1375371)) = hAPP(c_Int_Oring__1__class_Oof__int(_1375369), _1375371))], (31350 ^ _784416) ^ [_1375526, _1375528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1375526)), 31353 ^ _784416 : [(31354 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1375526)), _1375528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1375526), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1375528))))], (31360 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1375526), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1375528))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1375526)), _1375528)))]]], (31382 ^ _784416) ^ [_1376092, _1376094, _1376096] : [-(hBOOL(hAPP(_1376092, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1376094), _1376096))))), 31385 ^ _784416 : [(31386 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1376096), _1376094)))], (31388 ^ _784416) ^ [] : [hBOOL(hAPP(_1376092, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1376094)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1376096))))]], 31389 ^ _784416 : [(31390 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1376094), _1376096)))], (31392 ^ _784416) ^ [] : [hBOOL(hAPP(_1376092, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (31366 ^ _784416) ^ [_1375803, _1375805, _1375807] : [hBOOL(hAPP(_1375803, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1375805), _1375807)))), 31369 ^ _784416 : [(31370 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1375807), _1375805)), -(hBOOL(hAPP(_1375803, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1375805)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1375807)))))], (31376 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1375805), _1375807)), -(hBOOL(hAPP(_1375803, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (31396 ^ _784416) ^ [] : [-(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)))))], (31398 ^ _784416) ^ [_1376385] : [-(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)))), _1376385)) = 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), _1376385), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (31400 ^ _784416) ^ [_1376426, _1376428] : [class_Int_Onumber__ring(_1376426), 31403 ^ _784416 : [(31404 ^ _784416) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1376428))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1376426), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1376428)) = c_Groups_Ozero__class_Ozero(_1376426))], (31410 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1376428)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1376426), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1376428)) = hAPP(c_Int_Onumber__class_Onumber__of(_1376426), _1376428))]]], (31416 ^ _784416) ^ [_1376666, _1376668] : [class_Int_Onumber__ring(_1376666), 31419 ^ _784416 : [(31420 ^ _784416) ^ [] : [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), _1376668))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1376666), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1376668)) = hAPP(c_Int_Onumber__class_Onumber__of(_1376666), _1376668))], (31426 ^ _784416) ^ [] : [-(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), _1376668)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1376666), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1376668)) = c_Groups_Ozero__class_Ozero(_1376666))]]], (31432 ^ _784416) ^ [_1376906, _1376908] : [class_Rings_Oring__1(_1376906), 31435 ^ _784416 : [(31436 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376908), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1376906), _1376908) = hAPP(c_Groups_Ouminus__class_Ouminus(_1376906), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1376906), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1376908)))))], (31442 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1376908), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1376906), _1376908) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1376906), hAPP(c_Int_Onat, _1376908)))]]], (31448 ^ _784416) ^ [] : [-(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)))], (31450 ^ _784416) ^ [_1377186, _1377188] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1377186, _1377188) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1377186), _1377188)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1377186, _1377188)))], (31452 ^ _784416) ^ [_1377230, _1377232, _1377234] : [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), _1377230), _1377232))), -(hBOOL(hAPP(hAPP(_1377234, _1377230), _1377232))), 31459 ^ _784416 : [(31460 ^ _784416) ^ [] : [-(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), 31457 ^ [_1377230, _1377232, _1377234]), 31458 ^ [_1377230, _1377232, _1377234]))))], (31472 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1377234, 31457 ^ [_1377230, _1377232, _1377234]), 31458 ^ [_1377230, _1377232, _1377234]))], (31462 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1377234, 31457 ^ [_1377230, _1377232, _1377234]), 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)))), 31458 ^ [_1377230, _1377232, _1377234])))), -(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), 31457 ^ [_1377230, _1377232, _1377234]), 31458 ^ [_1377230, _1377232, _1377234])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 31458 ^ [_1377230, _1377232, _1377234]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (31476 ^ _784416) ^ [_1377725, _1377727] : [class_Rings_Osemiring__1(_1377725), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1377725), _1377727) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1377725, hAPP(hAPP(c_COMBC(_1377725, _1377725, _1377725), c_Groups_Oplus__class_Oplus(_1377725)), c_Groups_Oone__class_Oone(_1377725)), _1377727, c_Groups_Ozero__class_Ozero(_1377725)))], (31482 ^ _784416) ^ [_1377852, _1377854] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1377852)), hAPP(c_Nat_OSuc, _1377854)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1377852))), 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)), _1377854)))))], (31484 ^ _784416) ^ [_1377924, _1377926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1377924), _1377926)), -(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)), _1377924)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1377926))))], (31490 ^ _784416) ^ [_1378029, _1378031] : [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)), _1378029)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1378031))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1378029), _1378031)))], (31496 ^ _784416) ^ [_1378155, _1378157] : [_1378155 = _1378157, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1378155) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1378157))], (31502 ^ _784416) ^ [_1378240, _1378242] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1378240) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1378242), -(_1378240 = _1378242)], (31508 ^ _784416) ^ [_1378346, _1378348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1378346), _1378348)), -(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)), _1378346)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1378348))))], (31514 ^ _784416) ^ [_1378451, _1378453] : [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)), _1378451)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1378453))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1378451), _1378453)))], (31520 ^ _784416) ^ [_1378577, _1378579] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378577) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378579), -(_1378577 = _1378579)], (31526 ^ _784416) ^ [_1378662, _1378664] : [_1378662 = _1378664, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378662) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378664))], (31532 ^ _784416) ^ [_1378768, _1378770] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378768) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378770), -(_1378768 = _1378770)], (31538 ^ _784416) ^ [_1378853, _1378855] : [_1378853 = _1378855, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378853) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378855))], (31544 ^ _784416) ^ [_1378944] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378944) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31546 ^ _784416) ^ [_1378970] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1378970), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31548 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (31550 ^ _784416) ^ [_1379023] : [class_Orderings_Olinorder(_1379023), -(c_Finite__Set_Ofun__left__comm__idem(_1379023, _1379023, c_Orderings_Oord__class_Omin(_1379023)))], (31556 ^ _784416) ^ [_1379102, _1379104, _1379106, _1379108, _1379110] : [class_Orderings_Olinorder(_1379102), class_Orderings_Olinorder(_1379104), c_Orderings_Oorder__class_Omono(_1379104, _1379102, _1379106), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1379102), hAPP(_1379106, _1379108)), hAPP(_1379106, _1379110)) = hAPP(_1379106, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1379104), _1379108), _1379110)))], (31570 ^ _784416) ^ [_1379351, _1379353, _1379355, _1379357] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1379351), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1379351), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1379351), _1379353), _1379355)), _1379357) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1379351), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1379351), _1379353), _1379357)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1379351), _1379355), _1379357)))], (31576 ^ _784416) ^ [_1379510, _1379512, _1379514, _1379516] : [class_Groups_Oordered__ab__group__add(_1379510), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1379510), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1379510), _1379512), _1379514)), _1379516) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1379510), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1379510), _1379512), _1379516)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1379510), _1379514), _1379516)))], (31582 ^ _784416) ^ [_1379669] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1379669) = c_Orderings_Oord__class_Omin(_1379669)), class_Lattices_Osemilattice__inf(_1379669), class_Orderings_Olinorder(_1379669)], (31592 ^ _784416) ^ [_1379798, _1379800] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1379798)), hAPP(c_Nat_OSuc, _1379800)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1379798), _1379800)))], (31594 ^ _784416) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (31596 ^ _784416) ^ [_1379862, _1379864] : [class_Orderings_Olinorder(_1379862), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1379862), _1379864), _1379864) = _1379864)], (31602 ^ _784416) ^ [_1379953, _1379955, _1379957] : [class_Orderings_Olinorder(_1379953), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1379953), _1379955), _1379957) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1379953), _1379957), _1379955))], (31608 ^ _784416) ^ [_1380062, _1380064, _1380066] : [class_Orderings_Olinorder(_1380062), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380062), _1380064), _1380066) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380062), _1380066), _1380064))], (31614 ^ _784416) ^ [_1380171, _1380173, _1380175] : [class_Orderings_Olinorder(_1380171), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380171), _1380173), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380171), _1380173), _1380175)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380171), _1380173), _1380175))], (31620 ^ _784416) ^ [_1380296, _1380298, _1380300] : [class_Orderings_Olinorder(_1380296), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380296), _1380298), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380296), _1380298), _1380300)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380296), _1380298), _1380300))], (31626 ^ _784416) ^ [_1380421, _1380423, _1380425, _1380427] : [class_Orderings_Olinorder(_1380421), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380421), _1380423), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380421), _1380425), _1380427)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380421), _1380425), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380421), _1380423), _1380427)))], (31632 ^ _784416) ^ [_1380564, _1380566, _1380568, _1380570] : [class_Orderings_Olinorder(_1380564), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380564), _1380566), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380564), _1380568), _1380570)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380564), _1380568), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380564), _1380566), _1380570)))], (31638 ^ _784416) ^ [_1380707, _1380709, _1380711, _1380713] : [class_Orderings_Olinorder(_1380707), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380707), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380707), _1380709), _1380711)), _1380713) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380707), _1380709), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380707), _1380711), _1380713)))], (31644 ^ _784416) ^ [_1380850, _1380852, _1380854, _1380856] : [class_Orderings_Olinorder(_1380850), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380850), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380850), _1380852), _1380854)), _1380856) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380850), _1380852), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380850), _1380854), _1380856)))], (31650 ^ _784416) ^ [_1380993, _1380995] : [class_Orderings_Olinorder(_1380993), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1380993), _1380995), _1380995) = _1380995)], (31656 ^ _784416) ^ [_1381084, _1381086, _1381088, _1381090] : [class_Orderings_Olinorder(_1381084), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381084), _1381086), _1381088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381084), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1381084), _1381090), _1381086)), _1381088)))], (31666 ^ _784416) ^ [_1381263, _1381265, _1381267, _1381269] : [class_Orderings_Olinorder(_1381263), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381263), _1381265), _1381267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381263), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1381263), _1381265), _1381269)), _1381267)))], (31676 ^ _784416) ^ [_1381442, _1381444, _1381446, _1381448] : [class_Orderings_Olinorder(_1381442), 31679 ^ _784416 : [(31690 ^ _784416) ^ [] : [31691 ^ _784416 : [(31692 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381442), _1381444), _1381448))], (31694 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381442), _1381446), _1381448))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381442), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1381442), _1381444), _1381446)), _1381448)))], (31680 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381442), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1381442), _1381444), _1381446)), _1381448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381442), _1381444), _1381448))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381442), _1381446), _1381448)))]]], (31698 ^ _784416) ^ [_1381791, _1381793, _1381795, _1381797] : [class_Orderings_Olinorder(_1381791), 31701 ^ _784416 : [(31702 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381791), _1381793), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1381791), _1381795), _1381797))), 31705 ^ _784416 : [(31706 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381791), _1381793), _1381795)))], (31708 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381791), _1381793), _1381797)))]]], (31710 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381791), _1381793), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1381791), _1381795), _1381797)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381791), _1381793), _1381795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381791), _1381793), _1381797))]]], (31720 ^ _784416) ^ [_1382171, _1382173, _1382175, _1382177] : [class_Orderings_Olinorder(_1382171), 31723 ^ _784416 : [(31734 ^ _784416) ^ [] : [31735 ^ _784416 : [(31736 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382171), _1382173), _1382177))], (31738 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382171), _1382175), _1382177))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382171), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1382171), _1382173), _1382175)), _1382177)))], (31724 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382171), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1382171), _1382173), _1382175)), _1382177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382171), _1382173), _1382177))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382171), _1382175), _1382177)))]]], (31742 ^ _784416) ^ [_1382520, _1382522, _1382524, _1382526] : [class_Orderings_Olinorder(_1382520), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382520), _1382522), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1382520), _1382524), _1382526))), 31749 ^ _784416 : [(31750 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382520), _1382522), _1382524)))], (31752 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382520), _1382522), _1382526)))]]], (31754 ^ _784416) ^ [_1382743, _1382745, _1382747, _1382749, _1382751] : [class_Orderings_Olinorder(_1382743), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382743), _1382745), _1382747)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382743), _1382749), _1382751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382743), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1382743), _1382745), _1382749)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1382743), _1382747), _1382751))))], (31768 ^ _784416) ^ [_1383014, _1383016, _1383018, _1383020] : [class_Orderings_Olinorder(_1383014), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383014), _1383016), _1383018)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383014), _1383016), _1383020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383014), _1383016), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1383014), _1383018), _1383020))))], (31782 ^ _784416) ^ [_1383263, _1383265, _1383267, _1383269] : [class_Orderings_Olinorder(_1383263), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383263), _1383265), _1383267)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383263), _1383265), _1383269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383263), _1383265), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1383263), _1383267), _1383269))))], (31796 ^ _784416) ^ [_1383512, _1383514, _1383516] : [class_Orderings_Olinorder(_1383512), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383512), _1383514), _1383516)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1383512), _1383516), _1383514) = _1383514)], (31806 ^ _784416) ^ [_1383673, _1383675, _1383677] : [class_Orderings_Olinorder(_1383673), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383673), _1383675), _1383677)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1383673), _1383675), _1383677) = _1383675)], (31816 ^ _784416) ^ [_1383834, _1383836, _1383838, _1383840] : [class_Orderings_Olinorder(_1383834), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383834), _1383836), _1383838)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383834), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1383834), _1383840), _1383836)), _1383838)))], (31826 ^ _784416) ^ [_1384013, _1384015, _1384017, _1384019] : [class_Orderings_Olinorder(_1384013), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384013), _1384015), _1384017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384013), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1384013), _1384015), _1384019)), _1384017)))], (31836 ^ _784416) ^ [_1384192, _1384194, _1384196, _1384198] : [class_Orderings_Olinorder(_1384192), 31839 ^ _784416 : [(31840 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384192), _1384194), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1384192), _1384196), _1384198))), 31843 ^ _784416 : [(31844 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384192), _1384194), _1384196)))], (31846 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384192), _1384194), _1384198)))]]], (31848 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384192), _1384194), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1384192), _1384196), _1384198)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384192), _1384194), _1384196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384192), _1384194), _1384198))]]], (31858 ^ _784416) ^ [_1384572, _1384574, _1384576] : [class_Orderings_Olinorder(_1384572), 31861 ^ _784416 : [(31862 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384572), _1384574), _1384576)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1384572), _1384574), _1384576) = _1384574)], (31868 ^ _784416) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1384572), _1384574), _1384576) = _1384574, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384572), _1384574), _1384576)))]]], (31874 ^ _784416) ^ [_1384828, _1384830, _1384832] : [class_Orderings_Olinorder(_1384828), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384828), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1384828), _1384830), _1384832)), _1384832)))], (31880 ^ _784416) ^ [_1384935, _1384937, _1384939] : [class_Orderings_Olinorder(_1384935), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384935), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1384935), _1384937), _1384939)), _1384937)))], (31886 ^ _784416) ^ [_1385042, _1385044, _1385046] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1385042), _1385044)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1385046), _1385044)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1385042), _1385046)), _1385044))], (31888 ^ _784416) ^ [_1385099, _1385101, _1385103] : [class_Int_Onumber(_1385099), class_Orderings_Oord(_1385099), 31895 ^ _784416 : [(31896 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385099), hAPP(c_Int_Onumber__class_Onumber__of(_1385099), _1385101)), hAPP(c_Int_Onumber__class_Onumber__of(_1385099), _1385103))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1385099), hAPP(c_Int_Onumber__class_Onumber__of(_1385099), _1385101)), hAPP(c_Int_Onumber__class_Onumber__of(_1385099), _1385103)) = hAPP(c_Int_Onumber__class_Onumber__of(_1385099), _1385101))], (31902 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385099), hAPP(c_Int_Onumber__class_Onumber__of(_1385099), _1385101)), hAPP(c_Int_Onumber__class_Onumber__of(_1385099), _1385103)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1385099), hAPP(c_Int_Onumber__class_Onumber__of(_1385099), _1385101)), hAPP(c_Int_Onumber__class_Onumber__of(_1385099), _1385103)) = hAPP(c_Int_Onumber__class_Onumber__of(_1385099), _1385103))]]], (31908 ^ _784416) ^ [_1385491, _1385493, _1385495] : [class_Orderings_Olinorder(_1385491), hBOOL(hAPP(c_Finite__Set_Ofinite(_1385491), _1385493)), hBOOL(hAPP(hAPP(c_member(_1385491), _1385495), _1385493)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1385491), _1385495), c_Big__Operators_Olinorder__class_OMin(_1385491, _1385493)) = c_Big__Operators_Olinorder__class_OMin(_1385491, _1385493))], (31922 ^ _784416) ^ [_1385726, _1385728, _1385730, _1385732, _1385734] : [class_Lattices_Osemilattice__inf(_1385726), class_Orderings_Olinorder(_1385728), c_Orderings_Oorder__class_Omono(_1385728, _1385726, _1385730), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385726), hAPP(_1385730, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1385728), _1385732), _1385734))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1385726), hAPP(_1385730, _1385732)), hAPP(_1385730, _1385734)))))], (31936 ^ _784416) ^ [_1385989, _1385991, _1385993] : [class_Rings_Osemiring__1(_1385989), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1385989, _1385991, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1385993) = _1385993)], (31942 ^ _784416) ^ [_1386076, _1386078, _1386080, _1386082] : [class_Rings_Osemiring__1(_1386076), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1386076, _1386078, hAPP(c_Nat_OSuc, _1386080), _1386082) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1386076, _1386078, _1386080, hAPP(_1386078, _1386082)))], (31948 ^ _784416) ^ [_1386187, _1386189] : [class_Orderings_Olinorder(_1386187), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386187), _1386189)), -(c_Big__Operators_Olinorder__class_OMin(_1386187, _1386189) = hAPP(c_Finite__Set_Ofold1(_1386187, c_Orderings_Oord__class_Omin(_1386187)), _1386189))], (31958 ^ _784416) ^ [_1386344, _1386346] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1386344)), _1386346) = 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), _1386344)), _1386346))], (31960 ^ _784416) ^ [_1386389, _1386391] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1386389), hAPP(c_Nat_OSuc, _1386391)) = 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)), _1386391)), _1386389))], (31962 ^ _784416) ^ [_1386434, _1386436, _1386438] : [class_Orderings_Olinorder(_1386434), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386434), _1386436)), hBOOL(hAPP(hAPP(c_member(_1386434), _1386438), _1386436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386434), hAPP(c_Finite__Set_Ofold1(_1386434, c_Orderings_Oord__class_Omin(_1386434)), _1386436)), _1386438)))], (31976 ^ _784416) ^ [_1386671, _1386673, _1386675] : [class_Orderings_Olinorder(_1386671), hBOOL(hAPP(c_Finite__Set_Ofinite(_1386671), _1386673)), -(_1386673 = c_Orderings_Obot__class_Obot(tc_fun(_1386671, tc_HOL_Obool))), 31987 ^ _784416 : [(31998 ^ _784416) ^ [] : [32000 ^ _784416 : [(32001 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1386671), 31999 ^ [_1386671, _1386673, _1386675]), _1386673)))], (32003 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386671), _1386675), 31999 ^ [_1386671, _1386673, _1386675]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386671), _1386675), hAPP(c_Finite__Set_Ofold1(_1386671, c_Orderings_Oord__class_Omin(_1386671)), _1386673))))], (31988 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386671), _1386675), hAPP(c_Finite__Set_Ofold1(_1386671, c_Orderings_Oord__class_Omin(_1386671)), _1386673))), 31991 ^ _784416 : [(31992 ^ _784416) ^ [_1386964] : [hBOOL(hAPP(hAPP(c_member(_1386671), _1386964), _1386673)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386671), _1386675), _1386964)))]]]]], (32007 ^ _784416) ^ [_1387249, _1387251, _1387253] : [class_Orderings_Olinorder(_1387249), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387249), _1387251)), -(_1387251 = c_Orderings_Obot__class_Obot(tc_fun(_1387249, tc_HOL_Obool))), 32018 ^ _784416 : [(32019 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387249), hAPP(c_Finite__Set_Ofold1(_1387249, c_Orderings_Oord__class_Omin(_1387249)), _1387251)), _1387253)), 32023 ^ _784416 : [(32024 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1387249), 32022 ^ [_1387249, _1387251, _1387253]), _1387251)))], (32026 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387249), 32022 ^ [_1387249, _1387251, _1387253]), _1387253)))]]], (32028 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387249), hAPP(c_Finite__Set_Ofold1(_1387249, c_Orderings_Oord__class_Omin(_1387249)), _1387251)), _1387253))), 32029 ^ _784416 : [(32030 ^ _784416) ^ [_1387638] : [hBOOL(hAPP(hAPP(c_member(_1387249), _1387638), _1387251)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387249), _1387638), _1387253))]]]]], (32038 ^ _784416) ^ [_1387799, _1387801, _1387803] : [class_Orderings_Olinorder(_1387799), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387799), _1387801)), -(_1387801 = c_Orderings_Obot__class_Obot(tc_fun(_1387799, tc_HOL_Obool))), 32049 ^ _784416 : [(32060 ^ _784416) ^ [] : [32062 ^ _784416 : [(32063 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1387799), 32061 ^ [_1387799, _1387801, _1387803]), _1387801)))], (32065 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387799), _1387803), 32061 ^ [_1387799, _1387801, _1387803]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387799), _1387803), hAPP(c_Finite__Set_Ofold1(_1387799, c_Orderings_Oord__class_Omin(_1387799)), _1387801))))], (32050 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387799), _1387803), hAPP(c_Finite__Set_Ofold1(_1387799, c_Orderings_Oord__class_Omin(_1387799)), _1387801))), 32053 ^ _784416 : [(32054 ^ _784416) ^ [_1388092] : [hBOOL(hAPP(hAPP(c_member(_1387799), _1388092), _1387801)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387799), _1387803), _1388092)))]]]]], (32069 ^ _784416) ^ [_1388377, _1388379, _1388381] : [class_Orderings_Olinorder(_1388377), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388377), _1388379)), -(_1388379 = c_Orderings_Obot__class_Obot(tc_fun(_1388377, tc_HOL_Obool))), 32080 ^ _784416 : [(32081 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388377), 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tc_Nat_Onat, c_Int_Onat), _1393431))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1393429), _1393431)))]]], (32381 ^ _784416) ^ [_1393732, _1393734] : [c_Nat__Transfer_Onat__set(_1393732), c_Nat__Transfer_Onat__set(_1393734), 32388 ^ _784416 : [(32389 ^ _784416) ^ [] : [_1393732 = _1393734, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1393732) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1393734))], (32395 ^ _784416) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1393732) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1393734), -(_1393732 = _1393734)]]], (32401 ^ _784416) ^ [_1394005, _1394007] : [c_Nat__Transfer_Onat__set(_1394005), c_Nat__Transfer_Onat__set(_1394007), 32408 ^ _784416 : [(32409 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1394005), _1394007)), -(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), _1394005)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1394007))))], (32415 ^ _784416) ^ [] : [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), _1394005)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1394007))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1394005), _1394007)))]]], (32421 ^ _784416) ^ [_1394308, _1394310] : [c_Nat__Transfer_Onat__set(_1394308), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1394310), _1394308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1394310)))], (32431 ^ _784416) ^ [_1394449] : [-(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)))), _1394449))))], (32433 ^ _784416) ^ [_1394477] : [c_Nat__Transfer_Onat__set(_1394477), -(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), _1394477)) = _1394477)], (32439 ^ _784416) ^ [_1394562] : [c_Nat__Transfer_Onat__set(_1394562), 32442 ^ _784416 : [(32443 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1394562)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1394562))))], (32449 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1394562))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1394562)))]]], (32455 ^ _784416) ^ [_1394782] : [c_Nat__Transfer_Onat__set(_1394782), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1394782) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1394782)))], (32461 ^ _784416) ^ [_1394873, _1394875, _1394877] : [class_Groups_Ocomm__monoid__add(_1394873), class_Groups_Ocomm__monoid__mult(_1394873), c_Nat__Transfer_Onat__set(_1394875), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1394873), _1394877), _1394875) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1394873), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1394873, tc_Nat_Onat), _1394877), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1394875)))], (32475 ^ _784416) ^ [_1395118] : [class_Orderings_Oord(_1395118), -(c_Orderings_Oord__class_Omin(_1395118) = c_Orderings_Oord_Omin(_1395118, c_Orderings_Oord__class_Oless__eq(_1395118)))], (32481 ^ _784416) ^ [_1395205, _1395207] : [c_Nat__Transfer_Ois__nat(_1395205), c_Nat__Transfer_Onat__set(_1395207), 32488 ^ _784416 : [(32489 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1395205), _1395207)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1395205)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1395207))))], (32495 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1395205)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1395207))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1395205), _1395207)))]]], (32501 ^ _784416) ^ [_1395508, _1395510] : [class_Orderings_Olinorder(_1395508), hBOOL(hAPP(c_Finite__Set_Ofinite(_1395508), _1395510)), -(_1395510 = c_Orderings_Obot__class_Obot(tc_fun(_1395508, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1395508), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1395508), 32514 ^ [_1395508, _1395510]), 32515 ^ [_1395508, _1395510])), hAPP(hAPP(c_Set_Oinsert(_1395508), 32514 ^ [_1395508, _1395510]), hAPP(hAPP(c_Set_Oinsert(_1395508), 32515 ^ [_1395508, _1395510]), c_Orderings_Obot__class_Obot(tc_fun(_1395508, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1395508), c_Big__Operators_Olinorder__class_OMin(_1395508, _1395510)), _1395510)))], (32521 ^ _784416) ^ [] : [-(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))], (32523 ^ _784416) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (32525 ^ _784416) ^ [_1395988, _1395990] : [c_Nat__Transfer_Ois__nat(_1395988), c_Nat__Transfer_Ois__nat(_1395990), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1395988), _1395990)))], (32535 ^ _784416) ^ [_1396123] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1396123)))], (32537 ^ _784416) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (32539 ^ _784416) ^ [_1396166, _1396168] : [c_Nat__Transfer_Ois__nat(_1396166), c_Nat__Transfer_Ois__nat(_1396168), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1396166), _1396168)))], (32549 ^ _784416) ^ [_1396301, _1396303] : [c_Nat__Transfer_Ois__nat(_1396301), c_Nat__Transfer_Ois__nat(_1396303), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396301, _1396303)))], (32559 ^ _784416) ^ [_1396432, _1396434] : [c_Nat__Transfer_Ois__nat(_1396432), c_Nat__Transfer_Ois__nat(_1396434), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1396432), _1396434)))], (32569 ^ _784416) ^ [_1396567, _1396569] : [c_Nat__Transfer_Ois__nat(_1396567), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1396567), _1396569)))], (32575 ^ _784416) ^ [_1396652, _1396654] : [c_Nat__Transfer_Ois__nat(_1396652), c_Nat__Transfer_Ois__nat(_1396654), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1396652, _1396654)))], (32585 ^ _784416) ^ [_1396793] : [c_Nat__Transfer_Ois__nat(_1396793), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396793)))], (32591 ^ _784416) ^ [_1396866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396866)), -(c_Nat__Transfer_Ois__nat(_1396866))], (32597 ^ _784416) ^ [_1396945, _1396947] : [c_Nat__Transfer_Onat__set(_1396945), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1396947), _1396945)), -(c_Nat__Transfer_Ois__nat(_1396947))], (32607 ^ _784416) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (32609 ^ _784416) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (32611 ^ _784416) ^ [_1397116, _1397118, _1397120] : [32613 ^ _784416 : [(32614 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1397116), 32612 ^ [_1397116, _1397118, _1397120]), _1397118)))], (32616 ^ _784416) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1397120, 32612 ^ [_1397116, _1397118, _1397120]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397116, tc_Int_Oint), _1397120), _1397118) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1397116, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1397116), c_Int_Onat), _1397120)), _1397118)))], (32620 ^ _784416) ^ [_1397346] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1397346)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1397346)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (32622 ^ _784416) ^ [_1397381, _1397383] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1397381, _1397383)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1397383), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1397381), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (32624 ^ _784416) ^ [_1397443, _1397445] : [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)), _1397443), 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)), _1397445), 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)), _1397443), _1397445)), c_Int_Ointrel)))], (32630 ^ _784416) ^ [_1397574, _1397576] : [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)), _1397574), _1397576)), 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)), _1397574), 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)), _1397576), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (32636 ^ _784416) ^ [_1397711, _1397713] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1397711, _1397713))))], (32638 ^ _784416) ^ [_1397757, _1397759] : [c_Code__Numeral_OSuc__code__numeral(_1397757) = c_Code__Numeral_OSuc__code__numeral(_1397759), -(_1397757 = _1397759)], (32644 ^ _784416) ^ [_1397838, _1397840] : [_1397838 = _1397840, -(c_Code__Numeral_OSuc__code__numeral(_1397838) = c_Code__Numeral_OSuc__code__numeral(_1397840))], (32650 ^ _784416) ^ [] : [-(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))], (32652 ^ _784416) ^ [_1397952] : [c_Code__Numeral_OSuc__code__numeral(_1397952) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (32654 ^ _784416) ^ [_1397986] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1397986)], (32656 ^ _784416) ^ [_1398011, _1398013, _1398015] : [class_Orderings_Oorder(_1398011), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1398011), _1398013), _1398015)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1398011, _1398015, _1398013) = c_Orderings_Obot__class_Obot(tc_fun(_1398011, tc_HOL_Obool)))], (32666 ^ _784416) ^ [_1398174, _1398176, _1398178] : [class_Groups_Oordered__ab__group__add(_1398174), -(hAPP(c_Set_Oimage(_1398174, _1398174, c_Groups_Ouminus__class_Ouminus(_1398174)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1398174, _1398176, _1398178)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1398174, hAPP(c_Groups_Ouminus__class_Ouminus(_1398174), _1398178), hAPP(c_Groups_Ouminus__class_Ouminus(_1398174), _1398176)))], (32672 ^ _784416) ^ [_1398305] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1398305)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1398305)], (32674 ^ _784416) ^ [_1398357, _1398359, _1398361, _1398363] : [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), _1398357), _1398359)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1398361), _1398363))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398357), _1398363) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398361), _1398359))], (32680 ^ _784416) ^ [_1398504, _1398506, _1398508, _1398510] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398504), _1398510) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398508), _1398506), -(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), _1398504), _1398506)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1398508), _1398510))), c_Int_Ointrel)))], (32686 ^ _784416) ^ [_1398657, _1398659, _1398661] : [class_Rings_Oring__1(_1398657), -(hAPP(c_Int_Oring__1__class_Oof__int(_1398657), 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), _1398659), _1398661)), 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(_1398657), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1398657), _1398659)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1398657), _1398661)))], (32692 ^ _784416) ^ [] : [-(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))))))], (32694 ^ _784416) ^ [_1398834, _1398836, _1398838, _1398840] : [-(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), _1398834), _1398836)), 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), _1398838), _1398840)), 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), _1398834), _1398838)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1398836), _1398840))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1398834), _1398840)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1398836), _1398838)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (32696 ^ _784416) ^ [_1398980, _1398982, _1398984, _1398986] : [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), _1398980), _1398982)), 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), _1398984), _1398986)), 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), _1398980), _1398986)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1398984), _1398982))))], (32702 ^ _784416) ^ [_1399173, _1399175, _1399177, _1399179] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1399173), _1399179)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1399177), _1399175))), -(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), _1399173), _1399175)), 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), _1399177), _1399179)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (32708 ^ _784416) ^ [_1399372, _1399374] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1399372, _1399374))))], (32710 ^ _784416) ^ [_1399403, _1399405] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1399403, _1399405)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1399405), hAPP(c_Nat_OSuc, _1399403)))], (32712 ^ _784416) ^ [_1399444, _1399446] : [-(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), _1399444), _1399446)), 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), _1399446), _1399444)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (32714 ^ _784416) ^ [] : [-(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))))))], (32716 ^ _784416) ^ [_1399526] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1399526) = 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), _1399526), 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))))))], (32718 ^ _784416) ^ [_1399570, _1399572, _1399574, _1399576] : [-(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), _1399570), _1399572)), 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), _1399574), _1399576)), 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), _1399570), _1399574)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1399572), _1399576))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (32720 ^ _784416) ^ [_1399671, _1399673] : [-(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), _1399671), _1399673)), 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), _1399671), _1399673))], (32722 ^ _784416) ^ [_1399744, _1399746, _1399748, _1399750] : [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), _1399744), _1399746)), 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), _1399748), _1399750)), 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), _1399744), _1399750)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1399748), _1399746))))], (32728 ^ _784416) ^ [_1399937, _1399939, _1399941, _1399943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1399937), _1399943)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1399941), _1399939))), -(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), _1399937), _1399939)), 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), _1399941), _1399943)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (32734 ^ _784416) ^ [_1400136] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1400136) = 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, _1400136)), 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))))))))], (32736 ^ _784416) ^ [_1400174] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1400174)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1400174)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (32740 ^ _784416) ^ [_1400211] : [-(_1400211 = 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), 32737 ^ [_1400211]), 32738 ^ [_1400211])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (32742 ^ _784416) ^ [] : [-(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))], (32744 ^ _784416) ^ [_1400280] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1400280)), c_Int_OInteg)))], (32746 ^ _784416) ^ [_1400326, _1400328] : [hAPP(c_Int_ORep__Integ, _1400326) = hAPP(c_Int_ORep__Integ, _1400328), -(_1400326 = _1400328)], (32752 ^ _784416) ^ [_1400411, _1400413] : [_1400411 = _1400413, -(hAPP(c_Int_ORep__Integ, _1400411) = hAPP(c_Int_ORep__Integ, _1400413))], (32758 ^ _784416) ^ [_1400502] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1400502)) = _1400502)], (32760 ^ _784416) ^ [] : [-(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))], (32762 ^ _784416) ^ [_1400549] : [-(hAPP(c_Int_Onat, _1400549) = 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, _1400549)), 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)))))))], (32764 ^ _784416) ^ [_1400587, _1400589] : [class_Int_Onumber__ring(_1400587), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1400589)), -(hBOOL(hAPP(hAPP(c_member(_1400587), hAPP(c_Int_Onumber__class_Onumber__of(_1400587), _1400589)), c_Nat_Osemiring__1__class_ONats(_1400587))))], (32774 ^ _784416) ^ [_1400746, _1400748, _1400750] : [class_Orderings_Olinorder(_1400746), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1400746), _1400748), _1400750)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1400746, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1400746, _1400748, _1400750)), hAPP(hAPP(c_Set_Oinsert(_1400746), _1400750), c_Orderings_Obot__class_Obot(tc_fun(_1400746, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1400746, _1400748, _1400750))], (32784 ^ _784416) ^ [_1400970, _1400972] : [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), _1400970), _1400972)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1400970), _1400972)))], (32790 ^ _784416) ^ [_1401075, _1401077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1401075), _1401077)), -(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), _1401075), _1401077)), c_Wellfounded_Oless__than)))], (32796 ^ _784416) ^ [_1401186, _1401188, _1401190] : [class_Orderings_Olinorder(_1401186), hBOOL(hAPP(c_Finite__Set_Ofinite(_1401186), _1401188)), hBOOL(hAPP(hAPP(c_member(_1401186), _1401190), _1401188)), 32807 ^ _784416 : [(32808 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401186, tc_HOL_Obool)), _1401188), hAPP(hAPP(c_Set_Oinsert(_1401186), _1401190), c_Orderings_Obot__class_Obot(tc_fun(_1401186, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1401186, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1401186, c_Orderings_Oord__class_Omin(_1401186), _1401188) = _1401190)], (32814 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401186, tc_HOL_Obool)), _1401188), hAPP(hAPP(c_Set_Oinsert(_1401186), _1401190), c_Orderings_Obot__class_Obot(tc_fun(_1401186, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1401186, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1401186, c_Orderings_Oord__class_Omin(_1401186), _1401188) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1401186), _1401190), c_Big__Operators_Olattice_OInf__fin(_1401186, c_Orderings_Oord__class_Omin(_1401186), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401186, tc_HOL_Obool)), _1401188), hAPP(hAPP(c_Set_Oinsert(_1401186), _1401190), c_Orderings_Obot__class_Obot(tc_fun(_1401186, tc_HOL_Obool)))))))]]], (32820 ^ _784416) ^ [_1401710, _1401712] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1401710, _1401712))))], (32822 ^ _784416) ^ [_1401741, _1401743] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1401741, _1401743))))], (32824 ^ _784416) ^ [_1401772, _1401774, _1401776] : [class_Orderings_Oorder(_1401772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401772), _1401774), _1401776)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1401772, _1401776, _1401774) = c_Orderings_Obot__class_Obot(tc_fun(_1401772, tc_HOL_Obool)))], (32834 ^ _784416) ^ [_1401935, _1401937, _1401939] : [class_Orderings_Oorder(_1401935), 32837 ^ _784416 : [(32838 ^ _784416) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1401935, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1401935, _1401937, _1401939), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401935), _1401937), _1401939))], (32844 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401935), _1401937), _1401939))), -(c_Orderings_Obot__class_Obot(tc_fun(_1401935, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1401935, _1401937, _1401939))]]], (32850 ^ _784416) ^ [_1402154, _1402156, _1402158] : [class_Orderings_Oorder(_1402154), 32853 ^ _784416 : [(32854 ^ _784416) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1402154, _1402156, _1402158) = c_Orderings_Obot__class_Obot(tc_fun(_1402154, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402154), _1402156), _1402158))], (32860 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402154), _1402156), _1402158))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1402154, _1402156, _1402158) = c_Orderings_Obot__class_Obot(tc_fun(_1402154, tc_HOL_Obool)))]]], (32866 ^ _784416) ^ [_1402373, _1402375, _1402377, _1402379] : [class_Orderings_Olinorder(_1402373), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402373), _1402375), _1402377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402373), _1402377), _1402379)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1402373, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1402373, _1402375, _1402377)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1402373, _1402377, _1402379)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1402373, _1402375, _1402379))], (32880 ^ _784416) ^ [_1402638, _1402640, _1402642, _1402644] : [class_Orderings_Oorder(_1402638), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1402638, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1402638, _1402640, _1402642)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1402638, _1402642, _1402644)) = c_Orderings_Obot__class_Obot(tc_fun(_1402638, tc_HOL_Obool)))], (32886 ^ _784416) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (32888 ^ _784416) ^ [_1402783, _1402785] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1402783, _1402785)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1402785), _1402783))], (32890 ^ _784416) ^ [_1402821, _1402823, _1402825] : [class_Orderings_Olinorder(_1402821), hBOOL(hAPP(c_Finite__Set_Ofinite(_1402821), _1402823)), hBOOL(hAPP(hAPP(c_member(_1402821), _1402825), _1402823)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1402821), _1402825), c_Big__Operators_Olattice_OInf__fin(_1402821, c_Orderings_Oord__class_Omin(_1402821), _1402823)) = c_Big__Operators_Olattice_OInf__fin(_1402821, c_Orderings_Oord__class_Omin(_1402821), _1402823))], (32904 ^ _784416) ^ [_1403068, _1403070] : [class_Orderings_Olinorder(_1403068), -(c_Big__Operators_Olattice_OInf__fin(_1403068, c_Orderings_Oord__class_Omin(_1403068), hAPP(hAPP(c_Set_Oinsert(_1403068), _1403070), c_Orderings_Obot__class_Obot(tc_fun(_1403068, tc_HOL_Obool)))) = _1403070)], (32910 ^ _784416) ^ [_1403181, _1403183] : [class_Orderings_Olinorder(_1403181), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403181), _1403183)), -(c_Big__Operators_Olattice_OInf__fin(_1403181, c_Orderings_Oord__class_Omin(_1403181), _1403183) = hAPP(c_Finite__Set_Ofold1(_1403181, c_Orderings_Oord__class_Omin(_1403181)), _1403183))], (32920 ^ _784416) ^ [_1403344] : [class_Rings_Osemiring__1(_1403344), -(hBOOL(hAPP(hAPP(c_member(_1403344), c_Groups_Ozero__class_Ozero(_1403344)), c_Nat_Osemiring__1__class_ONats(_1403344))))], (32926 ^ _784416) ^ [_1403439, _1403441, _1403443] : [class_Rings_Osemiring__1(_1403439), hBOOL(hAPP(hAPP(c_member(_1403439), _1403441), c_Nat_Osemiring__1__class_ONats(_1403439))), hBOOL(hAPP(hAPP(c_member(_1403439), _1403443), c_Nat_Osemiring__1__class_ONats(_1403439))), -(hBOOL(hAPP(hAPP(c_member(_1403439), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1403439), _1403441), _1403443)), c_Nat_Osemiring__1__class_ONats(_1403439))))], (32940 ^ _784416) ^ [_1403694, _1403696, _1403698] : [class_Rings_Osemiring__1(_1403694), hBOOL(hAPP(hAPP(c_member(_1403694), _1403696), c_Nat_Osemiring__1__class_ONats(_1403694))), hBOOL(hAPP(hAPP(c_member(_1403694), _1403698), c_Nat_Osemiring__1__class_ONats(_1403694))), -(hBOOL(hAPP(hAPP(c_member(_1403694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1403694), _1403696), _1403698)), c_Nat_Osemiring__1__class_ONats(_1403694))))], (32954 ^ _784416) ^ [_1403949] : [class_Rings_Osemiring__1(_1403949), -(hBOOL(hAPP(hAPP(c_member(_1403949), c_Groups_Oone__class_Oone(_1403949)), c_Nat_Osemiring__1__class_ONats(_1403949))))], (32960 ^ _784416) ^ [_1404044, _1404046] : [class_Rings_Osemiring__1(_1404044), -(hBOOL(hAPP(hAPP(c_member(_1404044), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1404044), _1404046)), c_Nat_Osemiring__1__class_ONats(_1404044))))], (32966 ^ _784416) ^ [_1404147] : [-(c_Wellfounded_Omeasure(_1404147) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1404147), c_Wellfounded_Oless__than))], (32968 ^ _784416) ^ [_1404178, _1404180, _1404182, _1404184] : [class_Orderings_Oorder(_1404178), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404178, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1404178, _1404180, _1404182)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1404178, _1404182, _1404184)) = c_Orderings_Obot__class_Obot(tc_fun(_1404178, tc_HOL_Obool)))], (32974 ^ _784416) ^ [_1404305, _1404307, _1404309] : [class_Orderings_Olinorder(_1404305), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404305), _1404307)), -(_1404307 = c_Orderings_Obot__class_Obot(tc_fun(_1404305, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1404305, c_Orderings_Oord__class_Omin(_1404305), hAPP(hAPP(c_Set_Oinsert(_1404305), _1404309), _1404307)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1404305), _1404309), c_Big__Operators_Olattice_OInf__fin(_1404305, c_Orderings_Oord__class_Omin(_1404305), _1404307)))], (32988 ^ _784416) ^ [_1404525, _1404527, _1404529] : [class_Orderings_Olinorder(_1404525), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404525), _1404527)), -(_1404529 = c_Orderings_Obot__class_Obot(tc_fun(_1404525, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404525, tc_HOL_Obool)), _1404529), _1404527)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1404525), c_Big__Operators_Olattice_OInf__fin(_1404525, c_Orderings_Oord__class_Omin(_1404525), _1404529)), c_Big__Operators_Olattice_OInf__fin(_1404525, c_Orderings_Oord__class_Omin(_1404525), _1404527)) = c_Big__Operators_Olattice_OInf__fin(_1404525, c_Orderings_Oord__class_Omin(_1404525), _1404527))], (33006 ^ _784416) ^ [_1404857, _1404859, _1404861] : [class_Orderings_Olinorder(_1404857), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404857), _1404859)), -(_1404859 = c_Orderings_Obot__class_Obot(tc_fun(_1404857, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404857), _1404861)), -(_1404861 = c_Orderings_Obot__class_Obot(tc_fun(_1404857, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1404857, c_Orderings_Oord__class_Omin(_1404857), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404857, tc_HOL_Obool)), _1404859), _1404861)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1404857), c_Big__Operators_Olattice_OInf__fin(_1404857, c_Orderings_Oord__class_Omin(_1404857), _1404859)), c_Big__Operators_Olattice_OInf__fin(_1404857, c_Orderings_Oord__class_Omin(_1404857), _1404861)))], (33028 ^ _784416) ^ [_1405224, _1405226] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1405224, _1405226)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1405226), _1405224)))], (33030 ^ _784416) ^ [_1405265, _1405267, _1405269] : [class_Orderings_Olinorder(_1405265), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405265), _1405267)), -(hBOOL(hAPP(hAPP(c_member(_1405265), _1405269), _1405267))), -(_1405267 = c_Orderings_Obot__class_Obot(tc_fun(_1405265, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1405265, c_Orderings_Oord__class_Omin(_1405265), hAPP(hAPP(c_Set_Oinsert(_1405265), _1405269), _1405267)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1405265), _1405269), c_Big__Operators_Olattice_OInf__fin(_1405265, c_Orderings_Oord__class_Omin(_1405265), _1405267)))], (33048 ^ _784416) ^ [_1405514, _1405516, _1405518, _1405520] : [class_Orderings_Olinorder(_1405514), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405514), _1405516), _1405518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405514), _1405518), _1405520)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1405514, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1405514, _1405516, _1405518)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1405514, _1405518, _1405520)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1405514, _1405516, _1405520))], (33062 ^ _784416) ^ [_1405779, _1405781, _1405783] : [class_Orderings_Olinorder(_1405779), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405779), _1405781)), 33069 ^ _784416 : [(33070 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1405779, tc_HOL_Obool)), _1405781), hAPP(hAPP(c_Set_Oinsert(_1405779), _1405783), c_Orderings_Obot__class_Obot(tc_fun(_1405779, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1405779, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1405779, c_Orderings_Oord__class_Omin(_1405779), hAPP(hAPP(c_Set_Oinsert(_1405779), _1405783), _1405781)) = _1405783)], (33076 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1405779, tc_HOL_Obool)), _1405781), hAPP(hAPP(c_Set_Oinsert(_1405779), _1405783), c_Orderings_Obot__class_Obot(tc_fun(_1405779, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1405779, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1405779, c_Orderings_Oord__class_Omin(_1405779), hAPP(hAPP(c_Set_Oinsert(_1405779), _1405783), _1405781)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1405779), _1405783), c_Big__Operators_Olattice_OInf__fin(_1405779, c_Orderings_Oord__class_Omin(_1405779), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1405779, tc_HOL_Obool)), _1405781), hAPP(hAPP(c_Set_Oinsert(_1405779), _1405783), c_Orderings_Obot__class_Obot(tc_fun(_1405779, tc_HOL_Obool)))))))]]], (33082 ^ _784416) ^ [_1406267, _1406269, _1406271] : [class_Orderings_Olinorder(_1406267), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406267), _1406269)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406267), _1406271)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406267, tc_HOL_Obool)), _1406269), _1406271) = c_Orderings_Obot__class_Obot(tc_fun(_1406267, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1406267), c_Big__Operators_Olattice_OInf__fin(_1406267, c_Orderings_Oord__class_Omin(_1406267), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406267, tc_HOL_Obool)), _1406269), _1406271))), c_Big__Operators_Olattice_OInf__fin(_1406267, c_Orderings_Oord__class_Omin(_1406267), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406267, tc_HOL_Obool)), _1406269), _1406271))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1406267), c_Big__Operators_Olattice_OInf__fin(_1406267, c_Orderings_Oord__class_Omin(_1406267), _1406269)), c_Big__Operators_Olattice_OInf__fin(_1406267, c_Orderings_Oord__class_Omin(_1406267), _1406271)))], (33100 ^ _784416) ^ [_1406639, _1406641, _1406643] : [class_Orderings_Olinorder(_1406639), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406639), _1406641)), -(_1406641 = c_Orderings_Obot__class_Obot(tc_fun(_1406639, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406639), _1406643)), -(_1406643 = c_Orderings_Obot__class_Obot(tc_fun(_1406639, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1406639, tc_HOL_Obool)), _1406641), _1406643) = c_Orderings_Obot__class_Obot(tc_fun(_1406639, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1406639, c_Orderings_Oord__class_Omin(_1406639), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1406639, tc_HOL_Obool)), _1406641), _1406643)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1406639), c_Big__Operators_Olattice_OInf__fin(_1406639, c_Orderings_Oord__class_Omin(_1406639), _1406641)), c_Big__Operators_Olattice_OInf__fin(_1406639, c_Orderings_Oord__class_Omin(_1406639), _1406643)))], (33126 ^ _784416) ^ [_1407134, _1407136, _1407138] : [-(c_Wellfounded_Omlex__prod(_1407134, _1407136, _1407138) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1407134), _1407134), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1407134, c_Wellfounded_Oless__than, _1407138)), hAPP(hAPP(c_COMBS(_1407134, _1407134, tc_prod(tc_Nat_Onat, _1407134)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1407134, tc_prod(tc_Nat_Onat, _1407134)), _1407134), c_Product__Type_OPair(tc_Nat_Onat, _1407134)), _1407136)), c_COMBI(_1407134))))], (33128 ^ _784416) ^ [_1407216, _1407218] : [class_Orderings_Olinorder(_1407216), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407216), _1407218)), -(_1407218 = c_Orderings_Obot__class_Obot(tc_fun(_1407216, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1407216), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1407216), 33141 ^ [_1407216, _1407218]), 33142 ^ [_1407216, _1407218])), hAPP(hAPP(c_Set_Oinsert(_1407216), 33141 ^ [_1407216, _1407218]), hAPP(hAPP(c_Set_Oinsert(_1407216), 33142 ^ [_1407216, _1407218]), c_Orderings_Obot__class_Obot(tc_fun(_1407216, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1407216), c_Big__Operators_Olattice_OInf__fin(_1407216, c_Orderings_Oord__class_Omin(_1407216), _1407218)), _1407218)))], (33148 ^ _784416) ^ [_1407666, _1407668, _1407670] : [class_Orderings_Olinorder(_1407666), hBOOL(hAPP(c_Finite__Set_Ofinite(_1407666), _1407668)), -(_1407668 = c_Orderings_Obot__class_Obot(tc_fun(_1407666, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1407666), _1407670), c_Big__Operators_Olattice_OInf__fin(_1407666, c_Orderings_Oord__class_Omin(_1407666), _1407668)) = c_Big__Operators_Olattice_OInf__fin(_1407666, c_Orderings_Oord__class_Omin(_1407666), hAPP(c_Set_OCollect(_1407666), hAPP(hAPP(c_COMBB(tc_fun(_1407666, tc_HOL_Obool), tc_HOL_Obool, _1407666), c_HOL_OEx(_1407666)), hAPP(hAPP(c_COMBC(_1407666, tc_fun(_1407666, tc_HOL_Obool), tc_fun(_1407666, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407666, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1407666, tc_HOL_Obool), tc_fun(_1407666, tc_HOL_Obool)), _1407666), c_COMBS(_1407666, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407666, tc_HOL_Obool), tc_fun(_1407666, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1407666), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1407666), c_fconj)), hAPP(hAPP(c_COMBC(_1407666, tc_fun(_1407666, _1407666), tc_fun(_1407666, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1407666, tc_HOL_Obool), tc_fun(tc_fun(_1407666, _1407666), tc_fun(_1407666, tc_HOL_Obool)), _1407666), c_COMBB(_1407666, tc_HOL_Obool, _1407666)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1407666), _1407670))))), hAPP(hAPP(c_COMBC(_1407666, tc_fun(_1407666, tc_HOL_Obool), tc_HOL_Obool), c_member(_1407666)), _1407668))))))], (33162 ^ _784416) ^ [_1408164, _1408166, _1408168] : [class_Orderings_Olinorder(_1408164), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408164), _1408166)), -(_1408166 = c_Orderings_Obot__class_Obot(tc_fun(_1408164, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1408164), _1408168)), -(_1408168 = c_Orderings_Obot__class_Obot(tc_fun(_1408164, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1408164), c_Big__Operators_Olattice_OInf__fin(_1408164, c_Orderings_Oord__class_Omin(_1408164), _1408166)), c_Big__Operators_Olattice_OInf__fin(_1408164, c_Orderings_Oord__class_Omin(_1408164), _1408168)) = c_Big__Operators_Olattice_OInf__fin(_1408164, c_Orderings_Oord__class_Omin(_1408164), hAPP(c_Set_OCollect(_1408164), hAPP(hAPP(c_COMBB(tc_fun(_1408164, tc_HOL_Obool), tc_HOL_Obool, _1408164), c_HOL_OEx(_1408164)), hAPP(hAPP(c_COMBB(tc_fun(_1408164, tc_fun(_1408164, tc_HOL_Obool)), tc_fun(_1408164, tc_HOL_Obool), _1408164), hAPP(c_COMBB(tc_fun(_1408164, tc_HOL_Obool), tc_HOL_Obool, _1408164), c_HOL_OEx(_1408164))), hAPP(hAPP(c_COMBC(_1408164, tc_fun(_1408164, tc_fun(_1408164, tc_HOL_Obool)), tc_fun(_1408164, tc_fun(_1408164, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1408164, tc_fun(tc_fun(_1408164, tc_HOL_Obool), tc_fun(_1408164, tc_HOL_Obool))), tc_fun(tc_fun(_1408164, tc_fun(_1408164, tc_HOL_Obool)), tc_fun(_1408164, tc_fun(_1408164, tc_HOL_Obool))), _1408164), c_COMBS(_1408164, tc_fun(_1408164, tc_HOL_Obool), tc_fun(_1408164, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1408164, tc_fun(_1408164, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1408164, tc_fun(tc_fun(_1408164, tc_HOL_Obool), tc_fun(_1408164, tc_HOL_Obool))), _1408164), hAPP(c_COMBB(tc_fun(_1408164, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1408164, tc_HOL_Obool), tc_fun(_1408164, tc_HOL_Obool)), _1408164), c_COMBS(_1408164, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1408164, tc_fun(_1408164, tc_HOL_Obool)), tc_fun(_1408164, tc_fun(_1408164, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1408164), hAPP(c_COMBB(tc_fun(_1408164, tc_HOL_Obool), tc_fun(_1408164, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1408164), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1408164), c_fconj))), hAPP(hAPP(c_COMBC(_1408164, tc_fun(_1408164, tc_fun(_1408164, _1408164)), tc_fun(_1408164, tc_fun(_1408164, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1408164, _1408164), tc_fun(_1408164, tc_HOL_Obool)), tc_fun(tc_fun(_1408164, tc_fun(_1408164, _1408164)), tc_fun(_1408164, tc_fun(_1408164, tc_HOL_Obool))), _1408164), c_COMBB(tc_fun(_1408164, _1408164), tc_fun(_1408164, tc_HOL_Obool), _1408164)), hAPP(hAPP(c_COMBB(tc_fun(_1408164, tc_HOL_Obool), tc_fun(tc_fun(_1408164, _1408164), tc_fun(_1408164, tc_HOL_Obool)), _1408164), c_COMBB(_1408164, tc_HOL_Obool, _1408164)), c_fequal))), c_Orderings_Oord__class_Omax(_1408164)))))), hAPP(hAPP(c_COMBC(_1408164, tc_fun(_1408164, tc_HOL_Obool), tc_fun(_1408164, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1408164, tc_HOL_Obool), tc_fun(_1408164, tc_HOL_Obool)), _1408164), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1408164)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1408164), c_fconj), hAPP(hAPP(c_COMBC(_1408164, tc_fun(_1408164, tc_HOL_Obool), tc_HOL_Obool), c_member(_1408164)), _1408166)))), hAPP(hAPP(c_COMBC(_1408164, tc_fun(_1408164, tc_HOL_Obool), tc_HOL_Obool), c_member(_1408164)), _1408168))))))))], (33184 ^ _784416) ^ [] : [-(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))], (33186 ^ _784416) ^ [_1409299, _1409301, _1409303, _1409305] : [class_Groups_Oordered__ab__group__add(_1409299), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409299), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409299), _1409301), _1409303)), _1409305) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409299), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409299), _1409301), _1409305)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409299), _1409303), _1409305)))], (33192 ^ _784416) ^ [_1409458] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1409458) = c_Orderings_Oord__class_Omax(_1409458)), class_Lattices_Osemilattice__sup(_1409458), class_Orderings_Olinorder(_1409458)], (33202 ^ _784416) ^ [_1409587, _1409589] : [class_Orderings_Olinorder(_1409587), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409587), _1409589), _1409589) = _1409589)], (33208 ^ _784416) ^ [_1409678, _1409680, _1409682, _1409684] : [class_Orderings_Olinorder(_1409678), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409678), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409678), _1409680), _1409682)), _1409684) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409678), _1409680), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409678), _1409682), _1409684)))], (33214 ^ _784416) ^ [_1409821, _1409823, _1409825, _1409827] : [class_Orderings_Olinorder(_1409821), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409821), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409821), _1409823), _1409825)), _1409827) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409821), _1409823), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409821), _1409825), _1409827)))], (33220 ^ _784416) ^ [_1409964, _1409966, _1409968, _1409970] : [class_Orderings_Olinorder(_1409964), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409964), _1409966), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409964), _1409968), _1409970)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409964), _1409968), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1409964), _1409966), _1409970)))], (33226 ^ _784416) ^ [_1410107, _1410109, _1410111, _1410113] : [class_Orderings_Olinorder(_1410107), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410107), _1410109), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410107), _1410111), _1410113)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410107), _1410111), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410107), _1410109), _1410113)))], (33232 ^ _784416) ^ [_1410250, _1410252, _1410254] : [class_Orderings_Olinorder(_1410250), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410250), _1410252), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410250), _1410252), _1410254)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410250), _1410252), _1410254))], (33238 ^ _784416) ^ [_1410375, _1410377, _1410379] : [class_Orderings_Olinorder(_1410375), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410375), _1410377), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410375), _1410377), _1410379)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410375), _1410377), _1410379))], (33244 ^ _784416) ^ [_1410500, _1410502, _1410504] : [class_Orderings_Olinorder(_1410500), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410500), _1410502), _1410504) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410500), _1410504), _1410502))], (33250 ^ _784416) ^ [_1410609, _1410611, _1410613] : [class_Orderings_Olinorder(_1410609), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410609), _1410611), _1410613) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410609), _1410613), _1410611))], (33256 ^ _784416) ^ [_1410718, _1410720] : [class_Orderings_Olinorder(_1410718), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410718), _1410720), _1410720) = _1410720)], (33262 ^ _784416) ^ [_1410809, _1410811] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1410809)), hAPP(c_Nat_OSuc, _1410811)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1410809), _1410811)))], (33264 ^ _784416) ^ [_1410855, _1410857, _1410859, _1410861] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1410855), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1410855), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410855), _1410857), _1410859)), _1410861) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410855), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1410855), _1410857), _1410861)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1410855), _1410859), _1410861)))], (33270 ^ _784416) ^ [_1411014, _1411016, _1411018, _1411020, _1411022] : [class_Orderings_Olinorder(_1411014), class_Orderings_Olinorder(_1411016), c_Orderings_Oorder__class_Omono(_1411016, _1411014, _1411018), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1411014), hAPP(_1411018, _1411020)), hAPP(_1411018, _1411022)) = hAPP(_1411018, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1411016), _1411020), _1411022)))], (33284 ^ _784416) ^ [_1411263] : [class_Orderings_Olinorder(_1411263), -(c_Finite__Set_Ofun__left__comm__idem(_1411263, _1411263, c_Orderings_Oord__class_Omax(_1411263)))], (33290 ^ _784416) ^ [_1411342] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1411342), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1411342)], (33292 ^ _784416) ^ [_1411371] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1411371) = _1411371)], (33294 ^ _784416) ^ [_1411397, _1411399, _1411401, _1411403] : [class_Orderings_Olinorder(_1411397), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1411397), _1411399), _1411401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1411397), _1411399), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1411397), _1411403), _1411401))))], (33304 ^ _784416) ^ [_1411576, _1411578, _1411580, _1411582] : [class_Orderings_Olinorder(_1411576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1411576), _1411578), _1411580)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1411576), _1411578), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1411576), _1411580), _1411582))))], (33314 ^ _784416) ^ [_1411755, _1411757, _1411759, _1411761] : [class_Orderings_Olinorder(_1411755), 33317 ^ _784416 : [(33318 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1411755), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1411755), _1411757), _1411759)), _1411761)), 33321 ^ _784416 : [(33322 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1411755), _1411757), _1411761)))], (33324 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1411755), _1411759), _1411761)))]]], (33326 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1411755), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1411755), _1411757), _1411759)), _1411761))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1411755), _1411757), _1411761)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1411755), _1411759), _1411761))]]], (33336 ^ _784416) ^ [_1412135, _1412137, _1412139, _1412141] : [class_Orderings_Olinorder(_1412135), 33339 ^ _784416 : [(33350 ^ _784416) ^ [] : [33351 ^ _784416 : [(33352 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1412135), _1412137), _1412139))], (33354 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1412135), _1412137), _1412141))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1412135), _1412137), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1412135), _1412139), _1412141))))], (33340 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1412135), _1412137), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1412135), _1412139), _1412141))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1412135), _1412137), _1412139))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1412135), _1412137), _1412141)))]]], (33358 ^ _784416) ^ [_1412484, _1412486, _1412488, _1412490] : [class_Orderings_Olinorder(_1412484), 33361 ^ _784416 : [(33372 ^ _784416) ^ [] : [33373 ^ _784416 : [(33374 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412484), _1412486), _1412488))], (33376 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412484), _1412486), _1412490))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412484), _1412486), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1412484), _1412488), _1412490))))], (33362 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412484), _1412486), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1412484), _1412488), _1412490))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412484), _1412486), _1412488))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412484), _1412486), _1412490)))]]], (33380 ^ _784416) ^ [_1412833, _1412835, _1412837, _1412839] : [class_Orderings_Olinorder(_1412833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412833), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1412833), _1412835), _1412837)), _1412839)), 33387 ^ _784416 : [(33388 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412833), _1412835), _1412839)))], (33390 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412833), _1412837), _1412839)))]]], (33392 ^ _784416) ^ [_1413056, _1413058, _1413060, _1413062, _1413064] : [class_Orderings_Olinorder(_1413056), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413056), _1413058), _1413060)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413056), _1413062), _1413064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413056), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1413056), _1413058), _1413062)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1413056), _1413060), _1413064))))], (33406 ^ _784416) ^ [_1413327, _1413329, _1413331, _1413333] : [class_Orderings_Olinorder(_1413327), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413327), _1413329), _1413331)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413327), _1413333), _1413331)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413327), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1413327), _1413329), _1413333)), _1413331)))], (33420 ^ _784416) ^ [_1413576, _1413578, _1413580, _1413582] : [class_Orderings_Olinorder(_1413576), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413576), _1413578), _1413580)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413576), _1413582), _1413580)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413576), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1413576), _1413578), _1413582)), _1413580)))], (33434 ^ _784416) ^ [_1413825, _1413827, _1413829] : [class_Orderings_Olinorder(_1413825), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413825), _1413827), _1413829)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1413825), _1413829), _1413827) = _1413829)], (33444 ^ _784416) ^ [_1413986, _1413988, _1413990] : [class_Orderings_Olinorder(_1413986), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413986), _1413988), _1413990)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1413986), _1413988), _1413990) = _1413990)], (33454 ^ _784416) ^ [_1414147, _1414149, _1414151, _1414153] : [class_Orderings_Olinorder(_1414147), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414147), _1414149), _1414151)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414147), _1414149), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1414147), _1414153), _1414151))))], (33464 ^ _784416) ^ [_1414326, _1414328, _1414330, _1414332] : [class_Orderings_Olinorder(_1414326), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414326), _1414328), _1414330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414326), _1414328), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1414326), _1414330), _1414332))))], (33474 ^ _784416) ^ [_1414505, _1414507, _1414509, _1414511] : [class_Orderings_Olinorder(_1414505), 33477 ^ _784416 : [(33478 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414505), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1414505), _1414507), _1414509)), _1414511)), 33481 ^ _784416 : [(33482 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414505), _1414507), _1414511)))], (33484 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414505), _1414509), _1414511)))]]], (33486 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414505), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1414505), _1414507), _1414509)), _1414511))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414505), _1414507), _1414511)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414505), _1414509), _1414511))]]], (33496 ^ _784416) ^ [_1414885, _1414887, _1414889] : [class_Orderings_Olinorder(_1414885), 33499 ^ _784416 : [(33500 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414885), _1414887), _1414889)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1414885), _1414887), _1414889) = _1414889)], (33506 ^ _784416) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1414885), _1414887), _1414889) = _1414889, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1414885), _1414887), _1414889)))]]], (33512 ^ _784416) ^ [_1415141, _1415143, _1415145] : [class_Orderings_Olinorder(_1415141), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1415141), _1415143), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415141), _1415145), _1415143))))], (33518 ^ _784416) ^ [_1415248, _1415250, _1415252] : [class_Orderings_Olinorder(_1415248), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1415248), _1415250), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415248), _1415250), _1415252))))], (33524 ^ _784416) ^ [_1415355, _1415357, _1415359, _1415361] : [class_Orderings_Olinorder(_1415355), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1415355), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415355), _1415357), _1415359)), _1415361) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415355), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1415355), _1415357), _1415361)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1415355), _1415359), _1415361)))], (33530 ^ _784416) ^ [_1415514, _1415516, _1415518, _1415520] : [class_Orderings_Olinorder(_1415514), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415514), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1415514), _1415516), _1415518)), _1415520) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1415514), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415514), _1415516), _1415520)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415514), _1415518), _1415520)))], (33536 ^ _784416) ^ [_1415673, _1415675, _1415677, _1415679] : [class_Orderings_Olinorder(_1415673), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1415673), _1415675), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415673), _1415677), _1415679)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415673), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1415673), _1415675), _1415677)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1415673), _1415675), _1415679)))], (33542 ^ _784416) ^ [_1415832, _1415834, _1415836, _1415838] : [class_Orderings_Olinorder(_1415832), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415832), _1415834), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1415832), _1415836), _1415838)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1415832), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415832), _1415834), _1415836)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415832), _1415834), _1415838)))], (33548 ^ _784416) ^ [_1415991, _1415993, _1415995] : [class_Orderings_Olinorder(_1415991), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1415991), _1415993), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1415991), _1415993), _1415995)) = _1415993)], (33554 ^ _784416) ^ [_1416100, _1416102, _1416104] : [class_Orderings_Olinorder(_1416100), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1416100), _1416102), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1416100), _1416102), _1416104)) = _1416102)], (33560 ^ _784416) ^ [_1416209, _1416211, _1416213] : [class_Int_Onumber(_1416209), class_Orderings_Oord(_1416209), 33567 ^ _784416 : [(33568 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1416209), hAPP(c_Int_Onumber__class_Onumber__of(_1416209), _1416211)), hAPP(c_Int_Onumber__class_Onumber__of(_1416209), _1416213))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1416209), hAPP(c_Int_Onumber__class_Onumber__of(_1416209), _1416211)), hAPP(c_Int_Onumber__class_Onumber__of(_1416209), _1416213)) = hAPP(c_Int_Onumber__class_Onumber__of(_1416209), _1416213))], (33574 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1416209), hAPP(c_Int_Onumber__class_Onumber__of(_1416209), _1416211)), hAPP(c_Int_Onumber__class_Onumber__of(_1416209), _1416213)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1416209), hAPP(c_Int_Onumber__class_Onumber__of(_1416209), _1416211)), hAPP(c_Int_Onumber__class_Onumber__of(_1416209), _1416213)) = hAPP(c_Int_Onumber__class_Onumber__of(_1416209), _1416211))]]], (33580 ^ _784416) ^ [_1416601, _1416603, _1416605, _1416607] : [class_Orderings_Olinorder(_1416601), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1416601), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1416601), _1416603), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1416601), _1416605), _1416607))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1416601), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1416601), _1416603), _1416605)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1416601), _1416603), _1416607)))))], (33586 ^ _784416) ^ [_1416774, _1416776, _1416778, _1416780] : [class_Orderings_Olinorder(_1416774), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1416774), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1416774), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1416774), _1416776), _1416778)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1416774), _1416776), _1416780))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1416774), _1416776), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1416774), _1416778), _1416780)))))], (33592 ^ _784416) ^ [_1416947, _1416949, _1416951] : [class_Groups_Olinordered__ab__group__add(_1416947), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1416947), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1416947), _1416949), _1416951)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1416947), hAPP(c_Groups_Ouminus__class_Ouminus(_1416947), _1416949)), hAPP(c_Groups_Ouminus__class_Ouminus(_1416947), _1416951)))], (33598 ^ _784416) ^ [_1417086, _1417088, _1417090] : [class_Groups_Olinordered__ab__group__add(_1417086), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1417086), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1417086), _1417088), _1417090)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1417086), hAPP(c_Groups_Ouminus__class_Ouminus(_1417086), _1417088)), hAPP(c_Groups_Ouminus__class_Ouminus(_1417086), _1417090)))], (33604 ^ _784416) ^ [_1417225, _1417227] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1417225), _1417227)), _1417227) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1417225), _1417227))], (33606 ^ _784416) ^ [_1417268, _1417270] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1417268)), _1417270) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1417268), 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), _1417268)), _1417270))], (33608 ^ _784416) ^ [_1417316, _1417318] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1417316), hAPP(c_Nat_OSuc, _1417318)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1417318), 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)), _1417318)), _1417316))], (33610 ^ _784416) ^ [_1417364] : [class_Orderings_Oord(_1417364), -(c_Orderings_Oord__class_Omax(_1417364) = c_Orderings_Oord_Omax(_1417364, c_Orderings_Oord__class_Oless__eq(_1417364)))], (33616 ^ _784416) ^ [_1417451, _1417453, _1417455] : [class_Orderings_Olinorder(_1417451), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417451), _1417453)), hBOOL(hAPP(hAPP(c_member(_1417451), _1417455), _1417453)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1417451), _1417455), c_Big__Operators_Olinorder__class_OMax(_1417451, _1417453)) = c_Big__Operators_Olinorder__class_OMax(_1417451, _1417453))], (33630 ^ _784416) ^ [_1417686, _1417688, _1417690, _1417692, _1417694] : [class_Lattices_Osemilattice__sup(_1417686), class_Orderings_Olinorder(_1417688), c_Orderings_Oorder__class_Omono(_1417688, _1417686, _1417690), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1417686), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1417686), hAPP(_1417690, _1417692)), hAPP(_1417690, _1417694))), hAPP(_1417690, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1417688), _1417692), _1417694)))))], (33644 ^ _784416) ^ [_1417949, _1417951, _1417953, _1417955, _1417957] : [class_Orderings_Olinorder(_1417949), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1417949, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1417949, _1417951, _1417953)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1417949, _1417955, _1417957)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1417949, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1417949), _1417951), _1417955), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1417949), _1417953), _1417957)))], (33650 ^ _784416) ^ [_1418108, _1418110, _1418112, _1418114, _1418116] : [class_Orderings_Olinorder(_1418108), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418108, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1418108, _1418110, _1418112)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1418108, _1418114, _1418116)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1418108, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1418108), _1418110), _1418114), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1418108), _1418112), _1418116)))], (33656 ^ _784416) ^ [_1418267, _1418269] : [class_Orderings_Olinorder(_1418267), hBOOL(hAPP(c_Finite__Set_Ofinite(_1418267), _1418269)), -(c_Big__Operators_Olinorder__class_OMax(_1418267, _1418269) = hAPP(c_Finite__Set_Ofold1(_1418267, c_Orderings_Oord__class_Omax(_1418267)), _1418269))], (33666 ^ _784416) ^ [_1418424] : [class_Orderings_Olinorder(_1418424), -(c_Orderings_Oord_Omin(_1418424, hAPP(c_COMBC(_1418424, _1418424, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1418424))) = c_Orderings_Oord__class_Omax(_1418424))], (33672 ^ _784416) ^ [_1418525, _1418527, _1418529] : [class_Orderings_Olinorder(_1418525), hBOOL(hAPP(c_Finite__Set_Ofinite(_1418525), _1418527)), -(_1418527 = c_Orderings_Obot__class_Obot(tc_fun(_1418525, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1418525, hAPP(hAPP(c_Set_Oinsert(_1418525), _1418529), _1418527)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1418525), _1418529), c_Big__Operators_Olinorder__class_OMax(_1418525, _1418527)))], (33686 ^ _784416) ^ [_1418733, _1418735, _1418737] : [class_Orderings_Olinorder(_1418733), hBOOL(hAPP(c_Finite__Set_Ofinite(_1418733), _1418735)), -(_1418737 = c_Orderings_Obot__class_Obot(tc_fun(_1418733, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1418733, tc_HOL_Obool)), _1418737), _1418735)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1418733), c_Big__Operators_Olinorder__class_OMax(_1418733, _1418737)), c_Big__Operators_Olinorder__class_OMax(_1418733, _1418735)) = c_Big__Operators_Olinorder__class_OMax(_1418733, _1418735))], (33704 ^ _784416) ^ [_1419047, _1419049, _1419051] : [class_Orderings_Olinorder(_1419047), hBOOL(hAPP(c_Finite__Set_Ofinite(_1419047), _1419049)), hBOOL(hAPP(hAPP(c_member(_1419047), _1419051), _1419049)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1419047), _1419051), c_Big__Operators_Olattice_OInf__fin(_1419047, c_Orderings_Oord__class_Omin(_1419047), _1419049)) = _1419051)], (33718 ^ _784416) ^ [_1419282, _1419284, _1419286] : [class_Orderings_Olinorder(_1419282), hBOOL(hAPP(c_Finite__Set_Ofinite(_1419282), _1419284)), -(_1419284 = c_Orderings_Obot__class_Obot(tc_fun(_1419282, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1419282), _1419286)), -(_1419286 = c_Orderings_Obot__class_Obot(tc_fun(_1419282, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1419282, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1419282, tc_HOL_Obool)), _1419284), _1419286)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1419282), c_Big__Operators_Olinorder__class_OMax(_1419282, _1419284)), c_Big__Operators_Olinorder__class_OMax(_1419282, _1419286)))], (33740 ^ _784416) ^ [_1419631, _1419633, _1419635] : [class_Orderings_Olinorder(_1419631), hBOOL(hAPP(c_Finite__Set_Ofinite(_1419631), _1419633)), -(hBOOL(hAPP(hAPP(c_member(_1419631), _1419635), _1419633))), -(_1419633 = c_Orderings_Obot__class_Obot(tc_fun(_1419631, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1419631, hAPP(hAPP(c_Set_Oinsert(_1419631), _1419635), _1419633)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1419631), _1419635), c_Big__Operators_Olinorder__class_OMax(_1419631, _1419633)))], (33758 ^ _784416) ^ [_1419868, _1419870, _1419872] : [class_Orderings_Olinorder(_1419868), hBOOL(hAPP(c_Finite__Set_Ofinite(_1419868), _1419870)), 33765 ^ _784416 : [(33766 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1419868, tc_HOL_Obool)), _1419870), hAPP(hAPP(c_Set_Oinsert(_1419868), _1419872), c_Orderings_Obot__class_Obot(tc_fun(_1419868, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1419868, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1419868, hAPP(hAPP(c_Set_Oinsert(_1419868), _1419872), _1419870)) = _1419872)], (33772 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1419868, tc_HOL_Obool)), _1419870), hAPP(hAPP(c_Set_Oinsert(_1419868), _1419872), c_Orderings_Obot__class_Obot(tc_fun(_1419868, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1419868, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1419868, hAPP(hAPP(c_Set_Oinsert(_1419868), _1419872), _1419870)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1419868), _1419872), c_Big__Operators_Olinorder__class_OMax(_1419868, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1419868, tc_HOL_Obool)), _1419870), hAPP(hAPP(c_Set_Oinsert(_1419868), _1419872), c_Orderings_Obot__class_Obot(tc_fun(_1419868, tc_HOL_Obool)))))))]]], (33778 ^ _784416) ^ [_1420338, _1420340, _1420342] : [class_Orderings_Olinorder(_1420338), hBOOL(hAPP(c_Finite__Set_Ofinite(_1420338), _1420340)), -(_1420340 = c_Orderings_Obot__class_Obot(tc_fun(_1420338, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1420338), _1420342)), -(_1420342 = c_Orderings_Obot__class_Obot(tc_fun(_1420338, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420338, tc_HOL_Obool)), _1420340), _1420342) = c_Orderings_Obot__class_Obot(tc_fun(_1420338, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1420338, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420338, tc_HOL_Obool)), _1420340), _1420342)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1420338), c_Big__Operators_Olinorder__class_OMax(_1420338, _1420340)), c_Big__Operators_Olinorder__class_OMax(_1420338, _1420342)))], (33804 ^ _784416) ^ [_1420815, _1420817, _1420819] : [class_Orderings_Olinorder(_1420815), hBOOL(hAPP(c_Finite__Set_Ofinite(_1420815), _1420817)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1420815), _1420819)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420815, tc_HOL_Obool)), _1420817), _1420819) = c_Orderings_Obot__class_Obot(tc_fun(_1420815, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1420815), c_Big__Operators_Olinorder__class_OMax(_1420815, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420815, tc_HOL_Obool)), _1420817), _1420819))), c_Big__Operators_Olinorder__class_OMax(_1420815, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1420815, tc_HOL_Obool)), _1420817), _1420819))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1420815), c_Big__Operators_Olinorder__class_OMax(_1420815, _1420817)), c_Big__Operators_Olinorder__class_OMax(_1420815, _1420819)))], (33822 ^ _784416) ^ [_1421163, _1421165, _1421167] : [class_Orderings_Olinorder(_1421163), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421163), _1421165)), hBOOL(hAPP(hAPP(c_member(_1421163), _1421167), _1421165)), 33833 ^ _784416 : [(33834 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1421163, tc_HOL_Obool)), _1421165), hAPP(hAPP(c_Set_Oinsert(_1421163), _1421167), c_Orderings_Obot__class_Obot(tc_fun(_1421163, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1421163, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1421163, _1421165) = _1421167)], (33840 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1421163, tc_HOL_Obool)), _1421165), hAPP(hAPP(c_Set_Oinsert(_1421163), _1421167), c_Orderings_Obot__class_Obot(tc_fun(_1421163, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1421163, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1421163, _1421165) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1421163), _1421167), c_Big__Operators_Olinorder__class_OMax(_1421163, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1421163, tc_HOL_Obool)), _1421165), hAPP(hAPP(c_Set_Oinsert(_1421163), _1421167), c_Orderings_Obot__class_Obot(tc_fun(_1421163, tc_HOL_Obool)))))))]]], (33846 ^ _784416) ^ [_1421669, _1421671] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421669)), hAPP(c_Nat_OSuc, _1421671)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1421669))), 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, _1421671))), 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)), _1421671)))))], (33848 ^ _784416) ^ [_1421735, _1421737] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1421735)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1421737)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1421737))), 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, _1421735))), 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), _1421735)), c_Int_Onat)))))], (33850 ^ _784416) ^ [_1421807, _1421809, _1421811, _1421813, _1421815] : [c_Typedef_Otype__definition(_1421807, _1421809, _1421811, _1421813, _1421815), -(hAPP(c_Set_Oimage(_1421809, _1421807, _1421813), _1421815) = c_Orderings_Otop__class_Otop(tc_fun(_1421807, tc_HOL_Obool)))], (33856 ^ _784416) ^ [_1421920, _1421922, _1421924, _1421926, _1421928] : [c_Typedef_Otype__definition(_1421920, _1421922, _1421924, _1421926, _1421928), -(hAPP(c_Set_Oimage(_1421920, _1421922, _1421924), c_Orderings_Otop__class_Otop(tc_fun(_1421920, tc_HOL_Obool))) = _1421928)], (33862 ^ _784416) ^ [_1422033, _1422035, _1422037] : [class_Orderings_Olinorder(_1422033), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422033), _1422035)), -(_1422035 = c_Orderings_Obot__class_Obot(tc_fun(_1422033, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1422033), _1422037)), -(_1422037 = c_Orderings_Obot__class_Obot(tc_fun(_1422033, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1422033), c_Big__Operators_Olattice_OSup__fin(_1422033, c_Orderings_Oord__class_Omax(_1422033), _1422035)), c_Big__Operators_Olattice_OSup__fin(_1422033, c_Orderings_Oord__class_Omax(_1422033), _1422037)) = c_Big__Operators_Olattice_OSup__fin(_1422033, c_Orderings_Oord__class_Omax(_1422033), hAPP(c_Set_OCollect(_1422033), hAPP(hAPP(c_COMBB(tc_fun(_1422033, tc_HOL_Obool), tc_HOL_Obool, _1422033), c_HOL_OEx(_1422033)), hAPP(hAPP(c_COMBB(tc_fun(_1422033, tc_fun(_1422033, tc_HOL_Obool)), tc_fun(_1422033, tc_HOL_Obool), _1422033), hAPP(c_COMBB(tc_fun(_1422033, tc_HOL_Obool), tc_HOL_Obool, _1422033), c_HOL_OEx(_1422033))), hAPP(hAPP(c_COMBC(_1422033, tc_fun(_1422033, tc_fun(_1422033, tc_HOL_Obool)), tc_fun(_1422033, tc_fun(_1422033, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1422033, tc_fun(tc_fun(_1422033, tc_HOL_Obool), tc_fun(_1422033, tc_HOL_Obool))), tc_fun(tc_fun(_1422033, tc_fun(_1422033, tc_HOL_Obool)), tc_fun(_1422033, tc_fun(_1422033, tc_HOL_Obool))), _1422033), c_COMBS(_1422033, tc_fun(_1422033, tc_HOL_Obool), tc_fun(_1422033, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1422033, tc_fun(_1422033, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1422033, tc_fun(tc_fun(_1422033, tc_HOL_Obool), tc_fun(_1422033, tc_HOL_Obool))), _1422033), hAPP(c_COMBB(tc_fun(_1422033, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1422033, tc_HOL_Obool), tc_fun(_1422033, tc_HOL_Obool)), _1422033), c_COMBS(_1422033, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1422033, tc_fun(_1422033, tc_HOL_Obool)), tc_fun(_1422033, tc_fun(_1422033, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1422033), hAPP(c_COMBB(tc_fun(_1422033, tc_HOL_Obool), tc_fun(_1422033, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1422033), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1422033), c_fconj))), hAPP(hAPP(c_COMBC(_1422033, tc_fun(_1422033, tc_fun(_1422033, _1422033)), tc_fun(_1422033, tc_fun(_1422033, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1422033, _1422033), tc_fun(_1422033, tc_HOL_Obool)), tc_fun(tc_fun(_1422033, tc_fun(_1422033, _1422033)), tc_fun(_1422033, tc_fun(_1422033, tc_HOL_Obool))), _1422033), c_COMBB(tc_fun(_1422033, _1422033), tc_fun(_1422033, tc_HOL_Obool), _1422033)), hAPP(hAPP(c_COMBB(tc_fun(_1422033, tc_HOL_Obool), tc_fun(tc_fun(_1422033, _1422033), tc_fun(_1422033, tc_HOL_Obool)), _1422033), c_COMBB(_1422033, tc_HOL_Obool, _1422033)), c_fequal))), c_Orderings_Oord__class_Omin(_1422033)))))), hAPP(hAPP(c_COMBC(_1422033, tc_fun(_1422033, tc_HOL_Obool), tc_fun(_1422033, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1422033, tc_HOL_Obool), tc_fun(_1422033, tc_HOL_Obool)), _1422033), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1422033)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1422033), c_fconj), hAPP(hAPP(c_COMBC(_1422033, tc_fun(_1422033, tc_HOL_Obool), tc_HOL_Obool), c_member(_1422033)), _1422035)))), hAPP(hAPP(c_COMBC(_1422033, tc_fun(_1422033, tc_HOL_Obool), tc_HOL_Obool), c_member(_1422033)), _1422037))))))))], (33884 ^ _784416) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (33886 ^ _784416) ^ [_1423168, _1423170, _1423172] : [class_Orderings_Olinorder(_1423168), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423168), _1423170)), hBOOL(hAPP(hAPP(c_member(_1423168), _1423172), _1423170)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1423168), _1423172), c_Big__Operators_Olattice_OSup__fin(_1423168, c_Orderings_Oord__class_Omax(_1423168), _1423170)) = c_Big__Operators_Olattice_OSup__fin(_1423168, c_Orderings_Oord__class_Omax(_1423168), _1423170))], (33900 ^ _784416) ^ [_1423415, _1423417] : [class_Orderings_Olinorder(_1423415), -(c_Big__Operators_Olattice_OSup__fin(_1423415, c_Orderings_Oord__class_Omax(_1423415), hAPP(hAPP(c_Set_Oinsert(_1423415), _1423417), c_Orderings_Obot__class_Obot(tc_fun(_1423415, tc_HOL_Obool)))) = _1423417)], (33906 ^ _784416) ^ [_1423528, _1423530] : [class_Orderings_Olinorder(_1423528), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423528), _1423530)), -(c_Big__Operators_Olattice_OSup__fin(_1423528, c_Orderings_Oord__class_Omax(_1423528), _1423530) = hAPP(c_Finite__Set_Ofold1(_1423528, c_Orderings_Oord__class_Omax(_1423528)), _1423530))], (33916 ^ _784416) ^ [_1423691, _1423693, _1423695, _1423697, _1423699, _1423701, _1423703] : [c_Typedef_Otype__definition(_1423691, _1423693, _1423695, _1423697, _1423699), 33919 ^ _784416 : [(33920 ^ _784416) ^ [] : [hAPP(_1423695, _1423701) = hAPP(_1423695, _1423703), -(_1423701 = _1423703)], (33926 ^ _784416) ^ [] : [_1423701 = _1423703, -(hAPP(_1423695, _1423701) = hAPP(_1423695, _1423703))]]], (33932 ^ _784416) ^ [_1423952, _1423954, _1423956, _1423958, _1423960, _1423962] : [c_Typedef_Otype__definition(_1423952, _1423954, _1423956, _1423958, _1423960), -(hAPP(_1423958, hAPP(_1423956, _1423962)) = _1423962)], (33938 ^ _784416) ^ [_1424055, _1424057, _1424059] : [class_Orderings_Olinorder(_1424055), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424055), _1424057)), -(_1424057 = c_Orderings_Obot__class_Obot(tc_fun(_1424055, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1424055, c_Orderings_Oord__class_Omax(_1424055), hAPP(hAPP(c_Set_Oinsert(_1424055), _1424059), _1424057)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1424055), _1424059), c_Big__Operators_Olattice_OSup__fin(_1424055, c_Orderings_Oord__class_Omax(_1424055), _1424057)))], (33952 ^ _784416) ^ [_1424275, _1424277, _1424279] : [class_Orderings_Olinorder(_1424275), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424275), _1424277)), -(_1424279 = c_Orderings_Obot__class_Obot(tc_fun(_1424275, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1424275, tc_HOL_Obool)), _1424279), _1424277)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1424275), c_Big__Operators_Olattice_OSup__fin(_1424275, c_Orderings_Oord__class_Omax(_1424275), _1424279)), c_Big__Operators_Olattice_OSup__fin(_1424275, c_Orderings_Oord__class_Omax(_1424275), _1424277)) = c_Big__Operators_Olattice_OSup__fin(_1424275, c_Orderings_Oord__class_Omax(_1424275), _1424277))], (33970 ^ _784416) ^ [_1424607, _1424609, _1424611] : [class_Orderings_Olinorder(_1424607), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424607), _1424609)), hBOOL(hAPP(hAPP(c_member(_1424607), _1424611), _1424609)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1424607), _1424611), c_Big__Operators_Olattice_OSup__fin(_1424607, c_Orderings_Oord__class_Omax(_1424607), _1424609)) = _1424611)], (33984 ^ _784416) ^ [_1424842, _1424844, _1424846] : [class_Orderings_Olinorder(_1424842), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424842), _1424844)), -(_1424844 = c_Orderings_Obot__class_Obot(tc_fun(_1424842, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1424842), _1424846)), -(_1424846 = c_Orderings_Obot__class_Obot(tc_fun(_1424842, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1424842, c_Orderings_Oord__class_Omax(_1424842), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1424842, tc_HOL_Obool)), _1424844), _1424846)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1424842), c_Big__Operators_Olattice_OSup__fin(_1424842, c_Orderings_Oord__class_Omax(_1424842), _1424844)), c_Big__Operators_Olattice_OSup__fin(_1424842, c_Orderings_Oord__class_Omax(_1424842), _1424846)))], (34006 ^ _784416) ^ [_1425209, _1425211, _1425213] : [class_Orderings_Olinorder(_1425209), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425209), _1425211)), -(hBOOL(hAPP(hAPP(c_member(_1425209), _1425213), _1425211))), -(_1425211 = c_Orderings_Obot__class_Obot(tc_fun(_1425209, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1425209, c_Orderings_Oord__class_Omax(_1425209), hAPP(hAPP(c_Set_Oinsert(_1425209), _1425213), _1425211)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1425209), _1425213), c_Big__Operators_Olattice_OSup__fin(_1425209, c_Orderings_Oord__class_Omax(_1425209), _1425211)))], (34024 ^ _784416) ^ [_1425458, _1425460, _1425462] : [class_Orderings_Olinorder(_1425458), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425458), _1425460)), 34031 ^ _784416 : [(34032 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1425458, tc_HOL_Obool)), _1425460), hAPP(hAPP(c_Set_Oinsert(_1425458), _1425462), c_Orderings_Obot__class_Obot(tc_fun(_1425458, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1425458, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1425458, c_Orderings_Oord__class_Omax(_1425458), hAPP(hAPP(c_Set_Oinsert(_1425458), _1425462), _1425460)) = _1425462)], (34038 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1425458, tc_HOL_Obool)), _1425460), hAPP(hAPP(c_Set_Oinsert(_1425458), _1425462), c_Orderings_Obot__class_Obot(tc_fun(_1425458, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1425458, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1425458, c_Orderings_Oord__class_Omax(_1425458), hAPP(hAPP(c_Set_Oinsert(_1425458), _1425462), _1425460)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1425458), _1425462), c_Big__Operators_Olattice_OSup__fin(_1425458, c_Orderings_Oord__class_Omax(_1425458), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1425458, tc_HOL_Obool)), _1425460), hAPP(hAPP(c_Set_Oinsert(_1425458), _1425462), c_Orderings_Obot__class_Obot(tc_fun(_1425458, tc_HOL_Obool)))))))]]], (34044 ^ _784416) ^ [_1425946, _1425948, _1425950] : [class_Orderings_Olinorder(_1425946), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425946), _1425948)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425946), _1425950)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425946, tc_HOL_Obool)), _1425948), _1425950) = c_Orderings_Obot__class_Obot(tc_fun(_1425946, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1425946), c_Big__Operators_Olattice_OSup__fin(_1425946, c_Orderings_Oord__class_Omax(_1425946), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1425946, tc_HOL_Obool)), _1425948), _1425950))), c_Big__Operators_Olattice_OSup__fin(_1425946, c_Orderings_Oord__class_Omax(_1425946), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425946, tc_HOL_Obool)), _1425948), _1425950))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1425946), c_Big__Operators_Olattice_OSup__fin(_1425946, c_Orderings_Oord__class_Omax(_1425946), _1425948)), c_Big__Operators_Olattice_OSup__fin(_1425946, c_Orderings_Oord__class_Omax(_1425946), _1425950)))], (34062 ^ _784416) ^ [_1426318, _1426320, _1426322] : [class_Orderings_Olinorder(_1426318), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426318), _1426320)), -(_1426320 = c_Orderings_Obot__class_Obot(tc_fun(_1426318, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426318), _1426322)), -(_1426322 = c_Orderings_Obot__class_Obot(tc_fun(_1426318, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426318, tc_HOL_Obool)), _1426320), _1426322) = c_Orderings_Obot__class_Obot(tc_fun(_1426318, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1426318, c_Orderings_Oord__class_Omax(_1426318), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426318, tc_HOL_Obool)), _1426320), _1426322)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1426318), c_Big__Operators_Olattice_OSup__fin(_1426318, c_Orderings_Oord__class_Omax(_1426318), _1426320)), c_Big__Operators_Olattice_OSup__fin(_1426318, c_Orderings_Oord__class_Omax(_1426318), _1426322)))], (34088 ^ _784416) ^ [_1426813, _1426815, _1426817] : [class_Orderings_Olinorder(_1426813), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426813), _1426815)), hBOOL(hAPP(hAPP(c_member(_1426813), _1426817), _1426815)), 34099 ^ _784416 : [(34100 ^ _784416) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1426813, tc_HOL_Obool)), _1426815), hAPP(hAPP(c_Set_Oinsert(_1426813), _1426817), c_Orderings_Obot__class_Obot(tc_fun(_1426813, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1426813, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1426813, c_Orderings_Oord__class_Omax(_1426813), _1426815) = _1426817)], (34106 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1426813, tc_HOL_Obool)), _1426815), hAPP(hAPP(c_Set_Oinsert(_1426813), _1426817), c_Orderings_Obot__class_Obot(tc_fun(_1426813, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1426813, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1426813, c_Orderings_Oord__class_Omax(_1426813), _1426815) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1426813), _1426817), c_Big__Operators_Olattice_OSup__fin(_1426813, c_Orderings_Oord__class_Omax(_1426813), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1426813, tc_HOL_Obool)), _1426815), hAPP(hAPP(c_Set_Oinsert(_1426813), _1426817), c_Orderings_Obot__class_Obot(tc_fun(_1426813, tc_HOL_Obool)))))))]]], (34112 ^ _784416) ^ [_1427337, _1427339] : [class_Orderings_Olinorder(_1427337), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427337), _1427339)), -(_1427339 = c_Orderings_Obot__class_Obot(tc_fun(_1427337, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1427337), c_Big__Operators_Olattice_OInf__fin(_1427337, c_Orderings_Oord__class_Omin(_1427337), _1427339)), c_Big__Operators_Olattice_OSup__fin(_1427337, c_Orderings_Oord__class_Omax(_1427337), _1427339))))], (34126 ^ _784416) ^ [_1427535, _1427537, _1427539, _1427541, _1427543, _1427545, _1427547] : [c_Typedef_Otype__definition(_1427535, _1427537, _1427539, _1427541, _1427543), hBOOL(hAPP(hAPP(c_member(_1427537), _1427545), _1427543)), hBOOL(hAPP(hAPP(c_member(_1427537), _1427547), _1427543)), 34137 ^ _784416 : [(34138 ^ _784416) ^ [] : [hAPP(_1427541, _1427545) = hAPP(_1427541, _1427547), -(_1427545 = _1427547)], (34144 ^ _784416) ^ [] : [_1427545 = _1427547, -(hAPP(_1427541, _1427545) = hAPP(_1427541, _1427547))]]], (34150 ^ _784416) ^ [_1427948, _1427950, _1427952, _1427954, _1427956, _1427958] : [c_Typedef_Otype__definition(_1427948, _1427950, _1427952, _1427954, _1427956), hBOOL(hAPP(hAPP(c_member(_1427950), _1427958), _1427956)), -(hAPP(_1427952, hAPP(_1427954, _1427958)) = _1427958)], (34160 ^ _784416) ^ [_1428125, _1428127, _1428129, _1428131, _1428133, _1428135] : [c_Typedef_Otype__definition(_1428125, _1428127, _1428129, _1428131, _1428133), -(hBOOL(hAPP(hAPP(c_member(_1428127), hAPP(_1428129, _1428135)), _1428133)))], (34166 ^ _784416) ^ [_1428236, _1428238, _1428240] : [class_Orderings_Olinorder(_1428236), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428236), _1428238)), -(_1428238 = c_Orderings_Obot__class_Obot(tc_fun(_1428236, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1428236), _1428240), c_Big__Operators_Olattice_OSup__fin(_1428236, c_Orderings_Oord__class_Omax(_1428236), _1428238)) = c_Big__Operators_Olattice_OSup__fin(_1428236, c_Orderings_Oord__class_Omax(_1428236), hAPP(c_Set_OCollect(_1428236), hAPP(hAPP(c_COMBB(tc_fun(_1428236, tc_HOL_Obool), tc_HOL_Obool, _1428236), c_HOL_OEx(_1428236)), hAPP(hAPP(c_COMBC(_1428236, tc_fun(_1428236, tc_HOL_Obool), tc_fun(_1428236, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1428236, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1428236, tc_HOL_Obool), tc_fun(_1428236, tc_HOL_Obool)), _1428236), c_COMBS(_1428236, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1428236, tc_HOL_Obool), tc_fun(_1428236, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1428236), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1428236), c_fconj)), hAPP(hAPP(c_COMBC(_1428236, tc_fun(_1428236, _1428236), tc_fun(_1428236, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1428236, tc_HOL_Obool), tc_fun(tc_fun(_1428236, _1428236), tc_fun(_1428236, tc_HOL_Obool)), _1428236), c_COMBB(_1428236, tc_HOL_Obool, _1428236)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1428236), _1428240))))), hAPP(hAPP(c_COMBC(_1428236, tc_fun(_1428236, tc_HOL_Obool), tc_HOL_Obool), c_member(_1428236)), _1428238))))))], (34180 ^ _784416) ^ [_1428734, _1428736] : [class_Orderings_Olinorder(_1428734), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428734), _1428736)), -(_1428736 = c_Orderings_Obot__class_Obot(tc_fun(_1428734, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1428734), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1428734), 34193 ^ [_1428734, _1428736]), 34194 ^ [_1428734, _1428736])), hAPP(hAPP(c_Set_Oinsert(_1428734), 34193 ^ [_1428734, _1428736]), hAPP(hAPP(c_Set_Oinsert(_1428734), 34194 ^ [_1428734, _1428736]), c_Orderings_Obot__class_Obot(tc_fun(_1428734, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1428734), c_Big__Operators_Olattice_OSup__fin(_1428734, c_Orderings_Oord__class_Omax(_1428734), _1428736)), _1428736)))], (34200 ^ _784416) ^ [_1429184, _1429186] : [class_Orderings_Olinorder(_1429184), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429184), _1429186)), -(_1429186 = c_Orderings_Obot__class_Obot(tc_fun(_1429184, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1429184), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1429184), 34213 ^ [_1429184, _1429186]), 34214 ^ [_1429184, _1429186])), hAPP(hAPP(c_Set_Oinsert(_1429184), 34213 ^ [_1429184, _1429186]), hAPP(hAPP(c_Set_Oinsert(_1429184), 34214 ^ [_1429184, _1429186]), c_Orderings_Obot__class_Obot(tc_fun(_1429184, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1429184), c_Big__Operators_Olinorder__class_OMax(_1429184, _1429186)), _1429186)))], (34220 ^ _784416) ^ [_1429628, _1429630, _1429632] : [class_Orderings_Olinorder(_1429628), hAPP(_1429630, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1429628), 34225 ^ [_1429628, _1429630, _1429632]), 34226 ^ [_1429628, _1429630, _1429632])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1429628), hAPP(_1429630, 34225 ^ [_1429628, _1429630, _1429632])), hAPP(_1429630, 34226 ^ [_1429628, _1429630, _1429632])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429628), _1429632)), -(_1429632 = c_Orderings_Obot__class_Obot(tc_fun(_1429628, tc_HOL_Obool))), -(hAPP(_1429630, c_Big__Operators_Olattice_OSup__fin(_1429628, c_Orderings_Oord__class_Omax(_1429628), _1429632)) = c_Big__Operators_Olattice_OSup__fin(_1429628, c_Orderings_Oord__class_Omax(_1429628), hAPP(c_Set_Oimage(_1429628, _1429628, _1429630), _1429632)))], (34240 ^ _784416) ^ [_1430043, _1430045, _1430047] : [class_Orderings_Olinorder(_1430043), hAPP(_1430045, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1430043), 34245 ^ [_1430043, _1430045, _1430047]), 34246 ^ [_1430043, _1430045, _1430047])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1430043), hAPP(_1430045, 34245 ^ [_1430043, _1430045, _1430047])), hAPP(_1430045, 34246 ^ [_1430043, _1430045, _1430047])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430043), _1430047)), -(_1430047 = c_Orderings_Obot__class_Obot(tc_fun(_1430043, tc_HOL_Obool))), -(hAPP(_1430045, c_Big__Operators_Olattice_OInf__fin(_1430043, c_Orderings_Oord__class_Omin(_1430043), _1430047)) = c_Big__Operators_Olattice_OInf__fin(_1430043, c_Orderings_Oord__class_Omin(_1430043), hAPP(c_Set_Oimage(_1430043, _1430043, _1430045), _1430047)))], (34260 ^ _784416) ^ [_1430458, _1430460, _1430462] : [class_Orderings_Olinorder(_1430458), hAPP(_1430460, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1430458), 34265 ^ [_1430458, _1430460, _1430462]), 34266 ^ [_1430458, _1430460, _1430462])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1430458), hAPP(_1430460, 34265 ^ [_1430458, _1430460, _1430462])), hAPP(_1430460, 34266 ^ [_1430458, _1430460, _1430462])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430458), _1430462)), -(_1430462 = c_Orderings_Obot__class_Obot(tc_fun(_1430458, tc_HOL_Obool))), -(hAPP(_1430460, c_Big__Operators_Olinorder__class_OMax(_1430458, _1430462)) = c_Big__Operators_Olinorder__class_OMax(_1430458, hAPP(c_Set_Oimage(_1430458, _1430458, _1430460), _1430462)))], (34280 ^ _784416) ^ [_1430861, _1430863, _1430865] : [class_Orderings_Olinorder(_1430861), hAPP(_1430863, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1430861), 34285 ^ [_1430861, _1430863, _1430865]), 34286 ^ [_1430861, _1430863, _1430865])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1430861), hAPP(_1430863, 34285 ^ [_1430861, _1430863, _1430865])), hAPP(_1430863, 34286 ^ [_1430861, _1430863, _1430865])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430861), _1430865)), -(_1430865 = c_Orderings_Obot__class_Obot(tc_fun(_1430861, tc_HOL_Obool))), -(hAPP(_1430863, c_Big__Operators_Olinorder__class_OMin(_1430861, _1430865)) = c_Big__Operators_Olinorder__class_OMin(_1430861, hAPP(c_Set_Oimage(_1430861, _1430861, _1430863), _1430865)))], (34300 ^ _784416) ^ [_1431264, _1431266, _1431268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1431264)), 34306 ^ _784416 : [(34307 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1431266, 34305 ^ [_1431264, _1431266, _1431268])))], (34309 ^ _784416) ^ [] : [hBOOL(hAPP(_1431266, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 34305 ^ [_1431264, _1431266, _1431268]), _1431264)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1431268)), 34314 ^ _784416 : [(34315 ^ _784416) ^ [_1431553] : [hBOOL(hAPP(_1431266, _1431553)), -(hBOOL(hAPP(_1431266, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1431553), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1431268), _1431264)))))]]], (34321 ^ _784416) ^ [_1431676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431676), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1431676 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 34324 ^ [_1431676]))))], (34328 ^ _784416) ^ [_1431789, _1431791, _1431793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1431789)), 34334 ^ _784416 : [(34335 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1431791, 34333 ^ [_1431789, _1431791, _1431793])))], (34337 ^ _784416) ^ [] : [hBOOL(hAPP(_1431791, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 34333 ^ [_1431789, _1431791, _1431793]), _1431789)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1431793)), 34342 ^ _784416 : [(34343 ^ _784416) ^ [_1432078] : [hBOOL(hAPP(_1431791, _1432078)), -(hBOOL(hAPP(_1431791, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1432078), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1431793), _1431789)))))]]], (34349 ^ _784416) ^ [_1432201, _1432203, _1432205, _1432207, _1432209, _1432211, _1432213, _1432215] : [class_Groups_Ocomm__monoid__mult(_1432201), c_Fun_Oinj__on(_1432203, _1432205, _1432207, _1432209), _1432211 = hAPP(c_Set_Oimage(_1432203, _1432205, _1432207), _1432209), 34363 ^ _784416 : [(34364 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1432203), 34362 ^ [_1432201, _1432203, _1432205, _1432207, _1432209, _1432211, _1432213, _1432215]), _1432209)))], (34366 ^ _784416) ^ [] : [hAPP(_1432213, 34362 ^ [_1432201, _1432203, _1432205, _1432207, _1432209, _1432211, _1432213, _1432215]) = hAPP(hAPP(c_Fun_Ocomp(_1432205, _1432201, _1432203, _1432215), _1432207), 34362 ^ [_1432201, _1432203, _1432205, _1432207, _1432209, _1432211, _1432213, _1432215])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1432205, _1432201), _1432215), _1432211) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1432203, _1432201), _1432213), _1432209))], (34370 ^ _784416) ^ [_1432709, _1432711, _1432713, _1432715, _1432717] : [class_Groups_Ocomm__monoid__mult(_1432709), hBOOL(hAPP(c_Finite__Set_Ofinite(_1432711), _1432713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432711, tc_HOL_Obool)), _1432715), _1432713)), 34384 ^ _784416 : [(34385 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1432711), 34383 ^ [_1432709, _1432711, _1432713, _1432715, _1432717]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1432711, tc_HOL_Obool)), _1432713), _1432715))))], (34387 ^ _784416) ^ [] : [hAPP(_1432717, 34383 ^ [_1432709, _1432711, _1432713, _1432715, _1432717]) = c_Groups_Oone__class_Oone(_1432709)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1432711, _1432709), _1432717), _1432715) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1432711, _1432709), _1432717), _1432713))], (34391 ^ _784416) ^ [_1433160, _1433162, _1433164, _1433166, _1433168] : [class_Groups_Ocomm__monoid__mult(_1433160), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433162), _1433164)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1433162, tc_HOL_Obool)), _1433166), _1433164)), 34405 ^ _784416 : [(34406 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1433162), 34404 ^ [_1433160, _1433162, _1433164, _1433166, _1433168]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1433162, tc_HOL_Obool)), _1433164), _1433166))))], (34408 ^ _784416) ^ [] : [hAPP(_1433168, 34404 ^ [_1433160, _1433162, _1433164, _1433166, _1433168]) = c_Groups_Oone__class_Oone(_1433160)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1433162, _1433160), _1433168), _1433164) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1433162, _1433160), _1433168), _1433166))], (34412 ^ _784416) ^ [_1433611] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1433611)), 34416 ^ _784416 : [(34417 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 34415 ^ [_1433611])))], (34419 ^ _784416) ^ [] : [-(_1433611 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 34415 ^ [_1433611]))]]], (34421 ^ _784416) ^ [_1433741, _1433743, _1433745, _1433747] : [class_Orderings_Olinorder(_1433741), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1433741), _1433743), _1433745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433741), _1433745), _1433747)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1433741, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1433741, _1433743, _1433745)), c_SetInterval_Oord__class_OatLeastAtMost(_1433741, _1433745, _1433747)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1433741, _1433743, _1433747))], (34435 ^ _784416) ^ [_1434006, _1434008, _1434010] : [class_Orderings_Olinorder(_1434006), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434006), _1434008), _1434010)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1434006, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1434006), _1434008), c_Orderings_Obot__class_Obot(tc_fun(_1434006, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1434006, _1434008, _1434010)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1434006, _1434008), _1434010))], (34445 ^ _784416) ^ [_1434219, _1434221] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1434219), _1434221))))], (34447 ^ _784416) ^ [_1434252, _1434254] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1434252, _1434254))))], (34449 ^ _784416) ^ [_1434283, _1434285] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1434283, _1434285))))], (34451 ^ _784416) ^ [_1434314, _1434316] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1434314), _1434316))))], (34453 ^ _784416) ^ [_1434347, _1434349] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1434347, _1434349) = 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), _1434347), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1434349))))], (34455 ^ _784416) ^ [_1434389, _1434391, _1434393] : [-(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)), _1434389)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1434391), _1434393)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1434391), _1434389)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1434393), _1434389)))], (34457 ^ _784416) ^ [_1434450, _1434452] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1434450), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1434452), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1434450, _1434452))], (34459 ^ _784416) ^ [_1434491, _1434493] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1434491), _1434493)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1434491)), hAPP(c_Nat_OSuc, _1434493)))], (34461 ^ _784416) ^ [_1434537, _1434539] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1434537, _1434539)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1434537), hAPP(c_Nat_OSuc, _1434539)))], (34463 ^ _784416) ^ [_1434579, _1434581, _1434583] : [-(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)), _1434579)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1434581, _1434583)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1434581), _1434579), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1434583), _1434579)))], (34465 ^ _784416) ^ [_1434636, _1434638] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1434636), hAPP(c_Nat_OSuc, _1434638)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1434636, _1434638))], (34467 ^ _784416) ^ [_1434674, _1434676, _1434678, _1434680, _1434682] : [class_Orderings_Olinorder(_1434674), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434674), _1434676), _1434678)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1434674), _1434680), _1434682)), 34478 ^ _784416 : [(34479 ^ _784416) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1434674, _1434676), _1434678) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1434674, _1434680), _1434682), 34482 ^ _784416 : [(34483 ^ _784416) ^ [] : [-(_1434676 = _1434680)], (34485 ^ _784416) ^ [] : [-(_1434678 = _1434682)]]], (34487 ^ _784416) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1434674, _1434676), _1434678) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1434674, _1434680), _1434682)), _1434676 = _1434680, _1434678 = _1434682]]], (34497 ^ _784416) ^ [_1435155, _1435157, _1435159, _1435161, _1435163] : [class_Orderings_Olinorder(_1435155), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1435155, _1435157), _1435159) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1435155, _1435161), _1435163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1435155), _1435157), _1435159)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1435155), _1435161), _1435163)), -(_1435157 = _1435161)], (34515 ^ _784416) ^ [_1435462, _1435464, _1435466, _1435468, _1435470] : [class_Orderings_Olinorder(_1435462), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1435462, _1435464), _1435466) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1435462, _1435468), _1435470), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1435462), _1435464), _1435466)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1435462), _1435468), _1435470)), -(_1435466 = _1435470)], (34533 ^ _784416) ^ [_1435769, _1435771, _1435773, _1435775] : [class_Orderings_Oorder(_1435769), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435769, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1435769, _1435771), _1435773)), c_SetInterval_Oord__class_OatLeastAtMost(_1435769, _1435773, _1435775)) = c_Orderings_Obot__class_Obot(tc_fun(_1435769, tc_HOL_Obool)))], (34539 ^ _784416) ^ [_1435900, _1435902, _1435904, _1435906] : [class_Orderings_Olinorder(_1435900), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435900), _1435902), _1435904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1435900), _1435904), _1435906)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1435900, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1435900, _1435902), _1435904)), c_SetInterval_Oord__class_OatLeastAtMost(_1435900, _1435904, _1435906)) = c_SetInterval_Oord__class_OatLeastAtMost(_1435900, _1435902, _1435906))], (34553 ^ _784416) ^ [_1436169, _1436171] : [c_Nat__Transfer_Ois__nat(_1436169), c_Nat__Transfer_Ois__nat(_1436171), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1436169, _1436171) = 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, _1436169), hAPP(c_Int_Onat, _1436171))))], (34563 ^ _784416) ^ [_1436328] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1436328), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (34565 ^ _784416) ^ [_1436357, _1436359, _1436361] : [class_Orderings_Olinorder(_1436357), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436357), _1436359), _1436361)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1436357, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1436357, _1436359), _1436361)), hAPP(hAPP(c_Set_Oinsert(_1436357), _1436361), c_Orderings_Obot__class_Obot(tc_fun(_1436357, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1436357, _1436359, _1436361))], (34575 ^ _784416) ^ [_1436570, _1436572] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1436570), _1436572)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1436572), _1436570))], (34577 ^ _784416) ^ [_1436610, _1436612] : [c_Nat__Transfer_Ois__nat(_1436610), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1436610, _1436612)))], (34583 ^ _784416) ^ [_1436691, _1436693, _1436695, _1436697] : [class_Orderings_Olinorder(_1436691), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436691), _1436693), _1436695)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436691), _1436695), _1436697)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1436691, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1436691, _1436693, _1436695)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1436691, _1436695, _1436697)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1436691, _1436693), _1436697))], (34597 ^ _784416) ^ [_1436960, _1436962, _1436964] : [class_Orderings_Oorder(_1436960), 34600 ^ _784416 : [(34601 ^ _784416) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1436960, _1436962, _1436964) = c_Orderings_Obot__class_Obot(tc_fun(_1436960, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436960), _1436962), _1436964))], (34607 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436960), _1436962), _1436964))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1436960, _1436962, _1436964) = c_Orderings_Obot__class_Obot(tc_fun(_1436960, tc_HOL_Obool)))]]], (34613 ^ _784416) ^ [_1437179, _1437181, _1437183] : [class_Orderings_Oorder(_1437179), 34616 ^ _784416 : [(34617 ^ _784416) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1437179, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1437179, _1437181, _1437183), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437179), _1437181), _1437183))], (34623 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437179), _1437181), _1437183))), -(c_Orderings_Obot__class_Obot(tc_fun(_1437179, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1437179, _1437181, _1437183))]]], (34629 ^ _784416) ^ [_1437398, _1437400, _1437402] : [class_Orderings_Oorder(_1437398), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1437398), _1437400), _1437402)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1437398, _1437402, _1437400) = c_Orderings_Obot__class_Obot(tc_fun(_1437398, tc_HOL_Obool)))], (34639 ^ _784416) ^ [_1437561, _1437563, _1437565, _1437567, _1437569] : [class_Orderings_Oorder(_1437561), 34642 ^ _784416 : [(34643 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437561, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1437561, _1437563, _1437565)), c_SetInterval_Oord__class_OatLeastAtMost(_1437561, _1437567, _1437569))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437561), _1437563), _1437565)), 34650 ^ _784416 : [(34651 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437561), _1437567), _1437563)))], (34653 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437561), _1437565), _1437569)))]]], (34655 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437561, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1437561, _1437563, _1437565)), c_SetInterval_Oord__class_OatLeastAtMost(_1437561, _1437567, _1437569)))), 34656 ^ _784416 : [(34657 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437561), _1437563), _1437565)))], (34659 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437561), _1437567), _1437563)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437561), _1437565), _1437569))]]]]], (34667 ^ _784416) ^ [_1438064, _1438066, _1438068] : [class_Orderings_Oorder(_1438064), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438064), _1438066), _1438068)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1438064, _1438068), _1438066) = c_Orderings_Obot__class_Obot(tc_fun(_1438064, tc_HOL_Obool)))], (34677 ^ _784416) ^ [_1438231, _1438233, _1438235] : [class_Orderings_Oorder(_1438231), 34680 ^ _784416 : [(34681 ^ _784416) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1438231, _1438233), _1438235) = c_Orderings_Obot__class_Obot(tc_fun(_1438231, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1438231), _1438233), _1438235))], (34687 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1438231), _1438233), _1438235))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1438231, _1438233), _1438235) = c_Orderings_Obot__class_Obot(tc_fun(_1438231, tc_HOL_Obool)))]]], (34693 ^ _784416) ^ [_1438456, _1438458, _1438460] : [class_Orderings_Oorder(_1438456), 34696 ^ _784416 : [(34697 ^ _784416) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1438456, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1438456, _1438458), _1438460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1438456), _1438458), _1438460))], (34703 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1438456), _1438458), _1438460))), -(c_Orderings_Obot__class_Obot(tc_fun(_1438456, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1438456, _1438458), _1438460))]]], (34709 ^ _784416) ^ [_1438681, _1438683, _1438685] : [class_Orderings_Oorder(_1438681), _1438683 = _1438685, -(c_SetInterval_Oord__class_OatLeastAtMost(_1438681, _1438683, _1438685) = hAPP(hAPP(c_Set_Oinsert(_1438681), _1438683), c_Orderings_Obot__class_Obot(tc_fun(_1438681, tc_HOL_Obool))))], (34719 ^ _784416) ^ [_1438846, _1438848, _1438850, _1438852] : [class_Orderings_Oorder(_1438846), 34722 ^ _784416 : [(34723 ^ _784416) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1438846, _1438848, _1438850) = hAPP(hAPP(c_Set_Oinsert(_1438846), _1438852), c_Orderings_Obot__class_Obot(tc_fun(_1438846, tc_HOL_Obool))), 34726 ^ _784416 : [(34727 ^ _784416) ^ [] : [-(_1438848 = _1438850)], (34729 ^ _784416) ^ [] : [-(_1438850 = _1438852)]]], (34731 ^ _784416) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1438846, _1438848, _1438850) = hAPP(hAPP(c_Set_Oinsert(_1438846), _1438852), c_Orderings_Obot__class_Obot(tc_fun(_1438846, tc_HOL_Obool)))), _1438848 = _1438850, _1438850 = _1438852]]], (34741 ^ _784416) ^ [_1439190, _1439192] : [class_Orderings_Oorder(_1439190), -(c_SetInterval_Oord__class_OatLeastAtMost(_1439190, _1439192, _1439192) = hAPP(hAPP(c_Set_Oinsert(_1439190), _1439192), c_Orderings_Obot__class_Obot(tc_fun(_1439190, tc_HOL_Obool))))], (34747 ^ _784416) ^ [_1439299, _1439301, _1439303, _1439305, _1439307] : [class_Orderings_Olinorder(_1439299), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1439299, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1439299, _1439301), _1439303)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1439299, _1439305), _1439307))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439299), _1439303), _1439301))), 34758 ^ _784416 : [(34759 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439299), _1439305), _1439301)))], (34761 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439299), _1439303), _1439307)))]]], (34763 ^ _784416) ^ [_1439580, _1439582, _1439584, _1439586] : [class_Orderings_Olinorder(_1439580), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439580), _1439582), _1439584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439580), _1439584), _1439586)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1439580, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1439580, _1439582), _1439584)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1439580, _1439584), _1439586)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1439580, _1439582), _1439586))], (34777 ^ _784416) ^ [_1439857, _1439859, _1439861] : [class_Groups_Oordered__ab__group__add(_1439857), -(hAPP(c_Set_Oimage(_1439857, _1439857, c_Groups_Ouminus__class_Ouminus(_1439857)), c_SetInterval_Oord__class_OatLeastAtMost(_1439857, _1439859, _1439861)) = c_SetInterval_Oord__class_OatLeastAtMost(_1439857, hAPP(c_Groups_Ouminus__class_Ouminus(_1439857), _1439861), hAPP(c_Groups_Ouminus__class_Ouminus(_1439857), _1439859)))], (34783 ^ _784416) ^ [_1439988, _1439990, _1439992, _1439994] : [class_Orderings_Olinorder(_1439988), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1439988), _1439990), _1439992)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1439988, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1439988, _1439990), _1439994)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1439988, _1439990), _1439992)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1439988, _1439992), _1439994))], (34793 ^ _784416) ^ [_1440195, _1440197] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1440195, 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(_1440195, tc_HOL_Obool)), tc_fun(_1440195, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1440195, tc_HOL_Obool)), tc_fun(_1440195, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1440195, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1440197)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1440195, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1440197))], (34795 ^ _784416) ^ [_1440291, _1440293, _1440295, _1440297] : [class_Orderings_Oorder(_1440291), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440291, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1440291, _1440293), _1440295)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1440291, _1440295), _1440297)) = c_Orderings_Obot__class_Obot(tc_fun(_1440291, tc_HOL_Obool)))], (34801 ^ _784416) ^ [_1440426, _1440428] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1440426)), _1440428) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1440426, _1440428))], (34803 ^ _784416) ^ [_1440464, _1440466] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1440464), _1440466) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1440464, _1440466))], (34805 ^ _784416) ^ [_1440500] : [-(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)), _1440500))))], (34807 ^ _784416) ^ [_1440528, _1440530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1440528)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1440528, _1440530)))], (34813 ^ _784416) ^ [_1440615, _1440617] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1440615, _1440617)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1440617)), _1440615))], (34815 ^ _784416) ^ [_1440656, _1440658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1440656), hAPP(c_Nat_OSuc, _1440658))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1440656, hAPP(c_Nat_OSuc, _1440658)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1440658)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1440656, _1440658)))], (34821 ^ _784416) ^ [_1440789] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1440789), hAPP(c_Nat_OSuc, _1440789)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1440789), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (34823 ^ _784416) ^ [_1440827, _1440829] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1440827), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1440829) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1440827, _1440829))], (34825 ^ _784416) ^ [_1440866, _1440868, _1440870, _1440872, _1440874] : [class_Orderings_Olinorder(_1440866), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1440866, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1440866, _1440868, _1440870)), c_SetInterval_Oord__class_OatLeastAtMost(_1440866, _1440872, _1440874)) = c_SetInterval_Oord__class_OatLeastAtMost(_1440866, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1440866), _1440868), _1440872), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1440866), _1440870), _1440874)))], (34831 ^ _784416) ^ [_1441025, _1441027, _1441029, _1441031, _1441033] : [class_Orderings_Oorder(_1441025), 34834 ^ _784416 : [(34835 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1441025, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1441025, _1441027, _1441029)), c_SetInterval_Oord__class_OatLeastAtMost(_1441025, _1441031, _1441033))), 34838 ^ _784416 : [(34853 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1441025), _1441031), _1441033)))], (34839 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1441025), _1441027), _1441029)), 34842 ^ _784416 : [(34843 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1441025), _1441031), _1441027)))], (34845 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1441025), _1441029), _1441033)))], (34847 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441025), _1441031), _1441027))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441025), _1441029), _1441033)))]]]]], (34855 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1441025, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1441025, _1441027, _1441029)), c_SetInterval_Oord__class_OatLeastAtMost(_1441025, _1441031, _1441033)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1441025), _1441031), _1441033)), 34858 ^ _784416 : [(34859 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1441025), _1441027), _1441029)))], (34861 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1441025), _1441031), _1441027)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1441025), _1441029), _1441033)), 34868 ^ _784416 : [(34869 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441025), _1441031), _1441027))], (34871 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441025), _1441029), _1441033))]]]]]]], (34877 ^ _784416) ^ [_1441796, _1441798, _1441800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1441796), _1441798)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1441796), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1441798), _1441800)) = 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, _1441796), _1441798)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1441798), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1441798), _1441800))))], (34883 ^ _784416) ^ [_1441957, _1441959, _1441961, _1441963, _1441965] : [class_Orderings_Olinorder(_1441957), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441957, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1441957, _1441959), _1441961)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1441957, _1441963), _1441965)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1441957, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1441957), _1441959), _1441963)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1441957), _1441961), _1441965)))], (34889 ^ _784416) ^ [_1442128, _1442130, _1442132, _1442134] : [class_Orderings_Olinorder(_1442128), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442128), _1442130), _1442132)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442128), _1442132), _1442134)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442128, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1442128, _1442130, _1442132)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1442128, _1442132, _1442134)) = c_SetInterval_Oord__class_OatLeastAtMost(_1442128, _1442130, _1442134))], (34903 ^ _784416) ^ [_1442393, _1442395, _1442397, _1442399] : [class_Orderings_Oorder(_1442393), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442393, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1442393, _1442395, _1442397)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1442393, _1442397, _1442399)) = c_Orderings_Obot__class_Obot(tc_fun(_1442393, tc_HOL_Obool)))], (34909 ^ _784416) ^ [_1442520, _1442522, _1442524, _1442526] : [class_Orderings_Oorder(_1442520), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442520, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1442520, _1442522, _1442524)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1442520, _1442524, _1442526)) = c_Orderings_Obot__class_Obot(tc_fun(_1442520, tc_HOL_Obool)))], (34915 ^ _784416) ^ [_1442647, _1442649, _1442651, _1442653] : [class_Orderings_Oorder(_1442647), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442647, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1442647, _1442649, _1442651)), c_SetInterval_Oord__class_OatLeastAtMost(_1442647, _1442651, _1442653)) = c_Orderings_Obot__class_Obot(tc_fun(_1442647, tc_HOL_Obool)))], (34921 ^ _784416) ^ [_1442774, _1442776] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1442774), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1442776), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1442776), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1442774))))), -(_1442774 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1442776), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1442776), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1442774))))], (34927 ^ _784416) ^ [_1442921, _1442923, _1442925, _1442927] : [class_Orderings_Oorder(_1442921), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442921, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1442921, _1442923, _1442925)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1442921, _1442925), _1442927)) = c_Orderings_Obot__class_Obot(tc_fun(_1442921, tc_HOL_Obool)))], (34933 ^ _784416) ^ [_1443052, _1443054, _1443056] : [class_Groups_Oordered__ab__group__add(_1443052), -(hAPP(c_Set_Oimage(_1443052, _1443052, c_Groups_Ouminus__class_Ouminus(_1443052)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1443052, _1443054, _1443056)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443052, hAPP(c_Groups_Ouminus__class_Ouminus(_1443052), _1443056)), hAPP(c_Groups_Ouminus__class_Ouminus(_1443052), _1443054)))], (34939 ^ _784416) ^ [_1443187, _1443189, _1443191] : [class_Groups_Oordered__ab__group__add(_1443187), -(hAPP(c_Set_Oimage(_1443187, _1443187, c_Groups_Ouminus__class_Ouminus(_1443187)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443187, _1443189), _1443191)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1443187, hAPP(c_Groups_Ouminus__class_Ouminus(_1443187), _1443191), hAPP(c_Groups_Ouminus__class_Ouminus(_1443187), _1443189)))], (34945 ^ _784416) ^ [_1443322, _1443324] : [-(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)), _1443322)), 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), _1443324), _1443322))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1443322), _1443324))], (34947 ^ _784416) ^ [_1443372] : [-(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)), _1443372)) = hAPP(c_Int_Onat, _1443372))], (34949 ^ _784416) ^ [_1443404, _1443406] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1443404), _1443406)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1443406), _1443404)))], (34951 ^ _784416) ^ [_1443447, _1443449] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1443447), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1443449) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1443447, _1443449))], (34953 ^ _784416) ^ [_1443497, _1443499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1443497), _1443499)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1443497), hAPP(c_Nat_OSuc, _1443499)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1443499), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1443497), _1443499)))], (34959 ^ _784416) ^ [_1443620, _1443622] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1443620), _1443622))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1443620), hAPP(c_Nat_OSuc, _1443622)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (34965 ^ _784416) ^ [_1443681, _1443683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1443681), _1443683)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1443683, _1443681) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (34971 ^ _784416) ^ [_1443770, _1443772] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1443770), _1443772))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1443772, _1443770) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1443772), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1443772), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1443770)))], (34977 ^ _784416) ^ [_1443833, _1443835, _1443837, _1443839] : [class_Orderings_Olinorder(_1443833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1443833), _1443835), _1443837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443833), _1443837), _1443839)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1443833, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1443833, _1443835, _1443837)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1443833, _1443837), _1443839)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1443833, _1443835, _1443839))], (34991 ^ _784416) ^ [_1444102, _1444104] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1444102, _1444104)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1444104), _1444102)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (34993 ^ _784416) ^ [_1444161, _1444163, _1444165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1444161), _1444163)), -(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)), _1444161)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1444165), _1444163)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1444165), _1444161)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1444163), _1444161)))], (34999 ^ _784416) ^ [_1444313, _1444315, _1444317] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1444313), _1444315))), 35002 ^ _784416 : [(35003 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1444317), _1444315)), -(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)), _1444313)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1444317), _1444315)) = 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))))], (35009 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1444317), _1444315))), -(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)), _1444313)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1444317), _1444315)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))]]], (35015 ^ _784416) ^ [_1444582, _1444584, _1444586] : [class_Orderings_Olinorder(_1444582), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1444582), _1444584), _1444586)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1444582, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1444582), _1444584), c_Orderings_Obot__class_Obot(tc_fun(_1444582, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1444582, _1444584, _1444586)) = c_SetInterval_Oord__class_OatLeastAtMost(_1444582, _1444584, _1444586))], (35025 ^ _784416) ^ [_1444791, _1444793, _1444795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1444791)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1444793), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1444795)), 35032 ^ _784416 : [(35033 ^ _784416) ^ [_1444999] : [35035 ^ _784416 : [(35036 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35034 ^ [_1444791, _1444793, _1444795, _1444999]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1444791))))], (35039 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35037 ^ [_1444791, _1444793, _1444795, _1444999]), _1444795)))], (35041 ^ _784416) ^ [] : [-(_1444999 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35037 ^ [_1444791, _1444793, _1444795, _1444999]), 35034 ^ [_1444791, _1444793, _1444795, _1444999]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1444793), _1444999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1444793), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1444999), _1444791))))]]], (35049 ^ _784416) ^ [_1445275, _1445277, _1445279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1445275)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445277), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1445279)), 35056 ^ _784416 : [(35057 ^ _784416) ^ [_1445483] : [35059 ^ _784416 : [(35060 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35058 ^ [_1445275, _1445277, _1445279, _1445483]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1445275))))], (35063 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35061 ^ [_1445275, _1445277, _1445279, _1445483]), _1445279)))], (35065 ^ _784416) ^ [] : [-(_1445483 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35061 ^ [_1445275, _1445277, _1445279, _1445483]), 35058 ^ [_1445275, _1445277, _1445279, _1445483]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1445483), _1445277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445483), _1445275)), _1445277)))]]], (35073 ^ _784416) ^ [_1445759, _1445761, _1445763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1445759)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1445761), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1445763)), 35083 ^ _784416 : [(35084 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35082 ^ [_1445759, _1445761, _1445763]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1445759))))], (35087 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35085 ^ [_1445759, _1445761, _1445763]), _1445763)))], (35089 ^ _784416) ^ [] : [-(_1445761 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35085 ^ [_1445759, _1445761, _1445763]), 35082 ^ [_1445759, _1445761, _1445763]))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1445761), _1445759) = _1445761)], (35093 ^ _784416) ^ [_1446113, _1446115] : [35101 ^ _784416 : [(35102 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 35100 ^ [_1446113, _1446115]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1446113))))], (35104 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1446115, 35100 ^ [_1446113, _1446115])))]], 35094 ^ _784416 : [(35095 ^ _784416) ^ [_1446182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1446182), _1446113)), hBOOL(hAPP(_1446115, _1446182))]]], (35106 ^ _784416) ^ [_1446343, _1446345] : [35114 ^ _784416 : [(35115 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 35113 ^ [_1446343, _1446345]), _1446343)))], (35117 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1446345, 35113 ^ [_1446343, _1446345])))]], 35107 ^ _784416 : [(35108 ^ _784416) ^ [_1446412] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1446412), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1446343))), hBOOL(hAPP(_1446345, _1446412))]]], (35119 ^ _784416) ^ [_1446598, _1446600] : [35121 ^ _784416 : [(35122 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 35120 ^ [_1446598, _1446600]), _1446598)))], (35124 ^ _784416) ^ [] : [hBOOL(hAPP(_1446600, 35120 ^ [_1446598, _1446600]))]], 35125 ^ _784416 : [(35126 ^ _784416) ^ [_1446749] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1446749), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1446598))), -(hBOOL(hAPP(_1446600, _1446749)))]]], (35132 ^ _784416) ^ [_1446852, _1446854] : [35134 ^ _784416 : [(35135 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 35133 ^ [_1446852, _1446854]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1446852))))], (35137 ^ _784416) ^ [] : [hBOOL(hAPP(_1446854, 35133 ^ [_1446852, _1446854]))]], 35138 ^ _784416 : [(35139 ^ _784416) ^ [_1447007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1447007), _1446852)), -(hBOOL(hAPP(_1446854, _1447007)))]]], (35145 ^ _784416) ^ [_1447123, _1447125] : [35147 ^ _784416 : [(35148 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 35146 ^ [_1447123, _1447125]), _1447123)))], (35150 ^ _784416) ^ [] : [hBOOL(hAPP(_1447125, 35146 ^ [_1447123, _1447125]))]], 35151 ^ _784416 : [(35152 ^ _784416) ^ [_1447273] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1447273), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1447123))), -(hBOOL(hAPP(_1447125, _1447273)))]]], (35158 ^ _784416) ^ [_1447374, _1447376] : [35160 ^ _784416 : [(35161 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 35159 ^ [_1447374, _1447376]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1447374))))], (35163 ^ _784416) ^ [] : [hBOOL(hAPP(_1447376, 35159 ^ [_1447374, _1447376]))]], 35164 ^ _784416 : [(35165 ^ _784416) ^ [_1447527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1447527), _1447374)), -(hBOOL(hAPP(_1447376, _1447527)))]]], (35171 ^ _784416) ^ [_1447643, _1447645] : [35179 ^ _784416 : [(35180 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 35178 ^ [_1447643, _1447645]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1447643))))], (35182 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1447645, 35178 ^ [_1447643, _1447645])))]], 35172 ^ _784416 : [(35173 ^ _784416) ^ [_1447711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1447711), _1447643)), hBOOL(hAPP(_1447645, _1447711))]]], (35184 ^ _784416) ^ [_1447871, _1447873] : [35192 ^ _784416 : [(35193 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 35191 ^ [_1447871, _1447873]), _1447871)))], (35195 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1447873, 35191 ^ [_1447871, _1447873])))]], 35185 ^ _784416 : [(35186 ^ _784416) ^ [_1447939] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1447939), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1447871))), hBOOL(hAPP(_1447873, _1447939))]]], (35197 ^ _784416) ^ [_1448108, _1448110, _1448112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1448108)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1448110), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1448112)), 35207 ^ _784416 : [(35208 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35206 ^ [_1448108, _1448110, _1448112]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1448108))))], (35211 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35209 ^ [_1448108, _1448110, _1448112]), _1448112)))], (35213 ^ _784416) ^ [] : [-(_1448110 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35209 ^ [_1448108, _1448110, _1448112]), 35206 ^ [_1448108, _1448110, _1448112]))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1448110), _1448108) = _1448110)], (35217 ^ _784416) ^ [_1448447, _1448449, _1448451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1448447)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1448449), _1448451)), 35224 ^ _784416 : [(35225 ^ _784416) ^ [_1448643] : [35227 ^ _784416 : [(35228 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35226 ^ [_1448447, _1448449, _1448451, _1448643]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1448447))))], (35231 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35229 ^ [_1448447, _1448449, _1448451, _1448643]), _1448451)))], (35233 ^ _784416) ^ [] : [-(_1448643 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35229 ^ [_1448447, _1448449, _1448451, _1448643]), 35226 ^ [_1448447, _1448449, _1448451, _1448643]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1448643), _1448449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1448643), _1448447)), _1448449)))]]], (35241 ^ _784416) ^ [_1448919, _1448921, _1448923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1448919)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1448921), _1448923)), 35248 ^ _784416 : [(35249 ^ _784416) ^ [_1449115] : [35251 ^ _784416 : [(35252 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35250 ^ [_1448919, _1448921, _1448923, _1449115]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1448919))))], (35255 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35253 ^ [_1448919, _1448921, _1448923, _1449115]), _1448923)))], (35257 ^ _784416) ^ [] : [-(_1449115 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35253 ^ [_1448919, _1448921, _1448923, _1449115]), 35250 ^ [_1448919, _1448921, _1448923, _1449115]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1448921), _1449115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1448921), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1449115), _1448919))))]]], (35265 ^ _784416) ^ [_1449391, _1449393, _1449395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449391)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1449393), _1449395)), 35272 ^ _784416 : [(35273 ^ _784416) ^ [_1449581] : [35275 ^ _784416 : [(35276 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35274 ^ [_1449391, _1449393, _1449395, _1449581]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1449391))))], (35279 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35277 ^ [_1449391, _1449393, _1449395, _1449581]), _1449395)))], (35281 ^ _784416) ^ [] : [-(_1449581 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35277 ^ [_1449391, _1449393, _1449395, _1449581]), 35274 ^ [_1449391, _1449393, _1449395, _1449581]))]], -(_1449581 = _1449393), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1449581), _1449391) = _1449393]]], (35289 ^ _784416) ^ [_1449841, _1449843, _1449845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449841)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1449843), _1449845)), 35296 ^ _784416 : [(35297 ^ _784416) ^ [_1450031] : [35299 ^ _784416 : [(35300 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35298 ^ [_1449841, _1449843, _1449845, _1450031]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1449841))))], (35303 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35301 ^ [_1449841, _1449843, _1449845, _1450031]), _1449845)))], (35305 ^ _784416) ^ [] : [-(_1450031 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35301 ^ [_1449841, _1449843, _1449845, _1450031]), 35298 ^ [_1449841, _1449843, _1449845, _1450031]))]], -(_1450031 = _1449843), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1450031), _1449841) = _1449843]]], (35313 ^ _784416) ^ [_1450291, _1450293, _1450295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1450291)), 35316 ^ _784416 : [(35317 ^ _784416) ^ [_1450425] : [35319 ^ _784416 : [(35320 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35318 ^ [_1450291, _1450293, _1450295, _1450425]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1450291))))], (35323 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35321 ^ [_1450291, _1450293, _1450295, _1450425]), _1450293)))], (35325 ^ _784416) ^ [] : [-(_1450425 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35321 ^ [_1450291, _1450293, _1450295, _1450425]), 35318 ^ [_1450291, _1450293, _1450295, _1450425]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1450295), _1450425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1450295), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1450425), _1450291))))]]], (35333 ^ _784416) ^ [_1450699, _1450701, _1450703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1450699)), 35336 ^ _784416 : [(35337 ^ _784416) ^ [_1450833] : [35339 ^ _784416 : [(35340 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35338 ^ [_1450699, _1450701, _1450703, _1450833]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1450699))))], (35343 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35341 ^ [_1450699, _1450701, _1450703, _1450833]), _1450701)))], (35345 ^ _784416) ^ [] : [-(_1450833 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35341 ^ [_1450699, _1450701, _1450703, _1450833]), 35338 ^ [_1450699, _1450701, _1450703, _1450833]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1450833), _1450703)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1450833), _1450699)), _1450703)))]]], (35353 ^ _784416) ^ [_1451107, _1451109, _1451111, _1451113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1451107, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1451107, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35354 ^ [_1451107, _1451109, _1451111, _1451113])), _1451109)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1451107, 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), 35354 ^ [_1451107, _1451109, _1451111, _1451113]), _1451111))), _1451113))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1451107, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1451107, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1451109)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1451107, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1451113))))], (35360 ^ _784416) ^ [_1451437, _1451439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1451437)), 35369 ^ _784416 : [(35370 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1451439, 35365 ^ [_1451437, _1451439])))], (35372 ^ _784416) ^ [] : [hBOOL(hAPP(_1451439, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35365 ^ [_1451437, _1451439]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 35366 ^ [_1451437, _1451439]), _1451437))))]], 35373 ^ _784416 : [(35374 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1451439, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35365 ^ [_1451437, _1451439]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 35366 ^ [_1451437, _1451439]), _1451437)))))], (35376 ^ _784416) ^ [] : [hBOOL(hAPP(_1451439, 35365 ^ [_1451437, _1451439]))]], 35377 ^ _784416 : [(35378 ^ _784416) ^ [] : [35379 ^ _784416 : [(35380 ^ _784416) ^ [_1451869] : [hBOOL(hAPP(_1451439, _1451869))]], 35382 ^ _784416 : [(35383 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35381 ^ [_1451437, _1451439]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1451437))))], (35385 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1451439, 35381 ^ [_1451437, _1451439])))]]], (35387 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1451439, 35394 ^ [_1451437, _1451439]))), 35388 ^ _784416 : [(35389 ^ _784416) ^ [_1451984] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1451984), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1451437))), hBOOL(hAPP(_1451439, _1451984))]]]]], (35398 ^ _784416) ^ [_1452131, _1452133, _1452135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1452131)), 35401 ^ _784416 : [(35402 ^ _784416) ^ [_1452265] : [35404 ^ _784416 : [(35405 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35403 ^ [_1452131, _1452133, _1452135, _1452265]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1452131))))], (35408 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35406 ^ [_1452131, _1452133, _1452135, _1452265]), _1452133)))], (35410 ^ _784416) ^ [] : [-(_1452265 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 35406 ^ [_1452131, _1452133, _1452135, _1452265]), 35403 ^ [_1452131, _1452133, _1452135, _1452265]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1452135), _1452265)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1452135), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1452265), _1452131))))]]], (35418 ^ _784416) ^ [_1452539, _1452541, _1452543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1452539)), 35421 ^ _784416 : [(35422 ^ _784416) ^ [_1452673] : [35424 ^ _784416 : [(35425 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35423 ^ [_1452539, _1452541, _1452543, _1452673]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1452539))))], (35428 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 35426 ^ [_1452539, _1452541, _1452543, _1452673]), _1452541)))], (35430 ^ _784416) ^ [] : [-(_1452673 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 35426 ^ [_1452539, _1452541, _1452543, _1452673]), 35423 ^ [_1452539, _1452541, _1452543, _1452673]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1452673), _1452543)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1452673), _1452539)), _1452543)))]]], (35438 ^ _784416) ^ [_1452947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1452947)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1452947) = 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, _1452947))))], (35444 ^ _784416) ^ [_1453050] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1453050))))], (35446 ^ _784416) ^ [_1453078, _1453080, _1453082] : [class_Orderings_Olinorder(_1453078), 35449 ^ _784416 : [(35450 ^ _784416) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1453078), _1453080) = hAPP(c_SetInterval_Oord__class_OlessThan(_1453078), _1453082), -(_1453080 = _1453082)], (35456 ^ _784416) ^ [] : [_1453080 = _1453082, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1453078), _1453080) = hAPP(c_SetInterval_Oord__class_OlessThan(_1453078), _1453082))]]], (35462 ^ _784416) ^ [_1453319] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1453319)) = _1453319)], (35464 ^ _784416) ^ [] : [-(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)))], (35466 ^ _784416) ^ [_1453366] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1453366) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1453366))], (35468 ^ _784416) ^ [] : [-(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)))], (35470 ^ _784416) ^ [_1453413] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1453413)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1453413), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1453413)))], (35472 ^ _784416) ^ [_1453451, _1453453, _1453455] : [class_Orderings_Oord(_1453451), 35475 ^ _784416 : [(35476 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1453451), _1453453), hAPP(c_SetInterval_Oord__class_OlessThan(_1453451), _1453455))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1453451), _1453453), _1453455)))], (35482 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1453451), _1453453), _1453455)), -(hBOOL(hAPP(hAPP(c_member(_1453451), _1453453), hAPP(c_SetInterval_Oord__class_OlessThan(_1453451), _1453455))))]]], (35488 ^ _784416) ^ [_1453719, _1453721, _1453723] : [class_Orderings_Olinorder(_1453719), 35491 ^ _784416 : [(35492 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1453719, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1453719), _1453721)), hAPP(c_SetInterval_Oord__class_OlessThan(_1453719), _1453723))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453719), _1453721), _1453723)))], (35498 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1453719), _1453721), _1453723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1453719, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1453719), _1453721)), hAPP(c_SetInterval_Oord__class_OlessThan(_1453719), _1453723))))]]], (35504 ^ _784416) ^ [_1454011, _1454013, _1454015] : [class_Orderings_Olinorder(_1454011), 35507 ^ _784416 : [(35508 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1454011, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454011), _1454013)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454011), _1454015))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454011), _1454013), _1454015)))], (35514 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454011), _1454013), _1454015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1454011, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454011), _1454013)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454011), _1454015))))]]], (35520 ^ _784416) ^ [_1454303, _1454305] : [class_Orderings_Oorder(_1454303), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1454303, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1454303), _1454305), c_Orderings_Obot__class_Obot(tc_fun(_1454303, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1454303), _1454305)) = hAPP(hAPP(c_Set_Oinsert(_1454303), _1454305), c_Orderings_Obot__class_Obot(tc_fun(_1454303, tc_HOL_Obool))))], (35526 ^ _784416) ^ [_1454462, _1454464, _1454466] : [class_Orderings_Olinorder(_1454462), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1454462), _1454464), _1454466)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1454462, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454462), _1454464)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1454462, _1454464), _1454466)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1454462), _1454466))], (35536 ^ _784416) ^ [_1454661, _1454663, _1454665] : [class_Orderings_Oorder(_1454661), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454661, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454661), _1454663)), c_SetInterval_Oord__class_OatLeastAtMost(_1454661, _1454663, _1454665)) = c_Orderings_Obot__class_Obot(tc_fun(_1454661, tc_HOL_Obool)))], (35542 ^ _784416) ^ [_1454788, _1454790, _1454792] : [class_Orderings_Oorder(_1454788), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454788, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1454788), _1454790)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1454788, _1454790), _1454792)) = c_Orderings_Obot__class_Obot(tc_fun(_1454788, tc_HOL_Obool)))], (35548 ^ _784416) ^ [_1454919] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1454919)) = 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), _1454919))))], (35550 ^ _784416) ^ [_1454957, _1454959, _1454961] : [-(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), _1454957)), 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))), _1454959))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1454961))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1454961)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1454957), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1454957), 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), _1454961), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1454959)))))], (35552 ^ _784416) ^ [_1455044, _1455046, _1455048, _1455050] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455044, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35553 ^ [_1455044, _1455046, _1455048, _1455050])), _1455046) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455044, 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), 35553 ^ [_1455044, _1455046, _1455048, _1455050]), _1455048))), _1455050), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455044, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1455046) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455044, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1455050))], (35559 ^ _784416) ^ [_1455324, _1455326, _1455328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1455324, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455324, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35560 ^ [_1455324, _1455326, _1455328])), _1455326)), _1455328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1455324, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1455324, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1455326)), _1455328)))], (35566 ^ _784416) ^ [_1455550, _1455552, _1455554, _1455556] : [class_Rings_Oring__1(_1455550), -(hAPP(c_Int_Oring__1__class_Oof__int(_1455550), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1455552, tc_Int_Oint), _1455554), _1455556)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1455552, _1455550), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1455550, _1455552), c_Int_Oring__1__class_Oof__int(_1455550)), _1455554)), _1455556))], (35572 ^ _784416) ^ [_1455699, _1455701, _1455703] : [class_Groups_Ocomm__monoid__add(_1455699), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1455701, _1455699), hAPP(c_COMBK(_1455699, _1455701), c_Groups_Ozero__class_Ozero(_1455699))), _1455703) = c_Groups_Ozero__class_Ozero(_1455699))], (35578 ^ _784416) ^ [_1455814, _1455816, _1455818, _1455820] : [class_Groups_Oab__group__add(_1455814), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1455816, _1455814), hAPP(hAPP(c_COMBB(_1455814, _1455814, _1455816), c_Groups_Ouminus__class_Ouminus(_1455814)), _1455818)), _1455820) = hAPP(c_Groups_Ouminus__class_Ouminus(_1455814), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1455816, _1455814), _1455818), _1455820)))], (35584 ^ _784416) ^ [_1455963, _1455965, _1455967, _1455969, _1455971] : [class_Fields_Ofield(_1455963), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1455963), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1455965, _1455963), _1455967), _1455969)), _1455971) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1455965, _1455963), hAPP(hAPP(c_COMBC(_1455965, _1455963, _1455963), hAPP(hAPP(c_COMBB(_1455963, tc_fun(_1455963, _1455963), _1455965), c_Rings_Oinverse__class_Odivide(_1455963)), _1455967)), _1455971)), _1455969))], (35590 ^ _784416) ^ [_1456146, _1456148, _1456150, _1456152, _1456154] : [class_Groups_Ocomm__monoid__add(_1456146), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456148, _1456146), hAPP(hAPP(c_COMBS(_1456148, _1456146, _1456146), hAPP(hAPP(c_COMBB(_1456146, tc_fun(_1456146, _1456146), _1456148), c_Groups_Oplus__class_Oplus(_1456146)), _1456150)), _1456152)), _1456154) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1456146), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456148, _1456146), _1456150), _1456154)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456148, _1456146), _1456152), _1456154)))], (35596 ^ _784416) ^ [_1456347, _1456349, _1456351, _1456353, _1456355, _1456357, _1456359] : [class_Rings_Osemiring__0(_1456347), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1456347), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456349, _1456347), _1456351), _1456353)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456355, _1456347), _1456357), _1456359)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456349, _1456347), hAPP(hAPP(c_COMBC(_1456349, tc_fun(_1456355, tc_HOL_Obool), _1456347), hAPP(hAPP(c_COMBB(tc_fun(_1456355, _1456347), tc_fun(tc_fun(_1456355, tc_HOL_Obool), _1456347), _1456349), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456355, _1456347)), hAPP(hAPP(c_COMBC(_1456349, tc_fun(_1456355, _1456347), tc_fun(_1456355, _1456347)), hAPP(hAPP(c_COMBB(tc_fun(_1456347, _1456347), tc_fun(tc_fun(_1456355, _1456347), tc_fun(_1456355, _1456347)), _1456349), c_COMBB(_1456347, _1456347, _1456355)), hAPP(hAPP(c_COMBB(_1456347, tc_fun(_1456347, _1456347), _1456349), c_Groups_Otimes__class_Otimes(_1456347)), _1456351))), _1456357))), _1456359)), _1456353))], (35602 ^ _784416) ^ [_1456686, _1456688, _1456690, _1456692, _1456694] : [class_Rings_Osemiring__0(_1456686), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1456686), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456688, _1456686), _1456690), _1456692)), _1456694) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456688, _1456686), hAPP(hAPP(c_COMBC(_1456688, _1456686, _1456686), hAPP(hAPP(c_COMBB(_1456686, tc_fun(_1456686, _1456686), _1456688), c_Groups_Otimes__class_Otimes(_1456686)), _1456690)), _1456694)), _1456692))], (35608 ^ _784416) ^ [_1456869, _1456871, _1456873, _1456875, _1456877] : [class_Rings_Osemiring__0(_1456869), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1456869), _1456871), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456873, _1456869), _1456875), _1456877)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456873, _1456869), hAPP(hAPP(c_COMBB(_1456869, _1456869, _1456873), hAPP(c_Groups_Otimes__class_Otimes(_1456869), _1456871)), _1456875)), _1456877))], (35614 ^ _784416) ^ [_1457032, _1457034, _1457036, _1457038, _1457040, _1457042] : [class_Groups_Ocomm__monoid__add(_1457032), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457034, _1457032), hAPP(hAPP(c_COMBC(_1457034, tc_fun(_1457036, tc_HOL_Obool), _1457032), hAPP(hAPP(c_COMBB(tc_fun(_1457036, _1457032), tc_fun(tc_fun(_1457036, tc_HOL_Obool), _1457032), _1457034), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457036, _1457032)), _1457038)), _1457040)), _1457042) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457036, _1457032), hAPP(hAPP(c_COMBC(_1457036, tc_fun(_1457034, tc_HOL_Obool), _1457032), hAPP(hAPP(c_COMBB(tc_fun(_1457034, _1457032), tc_fun(tc_fun(_1457034, tc_HOL_Obool), _1457032), _1457036), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457034, _1457032)), hAPP(c_COMBC(_1457034, _1457036, _1457032), _1457038))), _1457042)), _1457040))], (35620 ^ _784416) ^ [_1457305, _1457307, _1457309, _1457311, _1457313] : [class_Groups_Oab__group__add(_1457305), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457307, _1457305), hAPP(hAPP(c_COMBS(_1457307, _1457305, _1457305), hAPP(hAPP(c_COMBB(_1457305, tc_fun(_1457305, _1457305), _1457307), c_Groups_Ominus__class_Ominus(_1457305)), _1457309)), _1457311)), _1457313) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1457305), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457307, _1457305), _1457309), _1457313)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457307, _1457305), _1457311), _1457313)))], (35626 ^ _784416) ^ [_1457506, _1457508, _1457510, _1457512] : [class_Rings_Osemiring__1(_1457506), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1457506), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457508, tc_Nat_Onat), _1457510), _1457512)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457508, _1457506), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1457506, _1457508), c_Nat_Osemiring__1__class_Oof__nat(_1457506)), _1457510)), _1457512))], (35632 ^ _784416) ^ [_1457655, _1457657, _1457659] : [class_Groups_Ocomm__monoid__add(_1457655), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457657, _1457655), _1457659), c_Orderings_Obot__class_Obot(tc_fun(_1457657, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1457655))], (35638 ^ _784416) ^ [_1457764, _1457766, _1457768] : [class_Groups_Ocomm__monoid__add(_1457764), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457766, _1457764), _1457768), c_Orderings_Obot__class_Obot(tc_fun(_1457766, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1457764))], (35644 ^ _784416) ^ [_1457873, _1457875, _1457877, _1457879] : [class_Groups_Ocomm__monoid__add(_1457873), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1457875), _1457877))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457875, _1457873), _1457879), _1457877) = c_Groups_Ozero__class_Ozero(_1457873))], (35654 ^ _784416) ^ [_1457997, _1457999, _1458001, _1458003] : [class_Groups_Ocomm__monoid__add(_1457997), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1457999), _1458001))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1457999, _1457997), _1458003), _1458001) = c_Groups_Ozero__class_Ozero(_1457997))], (35664 ^ _784416) ^ [_1458121, _1458123, _1458125, _1458127, _1458129] : [class_Groups_Ocomm__monoid__add(_1458121), hBOOL(hAPP(c_Finite__Set_Ofinite(_1458123), _1458125)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458123, _1458121), hAPP(hAPP(c_COMBS(_1458123, _1458121, _1458121), hAPP(hAPP(c_COMBB(_1458121, tc_fun(_1458121, _1458121), _1458123), c_Groups_Oplus__class_Oplus(_1458121)), _1458127)), _1458129)), _1458125) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458121), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458123, _1458121), _1458127), _1458125)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1458123, _1458121), _1458129), _1458125)))], (35674 ^ _784416) ^ [_1458388, _1458390, _1458392, _1458394] : [class_Groups_Ocomm__monoid__add(_1458388), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1458388), _1458390), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1458392)), hAPP(c_Nat_OSuc, _1458394))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1458388), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1458388, tc_Nat_Onat), _1458390), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1458392), _1458394)))], (35680 ^ _784416) ^ [_1458559, _1458561, _1458563, _1458565, _1458567] : [class_Groups_Ocomm__monoid__add(_1458559), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1458559), _1458561), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1458563), _1458565)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1458567), _1458565))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1458559), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1458559, tc_Nat_Onat), _1458561), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1458565))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1458563), _1458567)))], (35686 ^ _784416) ^ [_1458750, _1458752, _1458754, _1458756] : [class_Groups_Ocomm__monoid__add(_1458750), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1458750), _1458752), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1458754), hAPP(c_Nat_OSuc, _1458756))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1458750), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1458750, tc_Nat_Onat), _1458752), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1458754, _1458756)))], (35692 ^ _784416) ^ [_1458913, _1458915, _1458917, _1458919, _1458921] : [class_Groups_Ocomm__monoid__add(_1458913), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1458913), _1458915), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1458917), _1458919), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1458921), _1458919))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1458913), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1458913, tc_Nat_Onat), _1458915), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1458919))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1458917, _1458921)))], (35698 ^ _784416) ^ [_1459096, _1459098, _1459100, _1459102, _1459104, _1459106] : [class_Groups_Ocomm__monoid__add(_1459096), c_Fun_Oinj__on(_1459098, _1459100, _1459102, _1459104), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459100, _1459096), _1459106), hAPP(c_Set_Oimage(_1459098, _1459100, _1459102), _1459104)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459098, _1459096), hAPP(c_Fun_Ocomp(_1459100, _1459096, _1459098, _1459106), _1459102)), _1459104))], (35708 ^ _784416) ^ [_1459309, _1459311, _1459313, _1459315, _1459317] : [class_Groups_Ocomm__monoid__add(_1459309), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1459311), _1459313)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1459313), _1459315)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1459309), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1459309), _1459317), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1459311), _1459313))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1459309), _1459317), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1459313), _1459315))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1459309), _1459317), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1459311), _1459315)))], (35722 ^ _784416) ^ [_1459632, _1459634, _1459636, _1459638, _1459640] : [class_Groups_Oab__group__add(_1459632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1459634), _1459636)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1459636), _1459638)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1459632), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1459632), _1459640), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1459634), _1459638))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1459632), _1459640), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1459634), _1459636))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1459632), _1459640), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1459636), _1459638)))], (35736 ^ _784416) ^ [_1459955, _1459957, _1459959, _1459961, _1459963] : [class_Groups_Ocomm__monoid__add(_1459955), hBOOL(hAPP(c_Finite__Set_Ofinite(_1459957), _1459959)), 35743 ^ _784416 : [(35744 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1459957), _1459961), _1459959)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459957, _1459955), hAPP(hAPP(c_COMBC(_1459957, _1459955, _1459955), hAPP(hAPP(c_COMBS(_1459957, _1459955, tc_fun(_1459955, _1459955)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1459955, tc_fun(_1459955, _1459955)), _1459957), c_If(_1459955)), hAPP(hAPP(c_COMBC(_1459957, _1459957, tc_HOL_Obool), c_fequal), _1459961))), _1459963)), c_Groups_Ozero__class_Ozero(_1459955))), _1459959) = hAPP(_1459963, _1459961))], (35750 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1459957), _1459961), _1459959))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1459957, _1459955), hAPP(hAPP(c_COMBC(_1459957, _1459955, _1459955), hAPP(hAPP(c_COMBS(_1459957, _1459955, tc_fun(_1459955, _1459955)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1459955, tc_fun(_1459955, _1459955)), _1459957), c_If(_1459955)), hAPP(hAPP(c_COMBC(_1459957, _1459957, tc_HOL_Obool), c_fequal), _1459961))), _1459963)), c_Groups_Ozero__class_Ozero(_1459955))), _1459959) = c_Groups_Ozero__class_Ozero(_1459955))]]], (35756 ^ _784416) ^ [_1460493, _1460495, _1460497, _1460499, _1460501] : [class_Groups_Ocomm__monoid__add(_1460493), hBOOL(hAPP(c_Finite__Set_Ofinite(_1460495), _1460497)), 35763 ^ _784416 : [(35764 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1460495), _1460499), _1460497)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460495, _1460493), hAPP(hAPP(c_COMBC(_1460495, _1460493, _1460493), hAPP(hAPP(c_COMBS(_1460495, _1460493, tc_fun(_1460493, _1460493)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1460493, tc_fun(_1460493, _1460493)), _1460495), c_If(_1460493)), hAPP(c_fequal, _1460499))), _1460501)), c_Groups_Ozero__class_Ozero(_1460493))), _1460497) = hAPP(_1460501, _1460499))], (35770 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1460495), _1460499), _1460497))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1460495, _1460493), hAPP(hAPP(c_COMBC(_1460495, _1460493, _1460493), hAPP(hAPP(c_COMBS(_1460495, _1460493, tc_fun(_1460493, _1460493)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1460493, tc_fun(_1460493, _1460493)), _1460495), c_If(_1460493)), hAPP(c_fequal, _1460499))), _1460501)), c_Groups_Ozero__class_Ozero(_1460493))), _1460497) = c_Groups_Ozero__class_Ozero(_1460493))]]], (35776 ^ _784416) ^ [_1461003, _1461005, _1461007, _1461009, _1461011, _1461013, _1461015] : [class_Groups_Ocomm__monoid__add(_1461003), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461005), _1461007)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461009), _1461011)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1461005, _1461003), hAPP(hAPP(c_COMBS(_1461005, tc_fun(_1461009, tc_HOL_Obool), _1461003), hAPP(hAPP(c_COMBB(tc_fun(_1461009, _1461003), tc_fun(tc_fun(_1461009, tc_HOL_Obool), _1461003), _1461005), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1461009, _1461003)), _1461013)), hAPP(hAPP(c_COMBB(tc_fun(_1461009, tc_HOL_Obool), tc_fun(_1461009, tc_HOL_Obool), _1461005), c_Set_OCollect(_1461009)), hAPP(hAPP(c_COMBB(tc_fun(_1461009, tc_HOL_Obool), tc_fun(_1461009, tc_HOL_Obool), _1461005), hAPP(c_COMBS(_1461009, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1461009), c_fconj), hAPP(hAPP(c_COMBC(_1461009, tc_fun(_1461009, tc_HOL_Obool), tc_HOL_Obool), c_member(_1461009)), _1461011)))), _1461015)))), _1461007) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1461009, _1461003), hAPP(hAPP(c_COMBS(_1461009, tc_fun(_1461005, tc_HOL_Obool), _1461003), hAPP(hAPP(c_COMBB(tc_fun(_1461005, _1461003), tc_fun(tc_fun(_1461005, tc_HOL_Obool), _1461003), _1461009), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1461005, _1461003)), hAPP(c_COMBC(_1461005, _1461009, _1461003), _1461013))), hAPP(hAPP(c_COMBB(tc_fun(_1461005, tc_HOL_Obool), tc_fun(_1461005, tc_HOL_Obool), _1461009), c_Set_OCollect(_1461005)), hAPP(hAPP(c_COMBB(tc_fun(_1461005, tc_HOL_Obool), tc_fun(_1461005, tc_HOL_Obool), _1461009), hAPP(c_COMBS(_1461005, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1461005), c_fconj), hAPP(hAPP(c_COMBC(_1461005, tc_fun(_1461005, tc_HOL_Obool), tc_HOL_Obool), c_member(_1461005)), _1461007)))), hAPP(c_COMBC(_1461005, _1461009, tc_HOL_Obool), _1461015))))), _1461011))], (35790 ^ _784416) ^ [_1461696, _1461698, _1461700, _1461702] : [class_Rings_Osemiring__1(_1461696), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1461698, _1461696), hAPP(c_COMBK(_1461696, _1461698), _1461700)), _1461702) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1461696), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1461696), hAPP(c_Finite__Set_Ocard(_1461698), _1461702))), _1461700))], (35796 ^ _784416) ^ [_1461841, _1461843, _1461845] : [class_Groups_Ocomm__monoid__add(_1461841), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1461841), _1461843), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1461845))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1461841), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1461841), _1461843), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1461845))), hAPP(_1461843, _1461845)))], (35802 ^ _784416) ^ [_1461994, _1461996, _1461998, _1462000, _1462002] : [class_Groups_Ocomm__monoid__add(_1461994), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461996), _1461998)), -(hBOOL(hAPP(hAPP(c_member(_1461996), _1462000), _1461998))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1461996, _1461994), _1462002), hAPP(hAPP(c_Set_Oinsert(_1461996), _1462000), _1461998)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1461994), hAPP(_1462002, _1462000)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1461996, _1461994), _1462002), _1461998)))], (35816 ^ _784416) ^ [_1462244, _1462246, _1462248, _1462250, _1462252] : [class_Groups_Ocomm__monoid__add(_1462244), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462246), _1462248)), -(hBOOL(hAPP(hAPP(c_member(_1462246), _1462250), _1462248))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462246, _1462244), _1462252), hAPP(hAPP(c_Set_Oinsert(_1462246), _1462250), _1462248)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1462244), hAPP(_1462252, _1462250)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462246, _1462244), _1462252), _1462248)))], (35830 ^ _784416) ^ [_1462494, _1462496, _1462498, _1462500, _1462502] : [class_Groups_Ocomm__monoid__add(_1462494), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462496), _1462498)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462496), _1462500)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1462494), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462496, _1462494), _1462502), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1462496, tc_HOL_Obool)), _1462498), _1462500))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462496, _1462494), _1462502), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462496, tc_HOL_Obool)), _1462498), _1462500))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1462494), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462496, _1462494), _1462502), _1462498)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462496, _1462494), _1462502), _1462500)))], (35844 ^ _784416) ^ [_1462855, _1462857, _1462859, _1462861, _1462863] : [class_Groups_Oab__group__add(_1462855), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462857), _1462859)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462857, tc_HOL_Obool)), _1462861), _1462859)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462857, _1462855), _1462863), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1462857, tc_HOL_Obool)), _1462859), _1462861)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1462855), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462857, _1462855), _1462863), _1462859)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462857, _1462855), _1462863), _1462861)))], (35858 ^ _784416) ^ [_1463172, _1463174, _1463176, _1463178, _1463180] : [class_Groups_Ocomm__monoid__add(_1463172), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463174), _1463176)), c_Fun_Oinj__on(_1463174, _1463174, _1463178, _1463176), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463174, _1463172), _1463180), hAPP(c_Set_Oimage(_1463174, _1463174, _1463178), _1463176)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463174, _1463172), hAPP(c_Fun_Ocomp(_1463174, _1463172, _1463174, _1463180), _1463178)), _1463176))], (35872 ^ _784416) ^ [_1463447, _1463449, _1463451, _1463453] : [class_Groups_Ocomm__monoid__add(_1463447), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463449), _1463451)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463449, _1463447), _1463453), _1463451) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1463447, _1463449, c_Groups_Oplus__class_Oplus(_1463447)), _1463453), c_Groups_Ozero__class_Ozero(_1463447)), _1463451))], (35882 ^ _784416) ^ [_1463642, _1463644, _1463646, _1463648] : [class_Groups_Ocomm__monoid__add(_1463642), 35885 ^ _784416 : [(35886 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1463644), _1463646)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463644, _1463642), _1463648), _1463646) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1463642, _1463644, c_Groups_Oplus__class_Oplus(_1463642)), _1463648), c_Groups_Ozero__class_Ozero(_1463642)), _1463646))], (35892 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1463644), _1463646))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463644, _1463642), _1463648), _1463646) = c_Groups_Ozero__class_Ozero(_1463642))]]], (35898 ^ _784416) ^ [_1463914, _1463916, _1463918] : [class_Groups_Ocomm__monoid__add(_1463914), hAPP(_1463916, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1463914), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1463914), _1463916), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1463918)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1463914), _1463916), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1463918)))], (35908 ^ _784416) ^ [_1464103, _1464105, _1464107, _1464109] : [class_Groups_Ocomm__monoid__add(_1464103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1464105), _1464107)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1464103), _1464109), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1464105), _1464107)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1464103), hAPP(_1464109, _1464105)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1464103), _1464109), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1464105)), _1464107))))], (35918 ^ _784416) ^ [_1464336, _1464338, _1464340, _1464342] : [class_Groups_Ocomm__monoid__add(_1464336), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1464338), _1464340)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1464336), _1464342), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1464338, _1464340)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1464336), hAPP(_1464342, _1464338)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1464336), _1464342), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1464338), _1464340))))], (35928 ^ _784416) ^ [_1464561, _1464563, _1464565, _1464567, _1464569] : [class_Groups_Ocomm__monoid__add(_1464561), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464563), _1464565)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464563, _1464561), _1464567), hAPP(c_Set_OCollect(_1464563), hAPP(hAPP(c_COMBS(_1464563, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1464563), c_fconj), hAPP(hAPP(c_COMBC(_1464563, tc_fun(_1464563, tc_HOL_Obool), tc_HOL_Obool), c_member(_1464563)), _1464565))), hAPP(hAPP(c_COMBC(_1464563, tc_fun(_1464563, tc_HOL_Obool), tc_HOL_Obool), c_member(_1464563)), _1464569)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464563, _1464561), hAPP(hAPP(c_COMBC(_1464563, _1464561, _1464561), hAPP(hAPP(c_COMBS(_1464563, _1464561, tc_fun(_1464561, _1464561)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1464561, tc_fun(_1464561, _1464561)), _1464563), c_If(_1464561)), hAPP(hAPP(c_COMBC(_1464563, tc_fun(_1464563, tc_HOL_Obool), tc_HOL_Obool), c_member(_1464563)), _1464569))), _1464567)), c_Groups_Ozero__class_Ozero(_1464561))), _1464565))], (35938 ^ _784416) ^ [_1464970, _1464972, _1464974, _1464976, _1464978] : [class_Groups_Ocomm__monoid__add(_1464970), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464972), _1464974)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464972, _1464970), _1464976), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464972, tc_HOL_Obool)), _1464974), _1464978)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464972, _1464970), hAPP(hAPP(c_COMBC(_1464972, _1464970, _1464970), hAPP(hAPP(c_COMBS(_1464972, _1464970, tc_fun(_1464970, _1464970)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1464970, tc_fun(_1464970, _1464970)), _1464972), c_If(_1464970)), hAPP(hAPP(c_COMBC(_1464972, tc_fun(_1464972, tc_HOL_Obool), tc_HOL_Obool), c_member(_1464972)), _1464978))), _1464976)), c_Groups_Ozero__class_Ozero(_1464970))), _1464974))], (35948 ^ _784416) ^ [_1465291, _1465293, _1465295, _1465297, _1465299, _1465301] : [class_Groups_Ocomm__monoid__add(_1465291), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465293), _1465295)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465293, _1465291), _1465297), _1465295) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465299, _1465291), hAPP(hAPP(c_COMBB(tc_fun(_1465293, tc_HOL_Obool), _1465291, _1465299), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465293, _1465291), _1465297)), hAPP(hAPP(c_COMBB(tc_fun(_1465293, tc_HOL_Obool), tc_fun(_1465293, tc_HOL_Obool), _1465299), c_Set_OCollect(_1465293)), hAPP(hAPP(c_COMBB(tc_fun(_1465293, tc_HOL_Obool), tc_fun(_1465293, tc_HOL_Obool), _1465299), hAPP(c_COMBS(_1465293, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1465293), c_fconj), hAPP(hAPP(c_COMBC(_1465293, tc_fun(_1465293, tc_HOL_Obool), tc_HOL_Obool), c_member(_1465293)), _1465295)))), hAPP(c_COMBC(_1465293, _1465299, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1465299, tc_fun(_1465299, tc_HOL_Obool), _1465293), c_fequal), _1465301)))))), hAPP(c_Set_Oimage(_1465293, _1465299, _1465301), _1465295)))], (35958 ^ _784416) ^ [_1465702, _1465704, _1465706, _1465708, _1465710] : [class_Groups_Ocomm__monoid__add(_1465702), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465704), _1465706)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465704, _1465702), _1465708), hAPP(hAPP(c_Set_Oinsert(_1465704), _1465710), _1465706)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1465702), hAPP(_1465708, _1465710)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465704, _1465702), _1465708), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1465704, tc_HOL_Obool)), _1465706), hAPP(hAPP(c_Set_Oinsert(_1465704), _1465710), c_Orderings_Obot__class_Obot(tc_fun(_1465704, tc_HOL_Obool)))))))], (35968 ^ _784416) ^ [_1465971, _1465973, _1465975, _1465977, _1465979] : [class_Groups_Ocomm__monoid__add(_1465971), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465973), _1465975)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465973), _1465977)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1465973, tc_HOL_Obool)), _1465975), _1465977) = c_Orderings_Obot__class_Obot(tc_fun(_1465973, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465973, _1465971), _1465979), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1465973, tc_HOL_Obool)), _1465975), _1465977)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1465971), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465973, _1465971), _1465979), _1465975)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1465973, _1465971), _1465979), _1465977)))], (35986 ^ _784416) ^ [_1466366, _1466368, _1466370, _1466372, _1466374] : [class_Groups_Oab__group__add(_1466366), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466368), _1466370)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1466368), _1466372)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1466368, _1466366), _1466374), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1466368, tc_HOL_Obool)), _1466370), _1466372)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1466366), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1466366), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1466368, _1466366), _1466374), _1466370)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1466368, _1466366), _1466374), _1466372))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1466368, _1466366), _1466374), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466368, tc_HOL_Obool)), _1466370), _1466372))))], (36000 ^ _784416) ^ [_1466727, _1466729, _1466731, _1466733] : [class_Groups_Ocomm__monoid__add(_1466727), 36003 ^ _784416 : [(36004 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1466729), _1466731)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1466727), _1466733), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1466731), hAPP(c_Nat_OSuc, _1466729))) = c_Groups_Ozero__class_Ozero(_1466727))], (36010 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1466729), _1466731))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1466727), _1466733), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1466731), hAPP(c_Nat_OSuc, _1466729))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1466727), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1466727), _1466733), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1466731), _1466729))), hAPP(_1466733, _1466729)))]]], (36016 ^ _784416) ^ [_1467057, _1467059, _1467061, _1467063] : [class_Groups_Ocomm__monoid__add(_1467057), 36019 ^ _784416 : [(36020 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1467059)), _1467061)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1467057), _1467063), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1467061, hAPP(c_Nat_OSuc, _1467059))) = c_Groups_Ozero__class_Ozero(_1467057))], (36026 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1467059)), _1467061))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1467057), _1467063), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1467061, hAPP(c_Nat_OSuc, _1467059))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1467057), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1467057), _1467063), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1467061, _1467059))), hAPP(_1467063, hAPP(c_Nat_OSuc, _1467059))))]]], (36032 ^ _784416) ^ [_1467393, _1467395, _1467397, _1467399] : [class_Groups_Ocomm__monoid__add(_1467393), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1467395), _1467397)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1467393), _1467399), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1467395, _1467397)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1467393), hAPP(_1467399, _1467395)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1467393), _1467399), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1467395, _1467397))))], (36042 ^ _784416) ^ [_1467612, _1467614, _1467616, _1467618, _1467620] : [class_Groups_Ocomm__monoid__add(_1467612), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1467614), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1467616), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1467612), _1467618), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1467614, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1467616), _1467620))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1467612), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1467612), _1467618), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1467614, _1467616))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1467612), _1467618), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1467616), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1467616), _1467620)))))], (36052 ^ _784416) ^ [_1467903, _1467905, _1467907, _1467909, _1467911, _1467913] : [class_Groups_Ocomm__monoid__add(_1467903), hBOOL(hAPP(c_Finite__Set_Ofinite(_1467905), _1467907)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1467905, _1467903), hAPP(hAPP(c_COMBS(_1467905, _1467903, _1467903), hAPP(hAPP(c_COMBS(_1467905, _1467903, tc_fun(_1467903, _1467903)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1467903, tc_fun(_1467903, _1467903)), _1467905), c_If(_1467903)), _1467909)), _1467911)), _1467913)), _1467907) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1467903), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1467905, _1467903), _1467911), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467905, tc_HOL_Obool)), _1467907), hAPP(c_Set_OCollect(_1467905), _1467909)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1467905, _1467903), _1467913), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467905, tc_HOL_Obool)), _1467907), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1467905, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1467905), _1467909))))))], (36062 ^ _784416) ^ [_1468286, _1468288, _1468290, _1468292, _1468294] : [class_Groups_Ocomm__monoid__add(_1468286), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468288), _1468290)), hBOOL(hAPP(hAPP(c_member(_1468288), _1468292), _1468290)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1468288, _1468286), _1468294), _1468290) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1468286), hAPP(_1468294, _1468292)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1468288, _1468286), _1468294), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468288, tc_HOL_Obool)), _1468290), hAPP(hAPP(c_Set_Oinsert(_1468288), _1468292), c_Orderings_Obot__class_Obot(tc_fun(_1468288, tc_HOL_Obool)))))))], (36076 ^ _784416) ^ [_1468611, _1468613, _1468615, _1468617, _1468619] : [class_Groups_Ocomm__monoid__add(_1468611), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468613), _1468615)), hBOOL(hAPP(hAPP(c_member(_1468613), _1468617), _1468615)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1468613, _1468611), _1468619), _1468615) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1468611), hAPP(_1468619, _1468617)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1468613, _1468611), _1468619), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468613, tc_HOL_Obool)), _1468615), hAPP(hAPP(c_Set_Oinsert(_1468613), _1468617), c_Orderings_Obot__class_Obot(tc_fun(_1468613, tc_HOL_Obool)))))))], (36090 ^ _784416) ^ [_1468936, _1468938, _1468940, _1468942, _1468944] : [class_Groups_Oab__group__add(_1468936), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468938), _1468940)), 36097 ^ _784416 : [(36098 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1468938), _1468942), _1468940)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1468938, _1468936), _1468944), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468938, tc_HOL_Obool)), _1468940), hAPP(hAPP(c_Set_Oinsert(_1468938), _1468942), c_Orderings_Obot__class_Obot(tc_fun(_1468938, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1468936), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1468938, _1468936), _1468944), _1468940)), hAPP(_1468944, _1468942)))], (36104 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1468938), _1468942), _1468940))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1468938, _1468936), _1468944), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468938, tc_HOL_Obool)), _1468940), hAPP(hAPP(c_Set_Oinsert(_1468938), _1468942), c_Orderings_Obot__class_Obot(tc_fun(_1468938, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1468938, _1468936), _1468944), _1468940))]]], (36110 ^ _784416) ^ [_1469406, _1469408, _1469410, _1469412, _1469414] : [class_Rings_Oring(_1469406), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469408), _1469410)), hBOOL(hAPP(hAPP(c_member(_1469408), _1469412), _1469410)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469408, _1469406), _1469414), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469408, tc_HOL_Obool)), _1469410), hAPP(hAPP(c_Set_Oinsert(_1469408), _1469412), c_Orderings_Obot__class_Obot(tc_fun(_1469408, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1469406), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1469408, _1469406), _1469414), _1469410)), hAPP(_1469414, _1469412)))], (36124 ^ _784416) ^ [_1469731, _1469733, _1469735] : [class_Fields_Ofield(_1469731), -(_1469733 = c_Groups_Oone__class_Oone(_1469731)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1469731), hAPP(c_Power_Opower__class_Opower(_1469731), _1469733)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1469735)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1469731), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1469731), hAPP(hAPP(c_Power_Opower__class_Opower(_1469731), _1469733), _1469735)), c_Groups_Oone__class_Oone(_1469731))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1469731), _1469733), c_Groups_Oone__class_Oone(_1469731))))], (36134 ^ _784416) ^ [_1469933, _1469935] : [class_Rings_Ocomm__semiring__1(_1469933), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1469933), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1469933), c_Groups_Oone__class_Oone(_1469933)), c_Groups_Oone__class_Oone(_1469933))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1469933), c_Nat_Osemiring__1__class_Oof__nat(_1469933)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1469935))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1469933), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1469933), _1469935)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1469933), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1469933), _1469935)), c_Groups_Oone__class_Oone(_1469933))))], (36140 ^ _784416) ^ [_1470134, _1470136, _1470138, _1470140] : [class_Groups_Oab__group__add(_1470134), 36143 ^ _784416 : [(36144 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1470136), _1470138)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1470134), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1470134, _1470134), hAPP(hAPP(c_COMBB(_1470134, tc_fun(_1470134, _1470134), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1470134)), _1470140)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1470134, tc_Nat_Onat), _1470140), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1470136, _1470138)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1470134), hAPP(_1470140, _1470136)), hAPP(_1470140, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1470138), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (36150 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1470136), _1470138))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1470134), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1470134, _1470134), hAPP(hAPP(c_COMBB(_1470134, tc_fun(_1470134, _1470134), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1470134)), _1470140)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1470134, tc_Nat_Onat), _1470140), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1470136, _1470138)) = c_Groups_Ozero__class_Ozero(_1470134))]]], (36156 ^ _784416) ^ [_1470572, _1470574, _1470576, _1470578] : [class_Rings_Ocomm__semiring__1(_1470572), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1470572), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1470572), c_Groups_Oone__class_Oone(_1470572)), c_Groups_Oone__class_Oone(_1470572))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1470572), hAPP(hAPP(c_COMBB(_1470572, _1470572, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1470572), _1470574)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1470572, _1470572), hAPP(hAPP(c_COMBB(_1470572, tc_fun(_1470572, _1470572), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1470572)), c_Nat_Osemiring__1__class_Oof__nat(_1470572))), _1470576))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1470578))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1470572), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1470572), _1470578)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1470572), _1470574), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1470572), _1470574), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1470572), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1470572), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1470578), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1470576)))))], (36162 ^ _784416) ^ [_1470895, _1470897, _1470899, _1470901, _1470903] : [class_Groups_Oordered__comm__monoid__add(_1470895), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470897), _1470899)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470897, tc_HOL_Obool)), _1470901), _1470899)), 36176 ^ _784416 : [(36177 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1470897), 36175 ^ [_1470895, _1470897, _1470899, _1470901, _1470903]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470897, tc_HOL_Obool)), _1470899), _1470901))))], (36179 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1470895), c_Groups_Ozero__class_Ozero(_1470895)), hAPP(_1470903, 36175 ^ [_1470895, _1470897, _1470899, _1470901, _1470903])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1470895), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470897, _1470895), _1470903), _1470901)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1470897, _1470895), _1470903), _1470899))))], (36183 ^ _784416) ^ [_1471381, _1471383, _1471385, _1471387, _1471389] : [class_Groups_Oordered__ab__semigroup__add(_1471381), class_Rings_Osemiring__1(_1471381), 36193 ^ _784416 : [(36194 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1471383), 36192 ^ [_1471381, _1471383, _1471385, _1471387, _1471389]), _1471385)))], (36196 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1471381), hAPP(_1471387, 36192 ^ [_1471381, _1471383, _1471385, _1471387, _1471389])), _1471389))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1471381), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1471383, _1471381), _1471387), _1471385)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1471381), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1471381), hAPP(c_Finite__Set_Ocard(_1471383), _1471385))), _1471389))))], (36200 ^ _784416) ^ [_1471771, _1471773, _1471775, _1471777, _1471779] : [class_Groups_Ocomm__monoid__add(_1471771), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471773), _1471775)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471773), _1471777)), 36214 ^ 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^ [] : [36237 ^ _784416 : [(36238 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1472266), 36236 ^ [_1472266, _1472268, _1472270]), _1472268)))], (36240 ^ _784416) ^ [] : [hAPP(_1472270, 36236 ^ [_1472266, _1472268, _1472270]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472266, tc_Nat_Onat), _1472270), _1472268) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36225 ^ _784416) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472266, tc_Nat_Onat), _1472270), _1472268) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 36228 ^ _784416 : [(36229 ^ _784416) ^ [_1472428] : [hBOOL(hAPP(hAPP(c_member(_1472266), _1472428), _1472268)), -(hAPP(_1472270, _1472428) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (36244 ^ _784416) ^ [_1472686, _1472688] : [-(hAPP(c_Finite__Set_Ocard(_1472686), _1472688) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472686, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1472686), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1472688))], (36246 ^ _784416) ^ [_1472731, _1472733, _1472735] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472731, tc_Nat_Onat), _1472733), _1472735)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472731, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1472731), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1472733)), _1472735))], (36248 ^ _784416) ^ [_1472789, _1472791, _1472793] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1472789), _1472791)), 36251 ^ _784416 : [(36252 ^ _784416) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472789, tc_Nat_Onat), _1472793), _1472791) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36256 ^ _784416 : [(36257 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1472789), 36255 ^ [_1472789, _1472791, _1472793]), _1472791)))], (36259 ^ _784416) ^ [] : [-(hAPP(_1472793, 36255 ^ [_1472789, _1472791, _1472793]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (36261 ^ _784416) ^ [_1473109] : [hBOOL(hAPP(hAPP(c_member(_1472789), _1473109), _1472791)), -(36255 ^ [_1472789, _1472791, _1472793] = _1473109), -(hAPP(_1472793, _1473109) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (36271 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1472789, tc_Nat_Onat), _1472793), _1472791) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 36272 ^ _784416 : [(36273 ^ _784416) ^ [_1473270] : [hBOOL(hAPP(hAPP(c_member(_1472789), _1473270), _1472791)), hAPP(_1472793, _1473270) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36281 ^ _784416 : [(36282 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1472789), 36280 ^ [_1472789, _1472791, _1472793, _1473270]), _1472791)))], (36284 ^ _784416) ^ [] : [_1473270 = 36280 ^ [_1472789, _1472791, _1472793, _1473270]], (36286 ^ _784416) ^ [] : [hAPP(_1472793, 36280 ^ [_1472789, _1472791, _1472793, _1473270]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (36290 ^ _784416) ^ [_1473623, _1473625, _1473627] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1473623), _1473625)), 36293 ^ _784416 : [(36294 ^ _784416) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473623, tc_Nat_Onat), _1473627), _1473625) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 36298 ^ _784416 : [(36299 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1473623), 36297 ^ [_1473623, _1473625, _1473627]), _1473625)))], (36301 ^ _784416) ^ [] : [-(hAPP(_1473627, 36297 ^ [_1473623, _1473625, _1473627]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (36303 ^ _784416) ^ [_1473943] : [hBOOL(hAPP(hAPP(c_member(_1473623), _1473943), _1473625)), -(36297 ^ [_1473623, _1473625, _1473627] = _1473943), -(hAPP(_1473627, _1473943) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (36313 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1473623, tc_Nat_Onat), _1473627), _1473625) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 36314 ^ _784416 : [(36315 ^ _784416) ^ [_1474104] : [hBOOL(hAPP(hAPP(c_member(_1473623), _1474104), _1473625)), hAPP(_1473627, _1474104) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 36323 ^ _784416 : [(36324 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1473623), 36322 ^ [_1473623, _1473625, _1473627, _1474104]), _1473625)))], (36326 ^ _784416) ^ [] : [_1474104 = 36322 ^ [_1473623, _1473625, _1473627, _1474104]], (36328 ^ _784416) ^ [] : [hAPP(_1473627, 36322 ^ [_1473623, _1473625, _1473627, _1474104]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (36332 ^ _784416) ^ [_1474457, _1474459] : [hAPP(_1474457, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1474457), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1474459)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1474457), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1474459)))], (36338 ^ _784416) ^ [_1474580, _1474582, _1474584] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474580, tc_Nat_Onat), _1474582), _1474584) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474580, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1474580), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1474582)), _1474584)))], (36340 ^ _784416) ^ [_1474638, _1474640, _1474642, _1474644] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1474638), _1474640)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1474638, tc_HOL_Obool)), _1474640), _1474642)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474638, tc_Nat_Onat), _1474644), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1474638, tc_HOL_Obool)), _1474642), _1474640)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474638, tc_Nat_Onat), _1474644), _1474642)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474638, tc_Nat_Onat), _1474644), _1474640)))], (36350 ^ _784416) ^ [_1474891, _1474893, _1474895] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1474891), _1474893), _1474895) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1474891), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1474891, tc_Int_Oint), _1474893), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1474895))), class_Groups_Ocomm__monoid__add(_1474891), class_Groups_Ocomm__monoid__mult(_1474891)], (36360 ^ _784416) ^ [_1475097, _1475099, _1475101, _1475103] : [hBOOL(hAPP(hAPP(c_member(_1475097), _1475099), _1475101)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475097, tc_Nat_Onat), _1475103), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1475097, tc_HOL_Obool)), _1475101), hAPP(hAPP(c_Set_Oinsert(_1475097), _1475099), c_Orderings_Obot__class_Obot(tc_fun(_1475097, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475097, tc_Nat_Onat), _1475103), _1475101)), hAPP(_1475103, _1475099)))], (36366 ^ _784416) ^ [_1475288, _1475290, _1475292, _1475294] : [-(hBOOL(hAPP(hAPP(c_member(_1475288), _1475290), _1475292))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475288, tc_Nat_Onat), _1475294), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1475288, tc_HOL_Obool)), _1475292), hAPP(hAPP(c_Set_Oinsert(_1475288), _1475290), c_Orderings_Obot__class_Obot(tc_fun(_1475288, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475288, tc_Nat_Onat), _1475294), _1475292))], (36372 ^ _784416) ^ [_1475379, _1475381, _1475383, _1475385] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1475379), _1475381)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1475379), _1475383)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475379, tc_Nat_Onat), _1475385), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1475379, tc_HOL_Obool)), _1475381), _1475383)) = 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(_1475379, tc_Nat_Onat), _1475385), _1475381)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475379, tc_Nat_Onat), _1475385), _1475383))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475379, tc_Nat_Onat), _1475385), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1475379, tc_HOL_Obool)), _1475381), _1475383))))], (36382 ^ _784416) ^ [_1475672, _1475674, _1475676] : [class_Groups_Ocomm__monoid__add(_1475672), class_Groups_Ocomm__monoid__mult(_1475672), c_Nat__Transfer_Onat__set(_1475674), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1475672), _1475676), _1475674) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1475672), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1475672, tc_Nat_Onat), _1475676), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1475674)))], (36396 ^ _784416) ^ [_1475917, _1475919, _1475921] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1475917)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1475919))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1475921))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1475921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1475917), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1475917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1475921), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1475919)))))], (36398 ^ _784416) ^ [_1475998, _1476000, _1476002] : [36400 ^ _784416 : [(36401 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475998), 36399 ^ [_1475998, _1476000, _1476002]), _1476000)))], (36403 ^ _784416) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1476002, 36399 ^ [_1475998, _1476000, _1476002]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475998, tc_Int_Oint), _1476002), _1476000) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1475998, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1475998), c_Int_Onat), _1476002)), _1476000)))], (36407 ^ _784416) ^ [_1476228, _1476230, _1476232, _1476234, _1476236, _1476238] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1476228), _1476230)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476232), _1476234)), 36417 ^ _784416 : [(36418 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1476232), 36416 ^ [_1476228, _1476230, _1476232, _1476234, _1476236, _1476238]), _1476234)))], (36420 ^ _784416) ^ [] : [hAPP(c_Finite__Set_Ocard(_1476228), hAPP(c_Set_OCollect(_1476228), hAPP(hAPP(c_COMBS(_1476228, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1476228), c_fconj), hAPP(hAPP(c_COMBC(_1476228, tc_fun(_1476228, tc_HOL_Obool), tc_HOL_Obool), c_member(_1476228)), _1476230))), hAPP(hAPP(c_COMBC(_1476228, _1476232, tc_HOL_Obool), _1476236), 36416 ^ [_1476228, _1476230, _1476232, _1476234, _1476236, _1476238])))) = _1476238]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476228, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1476232, tc_HOL_Obool), tc_Nat_Onat, _1476228), c_Finite__Set_Ocard(_1476232)), hAPP(hAPP(c_COMBB(tc_fun(_1476232, tc_HOL_Obool), tc_fun(_1476232, tc_HOL_Obool), _1476228), c_Set_OCollect(_1476232)), hAPP(hAPP(c_COMBB(tc_fun(_1476232, tc_HOL_Obool), tc_fun(_1476232, tc_HOL_Obool), _1476228), hAPP(c_COMBS(_1476232, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1476232), c_fconj), hAPP(hAPP(c_COMBC(_1476232, tc_fun(_1476232, tc_HOL_Obool), tc_HOL_Obool), c_member(_1476232)), _1476234)))), _1476236)))), _1476230) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1476238), hAPP(c_Finite__Set_Ocard(_1476232), _1476234)))], (36424 ^ _784416) ^ [_1476918, _1476920, _1476922, _1476924, _1476926] : [class_Groups_Ocomm__monoid__add(_1476918), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476920), _1476922)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476920), _1476924)), 36438 ^ _784416 : [(36439 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1476920), 36437 ^ [_1476918, _1476920, _1476922, _1476924, _1476926]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1476920, tc_HOL_Obool)), _1476922), _1476924))))], (36441 ^ _784416) ^ [] : [hAPP(_1476926, 36437 ^ [_1476918, _1476920, _1476922, _1476924, _1476926]) = c_Groups_Ozero__class_Ozero(_1476918)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476920, _1476918), _1476926), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1476920, tc_HOL_Obool)), _1476922), _1476924)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1476918), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476920, _1476918), _1476926), _1476922)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476920, _1476918), _1476926), _1476924)))], (36445 ^ _784416) ^ [_1477413, _1477415, _1477417, _1477419, _1477421] : [class_Groups_Ocomm__monoid__add(_1477413), class_Groups_Oordered__ab__semigroup__add(_1477413), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477415), _1477417)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1477415, tc_HOL_Obool)), _1477419), _1477417)), 36463 ^ _784416 : [(36464 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1477415), 36462 ^ [_1477413, _1477415, _1477417, _1477419, _1477421]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1477415, tc_HOL_Obool)), _1477417), _1477419))))], (36466 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1477413), c_Groups_Ozero__class_Ozero(_1477413)), hAPP(_1477421, 36462 ^ [_1477413, _1477415, _1477417, _1477419, _1477421])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1477413), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477415, _1477413), _1477421), _1477419)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477415, _1477413), _1477421), _1477417))))], (36470 ^ _784416) ^ [_1477957, _1477959, _1477961, _1477963, _1477965, _1477967] : [class_Groups_Ocomm__monoid__add(_1477957), hBOOL(hAPP(c_Finite__Set_Ofinite(_1477959), _1477961)), 36480 ^ _784416 : [(36481 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1477959), 36479 ^ [_1477957, _1477959, _1477961, _1477963, _1477965, _1477967]), _1477961)))], (36484 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1477959), 36482 ^ [_1477957, _1477959, _1477961, _1477963, _1477965, _1477967]), _1477961)))], (36486 ^ _784416) ^ [] : [36479 ^ [_1477957, _1477959, _1477961, _1477963, _1477965, _1477967] = 36482 ^ [_1477957, _1477959, _1477961, _1477963, _1477965, _1477967]], (36488 ^ _784416) ^ [] : [-(hAPP(_1477963, 36479 ^ [_1477957, _1477959, _1477961, _1477963, _1477965, _1477967]) = hAPP(_1477963, 36482 ^ [_1477957, _1477959, _1477961, _1477963, _1477965, _1477967]))], (36490 ^ _784416) ^ [] : [hAPP(_1477965, hAPP(_1477963, 36479 ^ [_1477957, _1477959, _1477961, _1477963, _1477965, _1477967])) = c_Groups_Ozero__class_Ozero(_1477957)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477967, _1477957), _1477965), hAPP(c_Set_Oimage(_1477959, _1477967, _1477963), _1477961)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477959, _1477957), hAPP(c_Fun_Ocomp(_1477967, _1477957, _1477959, _1477965), _1477963)), _1477961))], (36494 ^ _784416) ^ [_1478694, _1478696, _1478698] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1478694, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1478696)), _1478698) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1478694, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1478694, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1478696)), _1478698)), hAPP(_1478698, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36496 ^ _784416) ^ [_1478766] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1478766))))], (36498 ^ _784416) ^ [_1478794, _1478796, _1478798] : [class_Orderings_Olinorder(_1478794), 36501 ^ _784416 : [(36502 ^ _784416) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1478794), _1478796) = hAPP(c_SetInterval_Oord__class_OatMost(_1478794), _1478798), -(_1478796 = _1478798)], (36508 ^ _784416) ^ [] : [_1478796 = _1478798, -(hAPP(c_SetInterval_Oord__class_OatMost(_1478794), _1478796) = hAPP(c_SetInterval_Oord__class_OatMost(_1478794), _1478798))]]], (36514 ^ _784416) ^ [_1479035] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1479035) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1479035))], (36516 ^ _784416) ^ [_1479065] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1479065)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1479065))], (36518 ^ _784416) ^ [_1479097] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1479097)) = hAPP(c_Nat_OSuc, _1479097))], (36520 ^ _784416) ^ [_1479129] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1479129)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1479129)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1479129)))], (36522 ^ _784416) ^ [_1479170, _1479172, _1479174] : [class_Orderings_Oord(_1479170), 36525 ^ _784416 : [(36526 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1479170), _1479172), hAPP(c_SetInterval_Oord__class_OatMost(_1479170), _1479174))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1479170), _1479172), _1479174)))], (36532 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1479170), _1479172), _1479174)), -(hBOOL(hAPP(hAPP(c_member(_1479170), _1479172), hAPP(c_SetInterval_Oord__class_OatMost(_1479170), _1479174))))]]], (36538 ^ _784416) ^ [_1479438, _1479440, _1479442] : [class_Orderings_Oorder(_1479438), 36541 ^ _784416 : [(36542 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1479438, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1479438), _1479440)), hAPP(c_SetInterval_Oord__class_OatMost(_1479438), _1479442))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1479438), _1479440), _1479442)))], (36548 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1479438), _1479440), _1479442)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1479438, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1479438), _1479440)), hAPP(c_SetInterval_Oord__class_OatMost(_1479438), _1479442))))]]], (36554 ^ _784416) ^ [] : [-(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)))], (36556 ^ _784416) ^ [_1479748, _1479750, _1479752] : [class_Groups_Ocomm__monoid__add(_1479748), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1479748), _1479750), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1479752))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1479748), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1479748), _1479750), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1479752))), hAPP(_1479750, hAPP(c_Nat_OSuc, _1479752))))], (36562 ^ _784416) ^ [] : [-(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))))], (36564 ^ _784416) ^ [_1479925, _1479927, _1479929, _1479931] : [class_Orderings_Olinorder(_1479925), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1479925, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1479925), _1479927)), c_SetInterval_Oord__class_OatLeastAtMost(_1479925, _1479929, _1479931)) = c_SetInterval_Oord__class_OatLeastAtMost(_1479925, _1479929, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1479925), _1479927), _1479931)))], (36570 ^ _784416) ^ [_1480068, _1480070, _1480072, _1480074] : [class_Orderings_Olinorder(_1480068), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1480068, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1480068, _1480070, _1480072)), hAPP(c_SetInterval_Oord__class_OatMost(_1480068), _1480074)) = c_SetInterval_Oord__class_OatLeastAtMost(_1480068, _1480070, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1480068), _1480072), _1480074)))], (36576 ^ _784416) ^ [_1480211, _1480213, _1480215] : [class_Orderings_Olinorder(_1480211), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1480211), _1480213), _1480215)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480211, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1480211), _1480213)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1480211, _1480213, _1480215)) = hAPP(c_SetInterval_Oord__class_OatMost(_1480211), _1480215))], (36586 ^ _784416) ^ [_1480406, _1480408, _1480410, _1480412] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1480406, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1480408)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1480406, tc_HOL_Obool), tc_Nat_Onat), _1480410), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1480412))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1480406, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1480412, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1480408), _1480412))), _1480410))], (36588 ^ _784416) ^ [_1480488, _1480490, _1480492] : [class_Orderings_Oorder(_1480488), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1480488, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1480488), _1480490)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1480488, _1480490, _1480492)) = c_Orderings_Obot__class_Obot(tc_fun(_1480488, tc_HOL_Obool)))], (36594 ^ _784416) ^ [_1480615, _1480617, _1480619] : [class_Orderings_Oorder(_1480615), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1480615, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1480615), _1480617)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1480615, _1480617, _1480619)) = c_Orderings_Obot__class_Obot(tc_fun(_1480615, tc_HOL_Obool)))], (36600 ^ _784416) ^ [_1480742, _1480744] : [class_Orderings_Olinorder(_1480742), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480742, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1480742), _1480744)), hAPP(hAPP(c_Set_Oinsert(_1480742), _1480744), c_Orderings_Obot__class_Obot(tc_fun(_1480742, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1480742), _1480744))], (36606 ^ _784416) ^ [_1480885, _1480887, _1480889] : [class_Orderings_Olinorder(_1480885), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1480885), _1480887), _1480889)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480885, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1480885), _1480887)), c_SetInterval_Oord__class_OatLeastAtMost(_1480885, _1480887, _1480889)) = hAPP(c_SetInterval_Oord__class_OatMost(_1480885), _1480889))], (36616 ^ _784416) ^ [_1481080, _1481082, _1481084] : [class_Orderings_Olinorder(_1481080), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1481080), _1481082), _1481084)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481080, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1481080), _1481082)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1481080, _1481082, _1481084)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1481080), _1481084))], (36626 ^ _784416) ^ [_1481275] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1481275) = 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), _1481275))))], (36628 ^ _784416) ^ [_1481311, _1481313, _1481315, _1481317, _1481319, _1481321] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1481311), _1481313)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1481315), _1481317)), 36638 ^ _784416 : [(36639 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1481315), 36637 ^ [_1481311, _1481313, _1481315, _1481317, _1481319, _1481321]), _1481317)))], (36641 ^ _784416) ^ [] : [hAPP(c_Finite__Set_Ocard(_1481311), hAPP(c_Set_OCollect(_1481311), hAPP(hAPP(c_COMBS(_1481311, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1481311), c_fconj), hAPP(hAPP(c_COMBC(_1481311, tc_fun(_1481311, tc_HOL_Obool), tc_HOL_Obool), c_member(_1481311)), _1481313))), hAPP(hAPP(c_COMBC(_1481311, _1481315, tc_HOL_Obool), _1481319), 36637 ^ [_1481311, _1481313, _1481315, _1481317, _1481319, _1481321])))) = hAPP(_1481321, 36637 ^ [_1481311, _1481313, _1481315, _1481317, _1481319, _1481321])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1481311, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1481315, tc_HOL_Obool), tc_Nat_Onat, _1481311), c_Finite__Set_Ocard(_1481315)), hAPP(hAPP(c_COMBB(tc_fun(_1481315, tc_HOL_Obool), tc_fun(_1481315, tc_HOL_Obool), _1481311), c_Set_OCollect(_1481315)), hAPP(hAPP(c_COMBB(tc_fun(_1481315, tc_HOL_Obool), tc_fun(_1481315, tc_HOL_Obool), _1481311), hAPP(c_COMBS(_1481315, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1481315), c_fconj), hAPP(hAPP(c_COMBC(_1481315, tc_fun(_1481315, tc_HOL_Obool), tc_HOL_Obool), c_member(_1481315)), _1481317)))), _1481319)))), _1481313) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1481315, tc_Nat_Onat), _1481321), _1481317))], (36645 ^ _784416) ^ [_1482021, _1482023, _1482025, _1482027, _1482029] : [class_Groups_Oordered__ab__group__add(_1482021), hBOOL(hAPP(c_Finite__Set_Ofinite(_1482023), _1482025)), 36655 ^ _784416 : [(36656 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482023), 36654 ^ [_1482021, _1482023, _1482025, _1482027, _1482029]), _1482025)))], (36658 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1482021), c_Groups_Ozero__class_Ozero(_1482021)), hAPP(_1482027, 36654 ^ [_1482021, _1482023, _1482025, _1482027, _1482029])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1482023, _1482021), _1482027), _1482025) = c_Groups_Ozero__class_Ozero(_1482021), hBOOL(hAPP(hAPP(c_member(_1482023), _1482029), _1482025)), -(hAPP(_1482027, _1482029) = c_Groups_Ozero__class_Ozero(_1482021))], (36670 ^ _784416) ^ [_1482519, _1482521, _1482523, _1482525, _1482527, _1482529] : [class_Groups_Oordered__ab__group__add(_1482519), hBOOL(hAPP(c_Finite__Set_Ofinite(_1482521), _1482523)), 36680 ^ _784416 : [(36681 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1482521), 36679 ^ [_1482519, _1482521, _1482523, _1482525, _1482527, _1482529]), _1482523)))], (36683 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1482519), c_Groups_Ozero__class_Ozero(_1482519)), hAPP(_1482525, 36679 ^ [_1482519, _1482521, _1482523, _1482525, _1482527, _1482529])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1482521, _1482519), _1482525), _1482523) = _1482527, hBOOL(hAPP(hAPP(c_member(_1482521), _1482529), _1482523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1482519), hAPP(_1482525, _1482529)), _1482527)))], (36695 ^ _784416) ^ [] : [-(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))))], (36697 ^ _784416) ^ [_1483057, _1483059, _1483061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1483057, 36698 ^ [_1483057, _1483059, _1483061])), hAPP(_1483059, 36698 ^ [_1483057, _1483059, _1483061]))), -(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), _1483059), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1483061))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1483057), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1483061))) = 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)), _1483059)), _1483057)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1483061)))], (36704 ^ _784416) ^ [_1483290, _1483292, _1483294, _1483296, _1483298] : [class_Groups_Ocomm__monoid__add(_1483290), hBOOL(hAPP(c_Finite__Set_Ofinite(_1483292), _1483294)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1483292, tc_HOL_Obool)), _1483296), _1483294)), 36718 ^ _784416 : [(36719 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1483292), 36717 ^ [_1483290, _1483292, _1483294, _1483296, _1483298]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1483292, tc_HOL_Obool)), _1483294), _1483296))))], (36721 ^ _784416) ^ [] : [hAPP(_1483298, 36717 ^ [_1483290, _1483292, _1483294, _1483296, _1483298]) = c_Groups_Ozero__class_Ozero(_1483290)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1483292, _1483290), _1483298), _1483294) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1483292, _1483290), _1483298), _1483296))], (36725 ^ _784416) ^ [_1483741, _1483743, _1483745] : [class_Orderings_Olinorder(_1483741), 36728 ^ _784416 : [(36729 ^ _784416) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1483741), _1483743) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1483741), _1483745), -(_1483743 = _1483745)], (36735 ^ _784416) ^ [] : [_1483743 = _1483745, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1483741), _1483743) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1483741), _1483745))]]], (36741 ^ _784416) ^ [_1483982, _1483984, _1483986] : [class_Orderings_Oord(_1483982), 36744 ^ _784416 : [(36745 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1483982), _1483984), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1483982), _1483986))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1483982), _1483986), _1483984)))], (36751 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1483982), _1483986), _1483984)), -(hBOOL(hAPP(hAPP(c_member(_1483982), _1483984), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1483982), _1483986))))]]], (36757 ^ _784416) ^ [_1484250, _1484252, _1484254] : [class_Orderings_Olinorder(_1484250), 36760 ^ _784416 : [(36761 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484250, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1484250), _1484252)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1484250), _1484254))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1484250), _1484254), _1484252)))], (36767 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1484250), _1484254), _1484252)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484250, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1484250), _1484252)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1484250), _1484254))))]]], (36773 ^ _784416) ^ [_1484542, _1484544] : [class_Orderings_Olinorder(_1484542), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1484542, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1484542), _1484544)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1484542), _1484544))], (36779 ^ _784416) ^ [_1484653, _1484655] : [class_Orderings_Olinorder(_1484653), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1484653, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1484653), _1484655)) = hAPP(c_SetInterval_Oord__class_OatMost(_1484653), _1484655))], (36785 ^ _784416) ^ [_1484764, _1484766, _1484768] : [class_Orderings_Oorder(_1484764), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1484764, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1484764, _1484766, _1484768)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1484764), _1484768)) = c_Orderings_Obot__class_Obot(tc_fun(_1484764, tc_HOL_Obool)))], (36791 ^ _784416) ^ [_1484891, _1484893, _1484895] : [class_Orderings_Olinorder(_1484891), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1484891), _1484893), _1484895)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1484891, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1484891, _1484893, _1484895)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1484891), _1484895)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1484891), _1484893))], (36801 ^ _784416) ^ [_1485086, _1485088] : [class_Groups_Oordered__ab__group__add(_1485086), -(hAPP(c_Set_Oimage(_1485086, _1485086, c_Groups_Ouminus__class_Ouminus(_1485086)), hAPP(c_SetInterval_Oord__class_OlessThan(_1485086), _1485088)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1485086), hAPP(c_Groups_Ouminus__class_Ouminus(_1485086), _1485088)))], (36807 ^ _784416) ^ [_1485209, _1485211] : [class_Groups_Oordered__ab__group__add(_1485209), -(hAPP(c_Set_Oimage(_1485209, _1485209, c_Groups_Ouminus__class_Ouminus(_1485209)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1485209), _1485211)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1485209), hAPP(c_Groups_Ouminus__class_Ouminus(_1485209), _1485211)))], (36813 ^ _784416) ^ [_1485332, _1485334, _1485336] : [class_Orderings_Oorder(_1485332), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485332, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1485332, _1485334, _1485336)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1485332), _1485336)) = c_Orderings_Obot__class_Obot(tc_fun(_1485332, tc_HOL_Obool)))], (36819 ^ _784416) ^ [_1485459] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1485459)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1485459)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1485459)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (36821 ^ _784416) ^ [_1485506, _1485508, _1485510] : [class_Orderings_Olinorder(_1485506), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1485506), _1485508), _1485510)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1485506, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1485506, _1485508, _1485510)), hAPP(c_SetInterval_Oord__class_OatLeast(_1485506), _1485510)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1485506), _1485508))], (36831 ^ _784416) ^ [_1485701, _1485703, _1485705, _1485707, _1485709] : [class_Groups_Ocomm__monoid__add(_1485701), hBOOL(hAPP(c_Finite__Set_Ofinite(_1485703), _1485705)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1485703, tc_HOL_Obool)), _1485707), _1485705)), 36845 ^ _784416 : [(36846 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1485703), 36844 ^ [_1485701, _1485703, _1485705, _1485707, _1485709]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1485703, tc_HOL_Obool)), _1485705), _1485707))))], (36848 ^ _784416) ^ [] : [hAPP(_1485709, 36844 ^ [_1485701, _1485703, _1485705, _1485707, _1485709]) = c_Groups_Ozero__class_Ozero(_1485701)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1485703, _1485701), _1485709), _1485707) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1485703, _1485701), _1485709), _1485705))], (36852 ^ _784416) ^ [_1486152, _1486154, _1486156] : [class_Orderings_Olinorder(_1486152), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1486152), _1486154), _1486156)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1486152, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1486152, _1486154, _1486156)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1486152), _1486156)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1486152), _1486154))], (36862 ^ _784416) ^ [_1486347, _1486349, _1486351] : [class_Orderings_Olinorder(_1486347), 36865 ^ _784416 : [(36866 ^ _784416) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1486347), _1486349) = hAPP(c_SetInterval_Oord__class_OatLeast(_1486347), _1486351), -(_1486349 = _1486351)], (36872 ^ _784416) ^ [] : [_1486349 = _1486351, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1486347), _1486349) = hAPP(c_SetInterval_Oord__class_OatLeast(_1486347), _1486351))]]], (36878 ^ _784416) ^ [_1486588, _1486590, _1486592] : [class_Orderings_Oord(_1486588), 36881 ^ _784416 : [(36882 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1486588), _1486590), hAPP(c_SetInterval_Oord__class_OatLeast(_1486588), _1486592))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1486588), _1486592), _1486590)))], (36888 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1486588), _1486592), _1486590)), -(hBOOL(hAPP(hAPP(c_member(_1486588), _1486590), hAPP(c_SetInterval_Oord__class_OatLeast(_1486588), _1486592))))]]], (36894 ^ _784416) ^ [_1486856, _1486858, _1486860] : [class_Orderings_Oorder(_1486856), 36897 ^ _784416 : [(36898 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1486856, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1486856), _1486858)), hAPP(c_SetInterval_Oord__class_OatLeast(_1486856), _1486860))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1486856), _1486860), _1486858)))], (36904 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1486856), _1486860), _1486858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1486856, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1486856), _1486858)), hAPP(c_SetInterval_Oord__class_OatLeast(_1486856), _1486860))))]]], (36910 ^ _784416) ^ [] : [-(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)))], (36912 ^ _784416) ^ [_1487166, _1487168] : [class_Orderings_Olinorder(_1487166), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1487166, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1487166), _1487168)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1487166), _1487168))], (36918 ^ _784416) ^ [_1487277, _1487279] : [class_Orderings_Olinorder(_1487277), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1487277, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1487277), _1487279)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1487277), _1487279))], (36924 ^ _784416) ^ [_1487388] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1487388)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1487388))], (36926 ^ _784416) ^ [_1487420, _1487422, _1487424] : [class_Orderings_Olinorder(_1487420), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1487420), _1487422), _1487424)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1487420, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1487420, _1487422), _1487424)), hAPP(c_SetInterval_Oord__class_OatLeast(_1487420), _1487424)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1487420), _1487422))], (36936 ^ _784416) ^ [_1487619, _1487621, _1487623] : [class_Orderings_Oorder(_1487619), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487619, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1487619, _1487621), _1487623)), hAPP(c_SetInterval_Oord__class_OatLeast(_1487619), _1487623)) = c_Orderings_Obot__class_Obot(tc_fun(_1487619, tc_HOL_Obool)))], (36942 ^ _784416) ^ [_1487750, _1487752, _1487754, _1487756] : [class_Orderings_Olinorder(_1487750), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487750, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1487750, _1487752, _1487754)), hAPP(c_SetInterval_Oord__class_OatLeast(_1487750), _1487756)) = c_SetInterval_Oord__class_OatLeastAtMost(_1487750, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1487750), _1487752), _1487756), _1487754))], (36948 ^ _784416) ^ [_1487893, _1487895, _1487897, _1487899] : [class_Orderings_Olinorder(_1487893), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1487893, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1487893), _1487895)), c_SetInterval_Oord__class_OatLeastAtMost(_1487893, _1487897, _1487899)) = c_SetInterval_Oord__class_OatLeastAtMost(_1487893, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1487893), _1487895), _1487897), _1487899))], (36954 ^ _784416) ^ [] : [-(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)))], (36956 ^ _784416) ^ [_1488054, _1488056, _1488058] : [class_Orderings_Oorder(_1488054), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1488054, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1488054, _1488056, _1488058)), hAPP(c_SetInterval_Oord__class_OatLeast(_1488054), _1488058)) = c_Orderings_Obot__class_Obot(tc_fun(_1488054, tc_HOL_Obool)))], (36962 ^ _784416) ^ [_1488181, _1488183] : [class_Groups_Oordered__ab__group__add(_1488181), -(hAPP(c_Set_Oimage(_1488181, _1488181, c_Groups_Ouminus__class_Ouminus(_1488181)), hAPP(c_SetInterval_Oord__class_OatMost(_1488181), _1488183)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1488181), hAPP(c_Groups_Ouminus__class_Ouminus(_1488181), _1488183)))], (36968 ^ _784416) ^ [_1488304, _1488306] : [class_Groups_Oordered__ab__group__add(_1488304), -(hAPP(c_Set_Oimage(_1488304, _1488304, c_Groups_Ouminus__class_Ouminus(_1488304)), hAPP(c_SetInterval_Oord__class_OatLeast(_1488304), _1488306)) = hAPP(c_SetInterval_Oord__class_OatMost(_1488304), hAPP(c_Groups_Ouminus__class_Ouminus(_1488304), _1488306)))], (36974 ^ _784416) ^ [_1488427] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1488427)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1488427)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1488427), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (36976 ^ _784416) ^ [_1488471, _1488473] : [class_Orderings_Oorder(_1488471), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1488471, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1488471), _1488473)), hAPP(c_SetInterval_Oord__class_OatLeast(_1488471), _1488473)) = hAPP(hAPP(c_Set_Oinsert(_1488471), _1488473), c_Orderings_Obot__class_Obot(tc_fun(_1488471, tc_HOL_Obool))))], (36982 ^ _784416) ^ [_1488614, _1488616] : [class_Orderings_Olinorder(_1488614), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1488614, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1488614), _1488616), c_Orderings_Obot__class_Obot(tc_fun(_1488614, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1488614), _1488616)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1488614), _1488616))], (36988 ^ _784416) ^ [_1488757, _1488759, _1488761, _1488763, _1488765] : [class_Groups_Ocomm__monoid__add(_1488757), class_Groups_Oordered__cancel__ab__semigroup__add(_1488757), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488759), _1488761)), -(_1488761 = c_Orderings_Obot__class_Obot(tc_fun(_1488759, tc_HOL_Obool))), 37006 ^ _784416 : [(37007 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488759), 37005 ^ [_1488757, _1488759, _1488761, _1488763, _1488765]), _1488761)))], (37009 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1488757), hAPP(_1488763, 37005 ^ [_1488757, _1488759, _1488761, _1488763, _1488765])), hAPP(_1488765, 37005 ^ [_1488757, _1488759, _1488761, _1488763, _1488765])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1488757), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1488759, _1488757), _1488763), _1488761)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1488759, _1488757), _1488765), _1488761))))], (37013 ^ _784416) ^ [_1489288, _1489290, _1489292] : [class_Fields_Olinordered__field__inverse__zero(_1489288), 37019 ^ _784416 : [(37020 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1489288), c_Groups_Ozero__class_Ozero(_1489288)), 37018 ^ [_1489288, _1489290, _1489292])))], (37022 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1489288), 37018 ^ [_1489288, _1489290, _1489292]), c_Groups_Oone__class_Oone(_1489288))))], (37024 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1489288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1489288), 37018 ^ [_1489288, _1489290, _1489292]), _1489290)), _1489292))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1489288), _1489290), _1489292)))], (37028 ^ _784416) ^ [_1489637, _1489639, _1489641, _1489643, _1489645] : [class_Groups_Ocomm__monoid__add(_1489637), class_Groups_Ocomm__monoid__mult(_1489637), _1489639 = _1489641, c_Nat__Transfer_Onat__set(_1489641), 37046 ^ _784416 : [(37047 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37045 ^ [_1489637, _1489639, _1489641, _1489643, _1489645])))], (37049 ^ _784416) ^ [] : [hAPP(_1489643, 37045 ^ [_1489637, _1489639, _1489641, _1489643, _1489645]) = hAPP(_1489645, 37045 ^ [_1489637, _1489639, _1489641, _1489643, _1489645])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1489637), _1489643), _1489639) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1489637), _1489645), _1489641))], (37053 ^ _784416) ^ [_1490100, _1490102] : [class_Groups_Osgn__if(_1490100), 37056 ^ _784416 : [(37057 ^ _784416) ^ [] : [_1490102 = c_Groups_Ozero__class_Ozero(_1490100), -(c_Groups_Osgn__class_Osgn(_1490100, _1490102) = c_Groups_Ozero__class_Ozero(_1490100))], (37063 ^ _784416) ^ [] : [-(_1490102 = c_Groups_Ozero__class_Ozero(_1490100)), 37066 ^ _784416 : [(37067 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1490100), c_Groups_Ozero__class_Ozero(_1490100)), _1490102)), -(c_Groups_Osgn__class_Osgn(_1490100, _1490102) = c_Groups_Oone__class_Oone(_1490100))], (37073 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1490100), c_Groups_Ozero__class_Ozero(_1490100)), _1490102))), -(c_Groups_Osgn__class_Osgn(_1490100, _1490102) = hAPP(c_Groups_Ouminus__class_Ouminus(_1490100), c_Groups_Oone__class_Oone(_1490100)))]]]]], (37079 ^ _784416) ^ [_1490497, _1490499] : [class_Rings_Olinordered__idom(_1490497), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1490497), _1490499), c_Groups_Ozero__class_Ozero(_1490497))), -(c_Groups_Osgn__class_Osgn(_1490497, _1490499) = hAPP(c_Groups_Ouminus__class_Ouminus(_1490497), c_Groups_Oone__class_Oone(_1490497)))], (37089 ^ _784416) ^ [_1490662, _1490664] : [class_Rings_Olinordered__idom(_1490662), 37092 ^ _784416 : [(37093 ^ _784416) ^ [] : [c_Groups_Osgn__class_Osgn(_1490662, _1490664) = hAPP(c_Groups_Ouminus__class_Ouminus(_1490662), c_Groups_Oone__class_Oone(_1490662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1490662), _1490664), c_Groups_Ozero__class_Ozero(_1490662))))], (37099 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1490662), _1490664), c_Groups_Ozero__class_Ozero(_1490662))), -(c_Groups_Osgn__class_Osgn(_1490662, _1490664) = hAPP(c_Groups_Ouminus__class_Ouminus(_1490662), c_Groups_Oone__class_Oone(_1490662)))]]], (37105 ^ _784416) ^ [_1490924] : [class_Groups_Osgn__if(_1490924), -(c_Groups_Osgn__class_Osgn(_1490924, c_Groups_Ozero__class_Ozero(_1490924)) = c_Groups_Ozero__class_Ozero(_1490924))], (37111 ^ _784416) ^ [_1491011, _1491013] : [class_Rings_Olinordered__idom(_1491011), 37114 ^ _784416 : [(37115 ^ _784416) ^ [] : [c_Groups_Osgn__class_Osgn(_1491011, _1491013) = c_Groups_Ozero__class_Ozero(_1491011), -(_1491013 = c_Groups_Ozero__class_Ozero(_1491011))], (37121 ^ _784416) ^ [] : [_1491013 = c_Groups_Ozero__class_Ozero(_1491011), -(c_Groups_Osgn__class_Osgn(_1491011, _1491013) = c_Groups_Ozero__class_Ozero(_1491011))]]], (37127 ^ _784416) ^ [_1491237, _1491239] : [class_Rings_Olinordered__idom(_1491237), -(c_Groups_Osgn__class_Osgn(_1491237, c_Groups_Osgn__class_Osgn(_1491237, _1491239)) = c_Groups_Osgn__class_Osgn(_1491237, _1491239))], (37133 ^ _784416) ^ [_1491330, _1491332, _1491334] : [class_Rings_Olinordered__idom(_1491330), -(c_Groups_Osgn__class_Osgn(_1491330, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1491330), _1491332), _1491334)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1491330), c_Groups_Osgn__class_Osgn(_1491330, _1491332)), c_Groups_Osgn__class_Osgn(_1491330, _1491334)))], (37139 ^ _784416) ^ [_1491457, _1491459] : [class_Rings_Olinordered__idom(_1491457), 37142 ^ _784416 : [(37143 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1491457), c_Groups_Osgn__class_Osgn(_1491457, _1491459)), c_Groups_Ozero__class_Ozero(_1491457))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1491457), _1491459), c_Groups_Ozero__class_Ozero(_1491457))))], (37149 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1491457), _1491459), c_Groups_Ozero__class_Ozero(_1491457))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1491457), c_Groups_Osgn__class_Osgn(_1491457, _1491459)), c_Groups_Ozero__class_Ozero(_1491457))))]]], (37155 ^ _784416) ^ [_1491725, _1491727] : [class_Rings_Olinordered__idom(_1491725), 37158 ^ _784416 : [(37159 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1491725), c_Groups_Ozero__class_Ozero(_1491725)), c_Groups_Osgn__class_Osgn(_1491725, _1491727))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1491725), c_Groups_Ozero__class_Ozero(_1491725)), _1491727)))], (37165 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1491725), c_Groups_Ozero__class_Ozero(_1491725)), _1491727)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1491725), c_Groups_Ozero__class_Ozero(_1491725)), c_Groups_Osgn__class_Osgn(_1491725, _1491727))))]]], (37171 ^ _784416) ^ [_1491993, _1491995] : [class_Rings_Olinordered__idom(_1491993), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1491993), c_Groups_Ozero__class_Ozero(_1491993)), _1491995)), -(c_Groups_Osgn__class_Osgn(_1491993, _1491995) = c_Groups_Oone__class_Oone(_1491993))], (37181 ^ _784416) ^ [_1492148, _1492150] : [class_Rings_Olinordered__idom(_1492148), 37184 ^ _784416 : [(37185 ^ _784416) ^ [] : [c_Groups_Osgn__class_Osgn(_1492148, _1492150) = c_Groups_Oone__class_Oone(_1492148), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1492148), c_Groups_Ozero__class_Ozero(_1492148)), _1492150)))], (37191 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1492148), c_Groups_Ozero__class_Ozero(_1492148)), _1492150)), -(c_Groups_Osgn__class_Osgn(_1492148, _1492150) = c_Groups_Oone__class_Oone(_1492148))]]], (37197 ^ _784416) ^ [_1492401] : [_1492401 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1492401) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37203 ^ _784416) ^ [_1492477] : [-(_1492477 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37206 ^ _784416 : [(37207 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1492477)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1492477) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (37213 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1492477))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1492477) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (37219 ^ _784416) ^ [_1492669, _1492671, _1492673, _1492675] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1492669, _1492671, _1492673, c_Code__Numeral_OSuc__code__numeral(_1492675)) = hAPP(_1492673, _1492675))], (37221 ^ _784416) ^ [_1492708, _1492710, _1492712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1492708)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1492710), 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), _1492710), _1492712))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1492708))), _1492712)))], (37227 ^ _784416) ^ [_1492855, _1492857, _1492859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1492855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1492857), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1492859), 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), _1492859), _1492857))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1492855)))))], (37233 ^ _784416) ^ [_1493002, _1493004, _1493006, _1493008] : [class_Groups_Oordered__ab__group__add__abs(_1493002), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1493002), hAPP(c_Groups_Oabs__class_Oabs(_1493002), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1493004, _1493002), _1493006), _1493008))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1493004, _1493002), hAPP(hAPP(c_COMBB(_1493002, _1493002, _1493004), c_Groups_Oabs__class_Oabs(_1493002)), _1493006)), _1493008))))], (37239 ^ _784416) ^ [_1493165, _1493167, _1493169, _1493171] : [class_Groups_Oordered__ab__group__add__abs(_1493165), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1493165), c_Groups_Ozero__class_Ozero(_1493165)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1493167, _1493165), hAPP(hAPP(c_COMBB(_1493165, _1493165, _1493167), c_Groups_Oabs__class_Oabs(_1493165)), _1493169)), _1493171))))], (37245 ^ _784416) ^ [_1493304, _1493306, _1493308] : [class_Groups_Oordered__ab__group__add__abs(_1493304), -(hAPP(c_Groups_Oabs__class_Oabs(_1493304), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1493304), _1493306), _1493308)) = hAPP(c_Groups_Oabs__class_Oabs(_1493304), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1493304), _1493308), _1493306)))], (37251 ^ _784416) ^ [_1493433, _1493435] : [class_Groups_Oordered__ab__group__add__abs(_1493433), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1493433), hAPP(c_Groups_Oabs__class_Oabs(_1493433), _1493435)), c_Groups_Ozero__class_Ozero(_1493433)))], (37257 ^ _784416) ^ [_1493537, _1493539] : [class_Groups_Oordered__ab__group__add__abs(_1493537), 37260 ^ _784416 : [(37261 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1493537), c_Groups_Ozero__class_Ozero(_1493537)), hAPP(c_Groups_Oabs__class_Oabs(_1493537), _1493539))), _1493539 = c_Groups_Ozero__class_Ozero(_1493537)], (37267 ^ _784416) ^ [] : [-(_1493539 = c_Groups_Ozero__class_Ozero(_1493537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1493537), c_Groups_Ozero__class_Ozero(_1493537)), hAPP(c_Groups_Oabs__class_Oabs(_1493537), _1493539))))]]], (37273 ^ _784416) ^ [_1493752, _1493754] : [class_Groups_Oordered__ab__group__add__abs(_1493752), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1493752), c_Groups_Ozero__class_Ozero(_1493752)), _1493754)), -(hAPP(c_Groups_Oabs__class_Oabs(_1493752), _1493754) = _1493754)], (37283 ^ _784416) ^ [_1493907, _1493909] : [class_Groups_Oordered__ab__group__add__abs(_1493907), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1493907), c_Groups_Ozero__class_Ozero(_1493907)), hAPP(c_Groups_Oabs__class_Oabs(_1493907), _1493909))))], (37289 ^ _784416) ^ [_1494010, _1494012] : [class_Groups_Oordered__ab__group__add__abs(_1494010), 37292 ^ _784416 : [(37293 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1494010), hAPP(c_Groups_Oabs__class_Oabs(_1494010), _1494012)), c_Groups_Ozero__class_Ozero(_1494010))), -(_1494012 = c_Groups_Ozero__class_Ozero(_1494010))], (37299 ^ _784416) ^ [] : [_1494012 = c_Groups_Ozero__class_Ozero(_1494010), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1494010), hAPP(c_Groups_Oabs__class_Oabs(_1494010), _1494012)), c_Groups_Ozero__class_Ozero(_1494010))))]]], (37305 ^ _784416) ^ [_1494263, _1494265] : [class_Groups_Oordered__ab__group__add__abs(_1494263), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1494263), c_Groups_Ozero__class_Ozero(_1494263)), _1494265)), -(hAPP(c_Groups_Oabs__class_Oabs(_1494263), _1494265) = _1494265)], (37315 ^ _784416) ^ [_1494418, _1494420, _1494422, _1494424] : [class_Groups_Oordered__ab__group__add__abs(_1494418), -(hAPP(c_Groups_Oabs__class_Oabs(_1494418), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1494420, _1494418), hAPP(hAPP(c_COMBB(_1494418, _1494418, _1494420), c_Groups_Oabs__class_Oabs(_1494418)), _1494422)), _1494424)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1494420, _1494418), hAPP(hAPP(c_COMBB(_1494418, _1494418, _1494420), c_Groups_Oabs__class_Oabs(_1494418)), _1494422)), _1494424))], (37321 ^ _784416) ^ [_1494591, _1494593] : [class_Rings_Olinordered__idom(_1494591), -(hAPP(c_Groups_Oabs__class_Oabs(_1494591), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1494591), _1494593)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1494591), _1494593))], (37327 ^ _784416) ^ [_1494696] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1494696)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1494696))], (37329 ^ _784416) ^ [_1494728, _1494730, _1494732, _1494734] : [class_Fields_Olinordered__field(_1494728), -(hAPP(c_Groups_Oabs__class_Oabs(_1494728), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1494730, _1494728), _1494732), _1494734)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1494730, _1494728), hAPP(hAPP(c_COMBB(_1494728, _1494728, _1494730), c_Groups_Oabs__class_Oabs(_1494728)), _1494732)), _1494734))], (37335 ^ _784416) ^ [_1494877] : [class_Rings_Olinordered__idom(_1494877), -(hAPP(c_Groups_Oabs__class_Oabs(_1494877), c_Groups_Oone__class_Oone(_1494877)) = c_Groups_Oone__class_Oone(_1494877))], (37341 ^ _784416) ^ [_1494968, _1494970, _1494972] : [class_Fields_Olinordered__field__inverse__zero(_1494968), -(hAPP(c_Groups_Oabs__class_Oabs(_1494968), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1494968), _1494970), _1494972)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1494968), hAPP(c_Groups_Oabs__class_Oabs(_1494968), _1494970)), hAPP(c_Groups_Oabs__class_Oabs(_1494968), _1494972)))], (37347 ^ _784416) ^ [_1495107, _1495109] : [class_Groups_Oordered__ab__group__add__abs(_1495107), -(hAPP(c_Groups_Oabs__class_Oabs(_1495107), hAPP(c_Groups_Ouminus__class_Ouminus(_1495107), _1495109)) = hAPP(c_Groups_Oabs__class_Oabs(_1495107), _1495109))], (37353 ^ _784416) ^ [_1495212, _1495214] : [class_Groups_Oordered__ab__group__add__abs(_1495212), -(hAPP(c_Groups_Oabs__class_Oabs(_1495212), hAPP(c_Groups_Oabs__class_Oabs(_1495212), _1495214)) = hAPP(c_Groups_Oabs__class_Oabs(_1495212), _1495214))], (37359 ^ _784416) ^ [_1495317, _1495319, _1495321] : [class_Rings_Olinordered__idom(_1495317), -(hAPP(c_Groups_Oabs__class_Oabs(_1495317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1495317), _1495319), _1495321)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1495317), hAPP(c_Groups_Oabs__class_Oabs(_1495317), _1495319)), hAPP(c_Groups_Oabs__class_Oabs(_1495317), _1495321)))], (37365 ^ _784416) ^ [_1495456, _1495458] : [class_Rings_Olinordered__idom(_1495456), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1495456), hAPP(c_Groups_Oabs__class_Oabs(_1495456), _1495458)), hAPP(c_Groups_Oabs__class_Oabs(_1495456), _1495458)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1495456), _1495458), _1495458))], (37371 ^ _784416) ^ [_1495583, _1495585, _1495587] : [class_Groups_Oordered__ab__group__add__abs(_1495583), -(hAPP(c_Groups_Oabs__class_Oabs(_1495583), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1495583), hAPP(c_Groups_Oabs__class_Oabs(_1495583), _1495585)), hAPP(c_Groups_Oabs__class_Oabs(_1495583), _1495587))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1495583), hAPP(c_Groups_Oabs__class_Oabs(_1495583), _1495585)), hAPP(c_Groups_Oabs__class_Oabs(_1495583), _1495587)))], (37377 ^ _784416) ^ [_1495742, _1495744, _1495746] : [class_Rings_Olinordered__idom(_1495742), -(hAPP(c_Groups_Oabs__class_Oabs(_1495742), hAPP(hAPP(c_Power_Opower__class_Opower(_1495742), _1495744), _1495746)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1495742), hAPP(c_Groups_Oabs__class_Oabs(_1495742), _1495744)), _1495746))], (37383 ^ _784416) ^ [_1495871, _1495873] : [class_Groups_Oordered__ab__group__add__abs(_1495871), 37386 ^ _784416 : [(37387 ^ _784416) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1495871), _1495873) = c_Groups_Ozero__class_Ozero(_1495871), -(_1495873 = c_Groups_Ozero__class_Ozero(_1495871))], (37393 ^ _784416) ^ [] : [_1495873 = c_Groups_Ozero__class_Ozero(_1495871), -(hAPP(c_Groups_Oabs__class_Oabs(_1495871), _1495873) = c_Groups_Ozero__class_Ozero(_1495871))]]], (37399 ^ _784416) ^ [_1496103] : [class_Groups_Oordered__ab__group__add__abs(_1496103), -(hAPP(c_Groups_Oabs__class_Oabs(_1496103), c_Groups_Ozero__class_Ozero(_1496103)) = c_Groups_Ozero__class_Ozero(_1496103))], (37405 ^ _784416) ^ [_1496194, _1496196, _1496198] : [class_Groups_Oordered__ab__group__add__abs(_1496194), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1496194), hAPP(c_Groups_Oabs__class_Oabs(_1496194), _1496196)), _1496198)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1496194), _1496196), _1496198)))], (37415 ^ _784416) ^ [_1496363, _1496365] : [class_Groups_Oordered__ab__group__add__abs(_1496363), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1496363), _1496365), hAPP(c_Groups_Oabs__class_Oabs(_1496363), _1496365))))], (37421 ^ _784416) ^ [_1496462, _1496464, _1496466] : [class_Groups_Oordered__ab__group__add__abs(_1496462), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1496462), hAPP(c_Groups_Oabs__class_Oabs(_1496462), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1496462), hAPP(c_Groups_Oabs__class_Oabs(_1496462), _1496464)), hAPP(c_Groups_Oabs__class_Oabs(_1496462), _1496466)))), hAPP(c_Groups_Oabs__class_Oabs(_1496462), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1496462), _1496464), _1496466)))))], (37427 ^ _784416) ^ [_1496625, _1496627, _1496629] : [class_Groups_Oordered__ab__group__add__abs(_1496625), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1496625), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1496625), hAPP(c_Groups_Oabs__class_Oabs(_1496625), _1496627)), hAPP(c_Groups_Oabs__class_Oabs(_1496625), _1496629))), hAPP(c_Groups_Oabs__class_Oabs(_1496625), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1496625), _1496627), _1496629)))))], (37433 ^ _784416) ^ [_1496778, _1496780, _1496782] : [class_Groups_Oordered__ab__group__add__abs(_1496778), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1496778), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1496778), hAPP(c_Groups_Oabs__class_Oabs(_1496778), _1496780)), hAPP(c_Groups_Oabs__class_Oabs(_1496778), _1496782))), hAPP(c_Groups_Oabs__class_Oabs(_1496778), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1496778), _1496782), _1496780)))))], (37439 ^ _784416) ^ [_1496931, _1496933, _1496935, _1496937, _1496939] : [class_Rings_Olinordered__idom(_1496931), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1496931), hAPP(c_Groups_Oabs__class_Oabs(_1496931), _1496933)), _1496935)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1496931), hAPP(c_Groups_Oabs__class_Oabs(_1496931), _1496937)), _1496939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1496931), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1496931), hAPP(c_Groups_Oabs__class_Oabs(_1496931), _1496933)), hAPP(c_Groups_Oabs__class_Oabs(_1496931), _1496937))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1496931), _1496935), _1496939))))], (37453 ^ _784416) ^ [_1497242, _1497244, _1497246] : [class_Groups_Oordered__ab__group__add__abs(_1497242), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497242), hAPP(c_Groups_Oabs__class_Oabs(_1497242), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1497242), _1497244), _1497246))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1497242), hAPP(c_Groups_Oabs__class_Oabs(_1497242), _1497244)), hAPP(c_Groups_Oabs__class_Oabs(_1497242), _1497246)))))], (37459 ^ _784416) ^ [_1497395, _1497397] : [class_Groups_Oordered__ab__group__add__abs(_1497395), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497395), hAPP(c_Groups_Ouminus__class_Ouminus(_1497395), _1497397)), hAPP(c_Groups_Oabs__class_Oabs(_1497395), _1497397))))], (37465 ^ _784416) ^ [_1497504, _1497506, _1497508] : [class_Groups_Oordered__ab__group__add__abs(_1497504), 37468 ^ _784416 : [(37469 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497504), hAPP(c_Groups_Oabs__class_Oabs(_1497504), _1497506)), _1497508)), 37472 ^ _784416 : [(37473 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497504), _1497506), _1497508)))], (37475 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497504), hAPP(c_Groups_Ouminus__class_Ouminus(_1497504), _1497506)), _1497508)))]]], (37477 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497504), hAPP(c_Groups_Oabs__class_Oabs(_1497504), _1497506)), _1497508))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497504), _1497506), _1497508)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497504), hAPP(c_Groups_Ouminus__class_Ouminus(_1497504), _1497506)), _1497508))]]], (37487 ^ _784416) ^ [_1497882, _1497884, _1497886] : [class_Groups_Oordered__ab__group__add__abs(_1497882), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497882), _1497884), _1497886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497882), hAPP(c_Groups_Ouminus__class_Ouminus(_1497882), _1497884)), _1497886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1497882), hAPP(c_Groups_Oabs__class_Oabs(_1497882), _1497884)), _1497886)))], (37501 ^ _784416) ^ [_1498129, _1498131, _1498133] : [class_Groups_Oordered__ab__group__add__abs(_1498129), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498129), hAPP(c_Groups_Oabs__class_Oabs(_1498129), _1498131)), _1498133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1498129), hAPP(c_Groups_Ouminus__class_Ouminus(_1498129), _1498131)), _1498133)))], (37511 ^ _784416) ^ [_1498308, _1498310, _1498312] : [class_Rings_Olinordered__idom(_1498308), 37514 ^ _784416 : [(37515 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1498308), hAPP(c_Groups_Oabs__class_Oabs(_1498308), _1498310)), _1498312)), 37518 ^ _784416 : [(37519 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1498308), _1498310), _1498312)))], (37521 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1498308), hAPP(c_Groups_Ouminus__class_Ouminus(_1498308), _1498310)), _1498312)))]]], (37523 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1498308), hAPP(c_Groups_Oabs__class_Oabs(_1498308), _1498310)), _1498312))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1498308), _1498310), _1498312)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1498308), hAPP(c_Groups_Ouminus__class_Ouminus(_1498308), _1498310)), _1498312))]]], (37533 ^ _784416) ^ [_1498686, _1498688, _1498690] : [class_Fields_Olinordered__field(_1498686), -(_1498688 = c_Groups_Ozero__class_Ozero(_1498686)), -(hAPP(c_Groups_Oabs__class_Oabs(_1498686), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1498686), _1498690), _1498688)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1498686), hAPP(c_Groups_Oabs__class_Oabs(_1498686), _1498690)), hAPP(c_Groups_Oabs__class_Oabs(_1498686), _1498688)))], (37543 ^ _784416) ^ [_1498844, _1498846, _1498848] : [class_Rings_Olinordered__idom(_1498844), -(hAPP(c_Groups_Oabs__class_Oabs(_1498844), hAPP(hAPP(c_Power_Opower__class_Opower(_1498844), hAPP(c_Groups_Ouminus__class_Ouminus(_1498844), _1498846)), _1498848)) = hAPP(c_Groups_Oabs__class_Oabs(_1498844), hAPP(hAPP(c_Power_Opower__class_Opower(_1498844), _1498846), _1498848)))], (37549 ^ _784416) ^ [_1498983, _1498985] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1498983), _1498985)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1498983) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (37555 ^ _784416) ^ [_1499084, _1499086] : [class_Rings_Olinordered__idom(_1499084), -(hAPP(c_Groups_Oabs__class_Oabs(_1499084), _1499086) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1499084), _1499086), c_Groups_Osgn__class_Osgn(_1499084, _1499086)))], (37561 ^ _784416) ^ [_1499191, _1499193] : [class_Rings_Olinordered__idom(_1499191), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1499191), c_Groups_Osgn__class_Osgn(_1499191, _1499193)), hAPP(c_Groups_Oabs__class_Oabs(_1499191), _1499193)) = _1499193)], (37567 ^ _784416) ^ [_1499298, _1499300, _1499302] : [class_Rings_Olinordered__idom(_1499298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499298), c_Groups_Ozero__class_Ozero(_1499298)), _1499300)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1499298), hAPP(c_Groups_Oabs__class_Oabs(_1499298), _1499302)), _1499300) = hAPP(c_Groups_Oabs__class_Oabs(_1499298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1499298), _1499302), _1499300)))], (37577 ^ _784416) ^ [_1499499, _1499501, _1499503] : [class_Rings_Oordered__ring__abs(_1499499), -(hAPP(c_Groups_Oabs__class_Oabs(_1499499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1499499), _1499501), _1499503)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1499499), hAPP(c_Groups_Oabs__class_Oabs(_1499499), _1499501)), hAPP(c_Groups_Oabs__class_Oabs(_1499499), _1499503))), 37584 ^ _784416 : [(37585 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499499), c_Groups_Ozero__class_Ozero(_1499499)), _1499501))], (37587 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499499), _1499501), c_Groups_Ozero__class_Ozero(_1499499)))]], 37588 ^ _784416 : [(37589 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499499), c_Groups_Ozero__class_Ozero(_1499499)), _1499503))], (37591 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499499), _1499503), c_Groups_Ozero__class_Ozero(_1499499)))]]], (37595 ^ _784416) ^ [_1499894, _1499896, _1499898, _1499900, _1499902] : [class_Groups_Oordered__ab__group__add__abs(_1499894), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1499894), hAPP(c_Groups_Oabs__class_Oabs(_1499894), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1499894), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1499894), _1499896), _1499898)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1499894), _1499900), _1499902)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1499894), hAPP(c_Groups_Oabs__class_Oabs(_1499894), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1499894), _1499896), _1499900))), hAPP(c_Groups_Oabs__class_Oabs(_1499894), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1499894), _1499898), _1499902))))))], (37601 ^ _784416) ^ [_1500115, _1500117, _1500119] : [class_Groups_Oordered__ab__group__add__abs(_1500115), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1500115), hAPP(c_Groups_Oabs__class_Oabs(_1500115), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1500115), _1500117), _1500119))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1500115), hAPP(c_Groups_Oabs__class_Oabs(_1500115), _1500117)), hAPP(c_Groups_Oabs__class_Oabs(_1500115), _1500119)))))], (37607 ^ _784416) ^ [_1500268, _1500270] : [class_Groups_Oordered__ab__group__add__abs(_1500268), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1500268), hAPP(c_Groups_Ouminus__class_Ouminus(_1500268), hAPP(c_Groups_Oabs__class_Oabs(_1500268), _1500270))), c_Groups_Ozero__class_Ozero(_1500268))))], (37613 ^ _784416) ^ [_1500381, _1500383] : [class_Groups_Oordered__ab__group__add__abs(_1500381), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1500381), _1500383), c_Groups_Ozero__class_Ozero(_1500381))), -(hAPP(c_Groups_Oabs__class_Oabs(_1500381), _1500383) = hAPP(c_Groups_Ouminus__class_Ouminus(_1500381), _1500383))], (37623 ^ _784416) ^ [_1500546, _1500548] : [class_Groups_Oabs__if(_1500546), 37626 ^ _784416 : [(37627 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500546), _1500548), c_Groups_Ozero__class_Ozero(_1500546))), -(hAPP(c_Groups_Oabs__class_Oabs(_1500546), _1500548) = hAPP(c_Groups_Ouminus__class_Ouminus(_1500546), _1500548))], (37633 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500546), _1500548), c_Groups_Ozero__class_Ozero(_1500546)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1500546), _1500548) = _1500548)]]], (37639 ^ _784416) ^ [_1500786, _1500788] : [class_Groups_Oordered__ab__group__add__abs(_1500786), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1500786), _1500788), c_Groups_Ozero__class_Ozero(_1500786))), -(hAPP(c_Groups_Oabs__class_Oabs(_1500786), _1500788) = hAPP(c_Groups_Ouminus__class_Ouminus(_1500786), _1500788))], (37649 ^ _784416) ^ [_1500951, _1500953, _1500955] : [class_Rings_Olinordered__idom(_1500951), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1500951), c_Groups_Ozero__class_Ozero(_1500951)), hAPP(hAPP(c_Power_Opower__class_Opower(_1500951), hAPP(c_Groups_Oabs__class_Oabs(_1500951), _1500953)), _1500955))))], (37655 ^ _784416) ^ [_1501072, _1501074, _1501076] : [class_Fields_Olinordered__field__inverse__zero(_1501072), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1501072), c_Groups_Ozero__class_Ozero(_1501072)), _1501074)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1501072), hAPP(c_Groups_Oabs__class_Oabs(_1501072), _1501076)), _1501074) = hAPP(c_Groups_Oabs__class_Oabs(_1501072), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1501072), _1501076), _1501074)))], (37665 ^ _784416) ^ [_1501273] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1501273), hAPP(c_Int_Onumber__class_Onumber__of(_1501273), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1501273)), class_Int_Onumber__ring(_1501273), class_Rings_Olinordered__idom(_1501273)], (37675 ^ _784416) ^ [_1501430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1501430)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1501430 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37681 ^ _784416) ^ [_1501517] : [_1501517 = 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), _1501517)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (37687 ^ _784416) ^ [_1501616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1501616), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1501616) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1501616))], (37693 ^ _784416) ^ [_1501707] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1501707), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1501707) = _1501707)], (37699 ^ _784416) ^ [_1501751, _1501753] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1501751), _1501753))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1501751))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1501753))))], (37701 ^ _784416) ^ [_1501806, _1501808] : [-(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), _1501806)), _1501808))))], (37703 ^ _784416) ^ [_1501842, _1501844] : [class_Int_Onumber__ring(_1501842), class_Rings_Olinordered__idom(_1501842), 37710 ^ _784416 : [(37711 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1501842), hAPP(c_Int_Onumber__class_Onumber__of(_1501842), _1501844)), c_Groups_Ozero__class_Ozero(_1501842))), -(hAPP(c_Groups_Oabs__class_Oabs(_1501842), hAPP(c_Int_Onumber__class_Onumber__of(_1501842), _1501844)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1501842), hAPP(c_Int_Onumber__class_Onumber__of(_1501842), _1501844)))], (37717 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1501842), hAPP(c_Int_Onumber__class_Onumber__of(_1501842), _1501844)), c_Groups_Ozero__class_Ozero(_1501842)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1501842), hAPP(c_Int_Onumber__class_Onumber__of(_1501842), _1501844)) = hAPP(c_Int_Onumber__class_Onumber__of(_1501842), _1501844))]]], (37723 ^ _784416) ^ [_1502194, _1502196] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1502194), hAPP(hAPP(c_Power_Opower__class_Opower(_1502194), hAPP(c_Int_Onumber__class_Onumber__of(_1502194), c_Int_OMin)), _1502196)) = c_Groups_Oone__class_Oone(_1502194)), class_Int_Onumber__ring(_1502194), class_Rings_Olinordered__idom(_1502194)], (37743 ^ _784416) ^ [_1502523, _1502525] : [37744 ^ _784416 : [(37745 ^ _784416) ^ [] : [-(_1502523 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37747 ^ _784416) ^ [] : [_1502525 = 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), _1502523)), _1502525))))], (37733 ^ _784416) ^ [_1502374, _1502376] : [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), _1502374)), _1502376))), _1502374 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1502376 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37751 ^ _784416) ^ [_1502659, _1502661] : [class_Rings_Olinordered__idom(_1502659), -(hAPP(c_Groups_Oabs__class_Oabs(_1502659), hAPP(hAPP(c_Power_Opower__class_Opower(_1502659), _1502661), 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(_1502659), _1502661), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (37757 ^ _784416) ^ [_1502776, _1502778] : [class_Rings_Olinordered__idom(_1502776), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1502776), hAPP(c_Groups_Oabs__class_Oabs(_1502776), _1502778)), 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(_1502776), _1502778), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (37763 ^ _784416) ^ [_1502893, _1502895, _1502897] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1502893, _1502895, _1502897, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1502895)], (37765 ^ _784416) ^ [_1502934, _1502936] : [_1502934 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1502934, _1502936) = 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)))], (37771 ^ _784416) ^ [_1503012, _1503014] : [-(_1503012 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37774 ^ _784416 : [(37775 ^ _784416) ^ [] : [_1503014 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1503012, _1503014) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1503012))], (37781 ^ _784416) ^ [] : [-(_1503014 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1503012, _1503014) = 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, _1503014))), 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)), _1503014)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1503012))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1503014), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1503012), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1503012, _1503014)), 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), _1503014))))), c_Divides_Opdivmod(_1503012, _1503014)))))]]], (37787 ^ _784416) ^ [_1503372, _1503374] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1503372), _1503374) = 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), _1503372)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1503374)))))], (37789 ^ _784416) ^ [_1503430, _1503432] : [_1503430 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1503430, _1503432) = 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)))], (37795 ^ _784416) ^ [_1503508, _1503510] : [-(_1503508 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37798 ^ _784416 : [(37799 ^ _784416) ^ [] : [_1503510 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1503508, _1503510) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1503508))], (37805 ^ _784416) ^ [] : [-(_1503510 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1503508, _1503510) = 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, _1503510))), 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, _1503508)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1503510))), c_Divides_Opdivmod(_1503508, _1503510)), 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), _1503510))))), c_Divides_Opdivmod(_1503508, _1503510)))))]]], (37811 ^ _784416) ^ [_1503820, _1503822, _1503824, _1503826, _1503828] : [-(hAPP(c_Product__Type_Ofst(_1503820, _1503822), hAPP(c_Product__Type_Oapsnd(_1503824, _1503822, _1503820, _1503826), _1503828)) = hAPP(c_Product__Type_Ofst(_1503820, _1503824), _1503828))], (37813 ^ _784416) ^ [_1503871, _1503873, _1503875, _1503877, _1503879, _1503881] : [-(hAPP(c_Product__Type_Oapsnd(_1503871, _1503873, _1503875, _1503877), hAPP(hAPP(c_Product__Type_OPair(_1503875, _1503871), _1503879), _1503881)) = hAPP(hAPP(c_Product__Type_OPair(_1503875, _1503873), _1503879), hAPP(_1503877, _1503881)))], (37815 ^ _784416) ^ [_1503933, _1503935, _1503937, _1503939, _1503941, _1503943, _1503945] : [-(hAPP(c_Product__Type_Oapsnd(_1503933, _1503935, _1503937, _1503939), hAPP(c_Product__Type_Oapsnd(_1503941, _1503933, _1503937, _1503943), _1503945)) = hAPP(c_Product__Type_Oapsnd(_1503941, _1503935, _1503937, hAPP(c_Fun_Ocomp(_1503933, _1503935, _1503941, _1503939), _1503943)), _1503945))], (37817 ^ _784416) ^ [_1504000, _1504002, _1504004, _1504006, _1504008] : [-(hAPP(c_Product__Type_Osnd(_1504000, _1504002), hAPP(c_Product__Type_Oapsnd(_1504004, _1504002, _1504000, _1504006), _1504008)) = hAPP(_1504006, hAPP(c_Product__Type_Osnd(_1504000, _1504004), _1504008)))], (37819 ^ _784416) ^ [_1504081, _1504083, _1504085, _1504087, _1504089, _1504091] : [hAPP(c_Product__Type_Oapsnd(_1504081, _1504083, _1504085, _1504087), _1504089) = hAPP(c_Product__Type_Oapsnd(_1504081, _1504083, _1504085, _1504091), _1504089), -(hAPP(_1504087, hAPP(c_Product__Type_Osnd(_1504085, _1504081), _1504089)) = hAPP(_1504091, hAPP(c_Product__Type_Osnd(_1504085, _1504081), _1504089)))], (37825 ^ _784416) ^ [_1504230, _1504232, _1504234, _1504236, _1504238, _1504240] : [hAPP(_1504236, hAPP(c_Product__Type_Osnd(_1504234, _1504230), _1504238)) = hAPP(_1504240, hAPP(c_Product__Type_Osnd(_1504234, _1504230), _1504238)), -(hAPP(c_Product__Type_Oapsnd(_1504230, _1504232, _1504234, _1504236), _1504238) = hAPP(c_Product__Type_Oapsnd(_1504230, _1504232, _1504234, _1504240), _1504238))], (37831 ^ _784416) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (37833 ^ _784416) ^ [_1504412, _1504414] : [_1504412 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1504414, _1504412) = _1504414)], (37839 ^ _784416) ^ [_1504489, _1504491] : [-(_1504489 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1504491, _1504489) = c_Nitpick_Onat__gcd(_1504489, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1504491, _1504489)))], (37845 ^ _784416) ^ [_1504537, _1504539] : [-(c_Divides_Opdivmod(_1504537, _1504539) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1504537)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1504539))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1504537), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1504539))))], (37847 ^ _784416) ^ [_1504602, _1504604] : [_1504602 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1504604, _1504602) = 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), _1504604)))], (37853 ^ _784416) ^ [_1504691, _1504693] : [-(_1504691 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1504693, _1504691) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1504693), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1504691)))], (37859 ^ _784416) ^ [_1504741, _1504743] : [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), _1504741), _1504743))), 37862 ^ _784416 : [(37863 ^ _784416) ^ [] : [_1504743 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1504741, _1504743) = _1504741)], (37869 ^ _784416) ^ [] : [-(_1504743 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1504741, _1504743) = c_Nitpick_Onat__gcd(_1504743, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1504741, _1504743)))]]], (37875 ^ _784416) ^ [_1504959, _1504961] : [-(c_Nitpick_Onat__lcm(_1504959, _1504961) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1504959), _1504961)), c_Nitpick_Onat__gcd(_1504959, _1504961)))], (37877 ^ _784416) ^ [_1505002, _1505004] : [-(c_Nitpick_Oint__lcm(_1505002, _1505004) = 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), _1505002)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1505004)))))], (37879 ^ _784416) ^ [_1505048, _1505050, _1505052] : [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), _1505048), _1505050))), -(hBOOL(hAPP(hAPP(_1505052, _1505048), _1505050))), 37886 ^ _784416 : [(37887 ^ _784416) ^ [] : [-(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), 37884 ^ [_1505048, _1505050, _1505052]), 37885 ^ [_1505048, _1505050, _1505052]))))], (37895 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1505052, 37884 ^ [_1505048, _1505050, _1505052]), 37885 ^ [_1505048, _1505050, _1505052]))], (37889 ^ _784416) ^ [] : [-(37885 ^ [_1505048, _1505050, _1505052] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1505052, 37885 ^ [_1505048, _1505050, _1505052]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 37884 ^ [_1505048, _1505050, _1505052], 37885 ^ [_1505048, _1505050, _1505052]))))]]], (37899 ^ _784416) ^ [_1505470, _1505472, _1505474, _1505476, _1505478, _1505480, _1505482] : [-(hAPP(c_Product__Type_Oapfst(_1505470, _1505472, _1505474, _1505476), hAPP(c_Product__Type_Oapsnd(_1505478, _1505474, _1505470, _1505480), _1505482)) = hAPP(hAPP(c_Product__Type_OPair(_1505472, _1505474), hAPP(_1505476, hAPP(c_Product__Type_Ofst(_1505470, _1505478), _1505482))), hAPP(_1505480, hAPP(c_Product__Type_Osnd(_1505470, _1505478), _1505482))))], (37901 ^ _784416) ^ [_1505548, _1505550, _1505552, _1505554, _1505556, _1505558, _1505560] : [-(hAPP(c_Product__Type_Oapsnd(_1505548, _1505550, _1505552, _1505554), hAPP(c_Product__Type_Oapfst(_1505556, _1505552, _1505548, _1505558), _1505560)) = hAPP(hAPP(c_Product__Type_OPair(_1505552, _1505550), hAPP(_1505558, hAPP(c_Product__Type_Ofst(_1505556, _1505548), _1505560))), hAPP(_1505554, hAPP(c_Product__Type_Osnd(_1505556, _1505548), _1505560))))], (37903 ^ _784416) ^ [_1505626, _1505628, _1505630, _1505632, _1505634] : [-(hAPP(c_Product__Type_Osnd(_1505626, _1505628), hAPP(c_Product__Type_Oapfst(_1505630, _1505626, _1505628, _1505632), _1505634)) = hAPP(c_Product__Type_Osnd(_1505630, _1505628), _1505634))], (37905 ^ _784416) ^ [_1505677, _1505679, _1505681, _1505683, _1505685, _1505687] : [-(hAPP(c_Product__Type_Oapfst(_1505677, _1505679, _1505681, _1505683), hAPP(hAPP(c_Product__Type_OPair(_1505677, _1505681), _1505685), _1505687)) = hAPP(hAPP(c_Product__Type_OPair(_1505679, _1505681), hAPP(_1505683, _1505685)), _1505687))], (37907 ^ _784416) ^ [_1505739, _1505741, _1505743, _1505745, _1505747, _1505749, _1505751] : [-(hAPP(c_Product__Type_Oapfst(_1505739, _1505741, _1505743, _1505745), hAPP(c_Product__Type_Oapfst(_1505747, _1505739, _1505743, _1505749), _1505751)) = hAPP(c_Product__Type_Oapfst(_1505747, _1505741, _1505743, hAPP(c_Fun_Ocomp(_1505739, _1505741, _1505747, _1505745), _1505749)), _1505751))], (37909 ^ _784416) ^ [_1505833, _1505835, _1505837, _1505839, _1505841, _1505843] : [hAPP(c_Product__Type_Oapfst(_1505833, _1505835, _1505837, _1505839), _1505841) = hAPP(c_Product__Type_Oapfst(_1505833, _1505835, _1505837, _1505843), _1505841), -(hAPP(_1505839, hAPP(c_Product__Type_Ofst(_1505833, _1505837), _1505841)) = hAPP(_1505843, hAPP(c_Product__Type_Ofst(_1505833, _1505837), _1505841)))], (37915 ^ _784416) ^ [_1505982, _1505984, _1505986, _1505988, _1505990, _1505992] : [hAPP(_1505988, hAPP(c_Product__Type_Ofst(_1505982, _1505986), _1505990)) = hAPP(_1505992, hAPP(c_Product__Type_Ofst(_1505982, _1505986), _1505990)), -(hAPP(c_Product__Type_Oapfst(_1505982, _1505984, _1505986, _1505988), _1505990) = hAPP(c_Product__Type_Oapfst(_1505982, _1505984, _1505986, _1505992), _1505990))], (37921 ^ _784416) ^ [_1506137, _1506139, _1506141, _1506143, _1506145] : [-(hAPP(c_Product__Type_Ofst(_1506137, _1506139), hAPP(c_Product__Type_Oapfst(_1506141, _1506137, _1506139, _1506143), _1506145)) = hAPP(_1506143, hAPP(c_Product__Type_Ofst(_1506141, _1506139), _1506145)))], (37923 ^ _784416) ^ [_1506191, _1506193, _1506195, _1506197, _1506199, _1506201, _1506203] : [-(hAPP(c_Product__Type_Oapsnd(_1506191, _1506193, _1506195, _1506197), hAPP(c_Product__Type_Oapfst(_1506199, _1506195, _1506191, _1506201), _1506203)) = hAPP(c_Product__Type_Oapfst(_1506199, _1506195, _1506193, _1506201), hAPP(c_Product__Type_Oapsnd(_1506191, _1506193, _1506199, _1506197), _1506203)))], (37925 ^ _784416) ^ [_1506258, _1506260, _1506262, _1506264, _1506266] : [class_Groups_Ocomm__monoid__add(_1506258), class_Groups_Ocomm__monoid__mult(_1506258), _1506260 = _1506262, c_Nat__Transfer_Onat__set(_1506262), 37943 ^ _784416 : [(37944 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37942 ^ [_1506258, _1506260, _1506262, _1506264, _1506266])))], (37946 ^ _784416) ^ [] : [hAPP(_1506264, 37942 ^ [_1506258, _1506260, _1506262, _1506264, _1506266]) = hAPP(_1506266, 37942 ^ [_1506258, _1506260, _1506262, _1506264, _1506266])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1506258), _1506264), _1506260) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1506258), _1506266), _1506262))], (37950 ^ _784416) ^ [_1506739, _1506741, _1506743] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1506739, hAPP(hAPP(c_COMBC(_1506739, tc_fun(tc_prod(_1506739, _1506739), tc_HOL_Obool), tc_fun(_1506739, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506739, tc_fun(tc_fun(tc_prod(_1506739, _1506739), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1506739, _1506739), tc_HOL_Obool), tc_fun(_1506739, tc_HOL_Obool)), _1506739), c_COMBC(_1506739, tc_fun(tc_prod(_1506739, _1506739), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506739, tc_prod(_1506739, _1506739)), tc_fun(_1506739, tc_fun(tc_fun(tc_prod(_1506739, _1506739), tc_HOL_Obool), tc_HOL_Obool)), _1506739), hAPP(c_COMBB(tc_prod(_1506739, _1506739), tc_fun(tc_fun(tc_prod(_1506739, _1506739), tc_HOL_Obool), tc_HOL_Obool), _1506739), c_member(tc_prod(_1506739, _1506739)))), c_Product__Type_OPair(_1506739, _1506739)))), _1506741)), _1506743)), -(hBOOL(hAPP(hAPP(c_member(_1506739), _1506743), c_Wellfounded_Oacc(_1506739, _1506741))))], (37956 ^ _784416) ^ [_1507080, _1507082, _1507084] : [hBOOL(hAPP(hAPP(c_member(_1507080), _1507084), c_Wellfounded_Oacc(_1507080, _1507082))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1507080, hAPP(hAPP(c_COMBC(_1507080, tc_fun(tc_prod(_1507080, _1507080), tc_HOL_Obool), tc_fun(_1507080, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507080, tc_fun(tc_fun(tc_prod(_1507080, _1507080), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1507080, _1507080), tc_HOL_Obool), tc_fun(_1507080, tc_HOL_Obool)), _1507080), c_COMBC(_1507080, tc_fun(tc_prod(_1507080, _1507080), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507080, tc_prod(_1507080, _1507080)), tc_fun(_1507080, tc_fun(tc_fun(tc_prod(_1507080, _1507080), tc_HOL_Obool), tc_HOL_Obool)), _1507080), hAPP(c_COMBB(tc_prod(_1507080, _1507080), tc_fun(tc_fun(tc_prod(_1507080, _1507080), tc_HOL_Obool), tc_HOL_Obool), _1507080), c_member(tc_prod(_1507080, _1507080)))), c_Product__Type_OPair(_1507080, _1507080)))), _1507082)), _1507084)))], (37962 ^ _784416) ^ [_1507427, _1507429, _1507431, _1507433, _1507435] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1507427, _1507429, _1507431), _1507433), _1507435) = hAPP(c_Set_OCollect(tc_prod(_1507427, _1507431)), hAPP(c_Product__Type_Oprod_Oprod__case(_1507427, _1507431, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1507431, tc_fun(_1507429, tc_HOL_Obool)), tc_fun(_1507431, tc_HOL_Obool), _1507427), hAPP(c_COMBB(tc_fun(_1507429, tc_HOL_Obool), tc_HOL_Obool, _1507431), c_HOL_OEx(_1507429))), hAPP(hAPP(c_COMBC(_1507427, tc_fun(_1507431, tc_fun(_1507429, tc_HOL_Obool)), tc_fun(_1507431, tc_fun(_1507429, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1507429, tc_HOL_Obool), tc_fun(_1507429, tc_HOL_Obool)), tc_fun(tc_fun(_1507431, tc_fun(_1507429, tc_HOL_Obool)), tc_fun(_1507431, tc_fun(_1507429, tc_HOL_Obool))), _1507427), c_COMBB(tc_fun(_1507429, tc_HOL_Obool), tc_fun(_1507429, tc_HOL_Obool), _1507431)), hAPP(hAPP(c_COMBB(tc_fun(_1507429, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1507429, tc_HOL_Obool), tc_fun(_1507429, tc_HOL_Obool)), _1507427), c_COMBS(_1507429, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507429, tc_HOL_Obool), tc_fun(_1507429, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1507427), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507429), c_fconj)), hAPP(hAPP(c_COMBC(_1507427, tc_fun(tc_prod(_1507427, _1507429), tc_HOL_Obool), tc_fun(_1507429, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507429, tc_fun(tc_fun(tc_prod(_1507427, _1507429), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1507427, _1507429), tc_HOL_Obool), tc_fun(_1507429, tc_HOL_Obool)), _1507427), c_COMBC(_1507429, tc_fun(tc_prod(_1507427, _1507429), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507429, tc_prod(_1507427, _1507429)), tc_fun(_1507429, tc_fun(tc_fun(tc_prod(_1507427, _1507429), tc_HOL_Obool), tc_HOL_Obool)), _1507427), hAPP(c_COMBB(tc_prod(_1507427, _1507429), tc_fun(tc_fun(tc_prod(_1507427, _1507429), tc_HOL_Obool), tc_HOL_Obool), _1507429), c_member(tc_prod(_1507427, _1507429)))), c_Product__Type_OPair(_1507427, _1507429)))), _1507433))))), hAPP(hAPP(c_COMBC(_1507431, tc_fun(tc_prod(_1507429, _1507431), tc_HOL_Obool), tc_fun(_1507429, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507429, tc_fun(tc_fun(tc_prod(_1507429, _1507431), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1507429, _1507431), tc_HOL_Obool), tc_fun(_1507429, tc_HOL_Obool)), _1507431), c_COMBC(_1507429, tc_fun(tc_prod(_1507429, _1507431), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507429, tc_prod(_1507429, _1507431)), tc_fun(_1507429, tc_fun(tc_fun(tc_prod(_1507429, _1507431), tc_HOL_Obool), tc_HOL_Obool)), _1507431), hAPP(c_COMBB(tc_prod(_1507429, _1507431), tc_fun(tc_fun(tc_prod(_1507429, _1507431), tc_HOL_Obool), tc_HOL_Obool), _1507429), c_member(tc_prod(_1507429, _1507431)))), hAPP(c_COMBC(_1507429, _1507431, tc_prod(_1507429, _1507431)), c_Product__Type_OPair(_1507429, _1507431))))), _1507435))))))], (37964 ^ _784416) ^ [_1507875, _1507877, _1507879, _1507881, _1507883, _1507885, _1507887, _1507889] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1507875, _1507877)), hAPP(hAPP(c_Product__Type_OPair(_1507875, _1507877), _1507879), _1507881)), _1507883)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1507877, _1507885)), hAPP(hAPP(c_Product__Type_OPair(_1507877, _1507885), _1507881), _1507887)), _1507889)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1507875, _1507885)), hAPP(hAPP(c_Product__Type_OPair(_1507875, _1507885), _1507879), _1507887)), hAPP(hAPP(c_Relation_Orel__comp(_1507875, _1507877, _1507885), _1507883), _1507889))))], (37974 ^ _784416) ^ [_1508162, _1508164, _1508166, _1508168] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1508162, _1508164, _1508166), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1508162, _1508164), tc_HOL_Obool))), _1508168) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1508162, _1508166), tc_HOL_Obool)))], (37976 ^ _784416) ^ [_1508217, _1508219, _1508221, _1508223] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1508217, _1508219, _1508221), _1508223), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1508219, _1508221), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1508217, _1508221), tc_HOL_Obool)))], (37978 ^ _784416) ^ [_1508272, _1508274, _1508276, _1508278, _1508280, _1508282, _1508284] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1508272, _1508274, _1508276), hAPP(hAPP(c_Relation_Orel__comp(_1508272, _1508278, _1508274), _1508280), _1508282)), _1508284) = hAPP(hAPP(c_Relation_Orel__comp(_1508272, _1508278, _1508276), _1508280), hAPP(hAPP(c_Relation_Orel__comp(_1508278, _1508274, _1508276), _1508282), _1508284)))], (37980 ^ _784416) ^ [_1508347, _1508349, _1508351, _1508353, _1508355, _1508357, _1508359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1508347, _1508349), tc_HOL_Obool)), _1508351), _1508353)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1508349, _1508355), tc_HOL_Obool)), _1508357), _1508359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1508347, _1508355), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1508347, _1508349, _1508355), _1508351), _1508357)), hAPP(hAPP(c_Relation_Orel__comp(_1508347, _1508349, _1508355), _1508353), _1508359))))], (37990 ^ _784416) ^ [_1508614, _1508616, _1508618, _1508620, _1508622, _1508624] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1508614, _1508616, _1508618), _1508620), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1508616, _1508618), tc_HOL_Obool)), _1508622), _1508624)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1508614, _1508618), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1508614, _1508616, _1508618), _1508620), _1508622)), hAPP(hAPP(c_Relation_Orel__comp(_1508614, _1508616, _1508618), _1508620), _1508624)))], (37992 ^ _784416) ^ [_1508705, _1508707, _1508709, _1508711, _1508713, _1508715] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1508705, _1508707, _1508709), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1508705, _1508707), tc_HOL_Obool)), _1508711), _1508713)), _1508715) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1508705, _1508709), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1508705, _1508707, _1508709), _1508711), _1508715)), hAPP(hAPP(c_Relation_Orel__comp(_1508705, _1508707, _1508709), _1508713), _1508715)))], (37994 ^ _784416) ^ [_1508796, _1508798, _1508800, _1508802, _1508804, _1508806, _1508808] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1508796, _1508798, _1508800), _1508802), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1508804, tc_fun(tc_prod(_1508798, _1508800), tc_HOL_Obool)), _1508806), _1508808)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1508804, tc_fun(tc_prod(_1508796, _1508800), tc_HOL_Obool)), _1508806), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1508798, _1508800), tc_HOL_Obool), tc_fun(tc_prod(_1508796, _1508800), tc_HOL_Obool), _1508804), hAPP(c_Relation_Orel__comp(_1508796, _1508798, _1508800), _1508802)), _1508808)))], (37996 ^ _784416) ^ [_1508900, _1508902, _1508904, _1508906, _1508908, _1508910, _1508912] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1508900, _1508902, _1508904), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1508906, tc_fun(tc_prod(_1508900, _1508902), tc_HOL_Obool)), _1508908), _1508910)), _1508912) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1508906, tc_fun(tc_prod(_1508900, _1508904), tc_HOL_Obool)), _1508908), hAPP(hAPP(c_COMBC(_1508906, tc_fun(tc_prod(_1508902, _1508904), tc_HOL_Obool), tc_fun(tc_prod(_1508900, _1508904), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1508900, _1508902), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1508902, _1508904), tc_HOL_Obool), tc_fun(tc_prod(_1508900, _1508904), tc_HOL_Obool)), _1508906), c_Relation_Orel__comp(_1508900, _1508902, _1508904)), _1508910)), _1508912)))], (37998 ^ _784416) ^ [_1509032, _1509034, _1509036, _1509038] : [hAPP(hAPP(c_Relation_Orel__comp(_1509032, _1509032, _1509032), _1509034), _1509036) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1509032, _1509032), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1509032, _1509032, _1509032), _1509034), _1509038) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1509032, _1509032), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1509032, _1509032, _1509032), _1509034), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509032, _1509032), tc_HOL_Obool)), _1509036), _1509038)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1509032, _1509032), tc_HOL_Obool)))], (38008 ^ _784416) ^ [_1509305, _1509307, _1509309, _1509311] : [hAPP(hAPP(c_Relation_Orel__comp(_1509305, _1509305, _1509305), _1509307), _1509309) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1509305, _1509305), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1509305, _1509305, _1509305), _1509311), _1509309) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1509305, _1509305), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1509305, _1509305, _1509305), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1509305, _1509305), tc_HOL_Obool)), _1509307), _1509311)), _1509309) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1509305, _1509305), tc_HOL_Obool)))], (38018 ^ _784416) ^ [_1509578, _1509580, _1509582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1509578, _1509578), tc_HOL_Obool)), _1509580), _1509582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509578, tc_HOL_Obool)), c_Wellfounded_Oacc(_1509578, _1509582)), c_Wellfounded_Oacc(_1509578, _1509580))))], (38034 ^ _784416) ^ [_1509986, _1509988, _1509990] : [38036 ^ _784416 : [(38037 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1509986, _1509986)), hAPP(hAPP(c_Product__Type_OPair(_1509986, _1509986), 38035 ^ [_1509986, _1509988, _1509990]), _1509988)), _1509990)))], (38039 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1509986), 38035 ^ [_1509986, _1509988, _1509990]), c_Wellfounded_Oacc(_1509986, _1509990)))]], -(hBOOL(hAPP(hAPP(c_member(_1509986), _1509988), c_Wellfounded_Oacc(_1509986, _1509990))))], (38024 ^ _784416) ^ [_1509733, _1509735, _1509737] : [hBOOL(hAPP(hAPP(c_member(_1509733), _1509735), c_Wellfounded_Oacc(_1509733, _1509737))), 38027 ^ _784416 : [(38028 ^ _784416) ^ [_1509847] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1509733, _1509733)), hAPP(hAPP(c_Product__Type_OPair(_1509733, _1509733), _1509847), _1509735)), _1509737)), -(hBOOL(hAPP(hAPP(c_member(_1509733), _1509847), c_Wellfounded_Oacc(_1509733, _1509737))))]]], (38043 ^ _784416) ^ [_1510226, _1510228, _1510230, _1510232] : [hBOOL(hAPP(hAPP(c_member(_1510226), _1510228), c_Wellfounded_Oacc(_1510226, _1510230))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1510226, _1510226)), hAPP(hAPP(c_Product__Type_OPair(_1510226, _1510226), _1510232), _1510228)), _1510230)), -(hBOOL(hAPP(hAPP(c_member(_1510226), _1510232), c_Wellfounded_Oacc(_1510226, _1510230))))], (38053 ^ _784416) ^ [_1510441, _1510443, _1510445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1510441, _1510441), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1510441, _1510441, _1510441), _1510443), _1510445)), _1510443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1510441, tc_HOL_Obool), tc_fun(_1510441, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1510441, tc_HOL_Obool), tc_fun(_1510441, tc_HOL_Obool), tc_fun(_1510441, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1510441, _1510443)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1510441, tc_HOL_Obool), tc_fun(_1510441, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1510441, _1510445)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1510441, tc_HOL_Obool), tc_fun(_1510441, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1510441, tc_HOL_Obool), tc_fun(_1510441, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1510441, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1510441, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1510441, tc_HOL_Obool), tc_fun(_1510441, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1510441, _1510443))))], (38059 ^ _784416) ^ [_1510812, _1510814, _1510816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1510812, _1510812), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1510812, _1510812, _1510812), _1510814), _1510816)), _1510814)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1510812, tc_HOL_Obool), tc_fun(_1510812, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1510812, tc_HOL_Obool), tc_fun(_1510812, tc_HOL_Obool), tc_fun(_1510812, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1510812, _1510814)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1510812, tc_HOL_Obool), tc_fun(_1510812, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1510812, _1510816)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1510812, tc_HOL_Obool), tc_fun(_1510812, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1510812, tc_HOL_Obool), tc_fun(_1510812, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1510812, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1510812, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1510812, tc_HOL_Obool), tc_fun(_1510812, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1510812, _1510814))))], (38065 ^ _784416) ^ [_1511213, _1511215, _1511217, _1511219, _1511221, _1511223, _1511225] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1511213, _1511215, _1511217, hAPP(hAPP(c_COMBC(_1511213, tc_fun(tc_prod(_1511213, _1511215), tc_HOL_Obool), tc_fun(_1511215, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511215, tc_fun(tc_fun(tc_prod(_1511213, _1511215), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511213, _1511215), tc_HOL_Obool), tc_fun(_1511215, tc_HOL_Obool)), _1511213), c_COMBC(_1511215, tc_fun(tc_prod(_1511213, _1511215), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511215, tc_prod(_1511213, _1511215)), tc_fun(_1511215, tc_fun(tc_fun(tc_prod(_1511213, _1511215), tc_HOL_Obool), tc_HOL_Obool)), _1511213), hAPP(c_COMBB(tc_prod(_1511213, _1511215), tc_fun(tc_fun(tc_prod(_1511213, _1511215), tc_HOL_Obool), tc_HOL_Obool), _1511215), c_member(tc_prod(_1511213, _1511215)))), c_Product__Type_OPair(_1511213, _1511215)))), _1511219), hAPP(hAPP(c_COMBC(_1511215, tc_fun(tc_prod(_1511215, _1511217), tc_HOL_Obool), tc_fun(_1511217, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511217, tc_fun(tc_fun(tc_prod(_1511215, _1511217), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511215, _1511217), tc_HOL_Obool), tc_fun(_1511217, tc_HOL_Obool)), _1511215), c_COMBC(_1511217, tc_fun(tc_prod(_1511215, _1511217), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511217, tc_prod(_1511215, _1511217)), tc_fun(_1511217, tc_fun(tc_fun(tc_prod(_1511215, _1511217), tc_HOL_Obool), tc_HOL_Obool)), _1511215), hAPP(c_COMBB(tc_prod(_1511215, _1511217), tc_fun(tc_fun(tc_prod(_1511215, _1511217), tc_HOL_Obool), tc_HOL_Obool), _1511217), c_member(tc_prod(_1511215, _1511217)))), c_Product__Type_OPair(_1511215, _1511217)))), _1511221)), _1511223), _1511225)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1511213, _1511217)), hAPP(hAPP(c_Product__Type_OPair(_1511213, _1511217), _1511223), _1511225)), hAPP(hAPP(c_Relation_Orel__comp(_1511213, _1511215, _1511217), _1511219), _1511221))))], (38071 ^ _784416) ^ [_1511848, _1511850, _1511852, _1511854, _1511856, _1511858, _1511860] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1511848, _1511852)), hAPP(hAPP(c_Product__Type_OPair(_1511848, _1511852), _1511858), _1511860)), hAPP(hAPP(c_Relation_Orel__comp(_1511848, _1511850, _1511852), _1511854), _1511856))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1511848, _1511850, _1511852, hAPP(hAPP(c_COMBC(_1511848, tc_fun(tc_prod(_1511848, _1511850), tc_HOL_Obool), tc_fun(_1511850, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511850, tc_fun(tc_fun(tc_prod(_1511848, _1511850), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511848, _1511850), tc_HOL_Obool), tc_fun(_1511850, tc_HOL_Obool)), _1511848), c_COMBC(_1511850, tc_fun(tc_prod(_1511848, _1511850), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511850, tc_prod(_1511848, _1511850)), tc_fun(_1511850, tc_fun(tc_fun(tc_prod(_1511848, _1511850), tc_HOL_Obool), tc_HOL_Obool)), _1511848), hAPP(c_COMBB(tc_prod(_1511848, _1511850), tc_fun(tc_fun(tc_prod(_1511848, _1511850), tc_HOL_Obool), tc_HOL_Obool), _1511850), c_member(tc_prod(_1511848, _1511850)))), c_Product__Type_OPair(_1511848, _1511850)))), _1511854), hAPP(hAPP(c_COMBC(_1511850, tc_fun(tc_prod(_1511850, _1511852), tc_HOL_Obool), tc_fun(_1511852, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511852, tc_fun(tc_fun(tc_prod(_1511850, _1511852), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511850, _1511852), tc_HOL_Obool), tc_fun(_1511852, tc_HOL_Obool)), _1511850), c_COMBC(_1511852, tc_fun(tc_prod(_1511850, _1511852), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511852, tc_prod(_1511850, _1511852)), tc_fun(_1511852, tc_fun(tc_fun(tc_prod(_1511850, _1511852), tc_HOL_Obool), tc_HOL_Obool)), _1511850), hAPP(c_COMBB(tc_prod(_1511850, _1511852), tc_fun(tc_fun(tc_prod(_1511850, _1511852), tc_HOL_Obool), tc_HOL_Obool), _1511852), c_member(tc_prod(_1511850, _1511852)))), c_Product__Type_OPair(_1511850, _1511852)))), _1511856)), _1511858), _1511860)))], (38077 ^ _784416) ^ [_1512489, _1512491, _1512493] : [c_Wellfounded_Owf(_1512489, _1512491), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1512489, _1512489), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1512489, _1512489, _1512489), _1512491), _1512493)), _1512491)), -(c_FunDef_Oreduction__pair(_1512489, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1512489, _1512489), tc_HOL_Obool), tc_fun(tc_prod(_1512489, _1512489), tc_HOL_Obool)), _1512491), _1512493)))], (38087 ^ _784416) ^ [_1512731, _1512733, _1512735, _1512737] : [c_Wellfounded_Omax__extp(_1512731, _1512733, _1512735, _1512737), 38090 ^ _784416 : [(38091 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1512731), _1512735)))], (38093 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1512731), _1512737)))], (38095 ^ _784416) ^ [] : [_1512737 = c_Orderings_Obot__class_Obot(tc_fun(_1512731, tc_HOL_Obool))], (38097 ^ _784416) ^ [_1512947] : [hBOOL(hAPP(hAPP(c_member(_1512731), _1512947), _1512735)), 38101 ^ _784416 : [(38102 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512731), 38100 ^ [_1512731, _1512733, _1512735, _1512737, _1512947]), _1512737)))], (38104 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1512733, _1512947), 38100 ^ [_1512731, _1512733, _1512735, _1512737, _1512947])))]]]]], (38106 ^ _784416) ^ [_1513131, _1513133, _1513135, _1513137] : [-(c_Wellfounded_Omax__extp(_1513131, _1513133, _1513135, _1513137)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513131), _1513135)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513131), _1513137)), -(_1513137 = c_Orderings_Obot__class_Obot(tc_fun(_1513131, tc_HOL_Obool))), 38120 ^ _784416 : [(38121 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513131), 38119 ^ [_1513131, _1513133, _1513135, _1513137]), _1513135)))], (38123 ^ _784416) ^ [_1513476] : [hBOOL(hAPP(hAPP(c_member(_1513131), _1513476), _1513137)), hBOOL(hAPP(hAPP(_1513133, 38119 ^ [_1513131, _1513133, _1513135, _1513137]), _1513476))]]], (38131 ^ _784416) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (38133 ^ _784416) ^ [_1513662, _1513664, _1513666, _1513668, _1513670, _1513672, _1513674, _1513676] : [hBOOL(hAPP(hAPP(_1513662, _1513664), _1513666)), hBOOL(hAPP(hAPP(_1513668, _1513666), _1513670)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1513672, _1513674, _1513676, _1513662, _1513668), _1513664), _1513670)))], (38143 ^ _784416) ^ [_1513857] : [-(c_Wellfounded_Owf(_1513857, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1513857, _1513857), tc_HOL_Obool))))], (38145 ^ _784416) ^ [_1513888, _1513890, _1513892, _1513894] : [c_Wellfounded_Owf(_1513888, _1513890), -(c_Wellfounded_Owf(_1513892, hAPP(hAPP(c_Relation_Oinv__image(_1513888, _1513892), _1513890), _1513894)))], (38151 ^ _784416) ^ [_1513987, _1513989, _1513991, _1513993] : [c_Wellfounded_Owf(_1513987, _1513989), c_Wellfounded_Owf(_1513991, _1513993), -(c_Wellfounded_Owf(tc_prod(_1513987, _1513991), c_Wellfounded_Olex__prod(_1513987, _1513991, _1513989, _1513993)))], (38161 ^ _784416) ^ [_1514140, _1514142] : [-(c_Wellfounded_Owf(_1514140, hAPP(c_Wellfounded_Omeasure(_1514140), _1514142)))], (38163 ^ _784416) ^ [_1514185, _1514187] : [c_Wellfounded_Owf(_1514185, _1514187), -(c_Wellfounded_Owf(_1514185, hAPP(hAPP(c_Relation_Orel__comp(_1514185, _1514185, _1514185), _1514187), _1514187)))], (38169 ^ _784416) ^ [_1514278, _1514280] : [c_Wellfounded_Owf(_1514278, hAPP(hAPP(c_Relation_Orel__comp(_1514278, _1514278, _1514278), _1514280), _1514280)), -(c_Wellfounded_Owf(_1514278, _1514280))], (38175 ^ _784416) ^ [_1514377] : [-(c_Wellfounded_Owf(tc_fun(_1514377, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1514377)))], (38177 ^ _784416) ^ [_1514405, _1514407, _1514409] : [c_Wellfounded_Owf(_1514405, _1514407), -(c_Wellfounded_Owf(_1514405, c_Wellfounded_Omlex__prod(_1514405, _1514409, _1514407)))], (38183 ^ _784416) ^ [_1514492, _1514494, _1514496] : [c_Wellfounded_Owf(_1514492, _1514494), -(c_Wellfounded_Owf(_1514492, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1514492, _1514492), tc_HOL_Obool)), _1514496), _1514494)))], (38189 ^ _784416) ^ [_1514599, _1514601, _1514603] : [c_Wellfounded_Owf(_1514599, _1514601), -(c_Wellfounded_Owf(_1514599, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1514599, _1514599), tc_HOL_Obool)), _1514601), _1514603)))], (38195 ^ _784416) ^ [_1514706, _1514708, _1514710] : [c_Wellfounded_Owf(_1514706, _1514708), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1514706, _1514706), tc_HOL_Obool)), _1514710), _1514708)), -(c_Wellfounded_Owf(_1514706, _1514710))], (38205 ^ _784416) ^ [_1514865, _1514867] : [c_Wellfounded_Owf(_1514865, _1514867), -(c_Wellfounded_Owf(tc_fun(_1514865, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1514865, _1514867)))], (38211 ^ _784416) ^ [_1514984, _1514986, _1514988, _1514990, _1514992, _1514994, _1514996] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1514984, _1514986, _1514988, _1514990, _1514992), _1514994), _1514996)), 38215 ^ _784416 : [(38216 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1514990, _1514994), 38214 ^ [_1514984, _1514986, _1514988, _1514990, _1514992, _1514994, _1514996])))], (38218 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1514992, 38214 ^ [_1514984, _1514986, _1514988, _1514990, _1514992, _1514994, _1514996]), _1514996)))]]], (38220 ^ _784416) ^ [_1515174, _1515176, _1515178, _1515180, _1515182, _1515184, _1515186] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1515174, _1515176, _1515178, _1515180, _1515182), _1515184), _1515186))), 38221 ^ _784416 : [(38222 ^ _784416) ^ [_1515245] : [hBOOL(hAPP(hAPP(_1515180, _1515184), _1515245)), hBOOL(hAPP(hAPP(_1515182, _1515245), _1515186))]]], (38230 ^ _784416) ^ [_1515394, _1515396] : [c_Wellfounded_Owf(_1515394, _1515396), -(c_Wellfounded_Owf(tc_fun(_1515394, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1515394, _1515396)))], (38236 ^ _784416) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (38238 ^ _784416) ^ [] : [-(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)))))], (38240 ^ _784416) ^ [_1515519, _1515521, _1515523] : [c_Wellfounded_Owf(_1515519, _1515521), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515519, _1515519)), hAPP(hAPP(c_Product__Type_OPair(_1515519, _1515519), _1515523), _1515523)), _1515521))], (38246 ^ _784416) ^ [_1515637, _1515639, _1515641, _1515643] : [c_Wellfounded_Owf(_1515637, _1515639), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515637, _1515637)), hAPP(hAPP(c_Product__Type_OPair(_1515637, _1515637), _1515641), _1515643)), _1515639)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515637, _1515637)), hAPP(hAPP(c_Product__Type_OPair(_1515637, _1515637), _1515643), _1515641)), _1515639))], (38256 ^ _784416) ^ [_1515851, _1515853, _1515855, _1515857] : [c_Wellfounded_Owf(_1515851, _1515853), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515851, _1515851)), hAPP(hAPP(c_Product__Type_OPair(_1515851, _1515851), _1515855), _1515857)), _1515853)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515851, _1515851)), hAPP(hAPP(c_Product__Type_OPair(_1515851, _1515851), _1515857), _1515855)), _1515853))], (38266 ^ _784416) ^ [_1516065, _1516067, _1516069] : [c_Wellfounded_Owf(_1516065, _1516067), hBOOL(hAPP(hAPP(c_member(tc_prod(_1516065, _1516065)), hAPP(hAPP(c_Product__Type_OPair(_1516065, _1516065), _1516069), _1516069)), _1516067))], (38272 ^ _784416) ^ [_1516183] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1516183)))], (38274 ^ _784416) ^ [_1516208] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1516208)))], (38276 ^ _784416) ^ [_1516248, _1516250] : [c_Wellfounded_Owf(_1516248, _1516250), 38279 ^ _784416 : [(38280 ^ _784416) ^ [_1516317] : [-(hBOOL(hAPP(hAPP(c_member(_1516248), _1516317), c_Wellfounded_Oacc(_1516248, _1516250))))]]], (38282 ^ _784416) ^ [_1516350, _1516352] : [hBOOL(hAPP(hAPP(c_member(_1516350), 38283 ^ [_1516350, _1516352]), c_Wellfounded_Oacc(_1516350, _1516352))), -(c_Wellfounded_Owf(_1516350, _1516352))], (38289 ^ _784416) ^ [_1516483, _1516485, _1516487] : [c_Wellfounded_Owf(_1516483, _1516485), -(hBOOL(hAPP(hAPP(c_member(_1516483), _1516487), c_Wellfounded_Oacc(_1516483, _1516485))))], (38295 ^ _784416) ^ [_1516582, _1516584] : [hAPP(hAPP(c_Relation_Orel__comp(_1516582, _1516582, _1516582), _1516584), _1516584) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1516582, _1516582), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1516582, _1516584))], (38301 ^ _784416) ^ [_1516713, _1516715, _1516717] : [c_Wellfounded_Owf(_1516713, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1516713, _1516713), tc_HOL_Obool)), _1516715), _1516717)), -(c_Wellfounded_Owf(_1516713, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1516713, _1516713), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1516713, _1516713), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1516713, _1516713, _1516713), _1516715), _1516715)), hAPP(hAPP(c_Relation_Orel__comp(_1516713, _1516713, _1516713), _1516717), _1516715))), _1516717)))], (38307 ^ _784416) ^ [_1516912, _1516914, _1516916] : [c_Wellfounded_Owf(_1516912, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1516912, _1516912), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1516912, _1516912), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1516912, _1516912, _1516912), _1516914), _1516914)), hAPP(hAPP(c_Relation_Orel__comp(_1516912, _1516912, _1516912), _1516916), _1516914))), _1516916)), -(c_Wellfounded_Owf(_1516912, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1516912, _1516912), tc_HOL_Obool)), _1516914), _1516916)))], (38313 ^ _784416) ^ [_1517132, _1517134] : [c_Wellfounded_Owf(_1517132, _1517134), 38317 ^ _784416 : [(38318 ^ _784416) ^ [_1517268] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1517132, _1517132)), hAPP(hAPP(c_Product__Type_OPair(_1517132, _1517132), hAPP(_1517268, hAPP(c_Nat_OSuc, 38316 ^ [_1517132, _1517134, _1517268]))), hAPP(_1517268, 38316 ^ [_1517132, _1517134, _1517268]))), _1517134))]]], (38320 ^ _784416) ^ [_1517335, _1517337] : [38322 ^ _784416 : [(38323 ^ _784416) ^ [_1517360] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517335, _1517335)), hAPP(hAPP(c_Product__Type_OPair(_1517335, _1517335), hAPP(38321 ^ [_1517335, _1517337], hAPP(c_Nat_OSuc, _1517360))), hAPP(38321 ^ [_1517335, _1517337], _1517360))), _1517337)))]], -(c_Wellfounded_Owf(_1517335, _1517337))], (38327 ^ _784416) ^ [_1517436, _1517438, _1517440] : [c_Wellfounded_Owf(_1517436, _1517438), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1517436, tc_HOL_Obool)), _1517440), hAPP(c_Relation_OImage(_1517436, _1517436, _1517438), _1517440))), -(_1517440 = c_Orderings_Obot__class_Obot(tc_fun(_1517436, tc_HOL_Obool)))], (38337 ^ _784416) ^ [_1517613, _1517615, _1517617] : [c_Wellfounded_Owf(_1517613, _1517615), c_Wellfounded_Owf(_1517613, _1517617), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1517613, _1517613), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1517613, _1517613, _1517613), _1517615), _1517617)), _1517615)), -(c_Wellfounded_Owf(_1517613, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517613, _1517613), tc_HOL_Obool)), _1517615), _1517617)))], (38351 ^ _784416) ^ [_1517874] : [class_Orderings_Owellorder(_1517874), -(c_Wellfounded_Owf(_1517874, hAPP(c_Set_OCollect(tc_prod(_1517874, _1517874)), hAPP(c_Product__Type_Oprod_Oprod__case(_1517874, _1517874, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1517874)))))], (38357 ^ _784416) ^ [_1517996, _1517998] : [c_FunDef_Oreduction__pair(_1517996, _1517998), 38360 ^ _784416 : [(38361 ^ _784416) ^ [] : [-(c_Wellfounded_Owf(_1517996, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1517996, _1517996), tc_HOL_Obool), tc_fun(tc_prod(_1517996, _1517996), tc_HOL_Obool)), _1517998)))], (38363 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1517996, _1517996), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1517996, _1517996, _1517996), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1517996, _1517996), tc_HOL_Obool), tc_fun(tc_prod(_1517996, _1517996), tc_HOL_Obool)), _1517998)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1517996, _1517996), tc_HOL_Obool), tc_fun(tc_prod(_1517996, _1517996), tc_HOL_Obool)), _1517998))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1517996, _1517996), tc_HOL_Obool), tc_fun(tc_prod(_1517996, _1517996), tc_HOL_Obool)), _1517998))))]]], (38365 ^ _784416) ^ [_1518285, _1518287] : [-(c_FunDef_Oreduction__pair(_1518285, _1518287)), c_Wellfounded_Owf(_1518285, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518285, _1518285), tc_HOL_Obool), tc_fun(tc_prod(_1518285, _1518285), tc_HOL_Obool)), _1518287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518285, _1518285), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1518285, _1518285, _1518285), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518285, _1518285), tc_HOL_Obool), tc_fun(tc_prod(_1518285, _1518285), tc_HOL_Obool)), _1518287)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1518285, _1518285), tc_HOL_Obool), tc_fun(tc_prod(_1518285, _1518285), tc_HOL_Obool)), _1518287))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518285, _1518285), tc_HOL_Obool), tc_fun(tc_prod(_1518285, _1518285), tc_HOL_Obool)), _1518287)))], (38375 ^ _784416) ^ [_1518606, _1518608, _1518610, _1518612] : [c_FunDef_Oreduction__pair(_1518606, _1518608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518606, _1518606), tc_HOL_Obool)), _1518610), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518606, _1518606), tc_HOL_Obool), tc_fun(tc_prod(_1518606, _1518606), tc_HOL_Obool)), _1518608))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518606, _1518606), tc_HOL_Obool)), _1518612), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1518606, _1518606), tc_HOL_Obool), tc_fun(tc_prod(_1518606, _1518606), tc_HOL_Obool)), _1518608))), c_Wellfounded_Owf(_1518606, _1518612), -(c_Wellfounded_Owf(_1518606, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518606, _1518606), tc_HOL_Obool)), _1518610), _1518612)))], (38393 ^ _784416) ^ [_1519007, _1519009] : [c_Wellfounded_Owf(_1519007, _1519009), -(c_Wellfounded_Owf(tc_List_Olist(_1519007), c_List_Olenlex(_1519007, _1519009)))], (38399 ^ _784416) ^ [_1519094, _1519096, _1519098, _1519100] : [38401 ^ _784416 : [(38402 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1519094, 38400 ^ [_1519094, _1519096, _1519098, _1519100])))], (38404 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1519096, hAPP(_1519098, 38400 ^ [_1519094, _1519096, _1519098, _1519100]))), hAPP(_1519096, 38400 ^ [_1519094, _1519096, _1519098, _1519100])))]], -(c_Wellfounded_Owf(_1519100, hAPP(c_Set_OCollect(tc_prod(_1519100, _1519100)), hAPP(c_Product__Type_Oprod_Oprod__case(_1519100, _1519100, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1519100, tc_HOL_Obool), tc_fun(_1519100, tc_HOL_Obool), _1519100), hAPP(c_COMBS(_1519100, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1519100), c_fconj), _1519094))), hAPP(hAPP(c_COMBC(_1519100, tc_fun(_1519100, _1519100), tc_fun(_1519100, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519100, tc_HOL_Obool), tc_fun(tc_fun(_1519100, _1519100), tc_fun(_1519100, tc_HOL_Obool)), _1519100), c_COMBB(_1519100, tc_HOL_Obool, _1519100)), c_fequal)), _1519098))))))], (38408 ^ _784416) ^ [_1519487, _1519489, _1519491, _1519493] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1519487), _1519489)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519487), _1519491)), -(_1519491 = c_Orderings_Obot__class_Obot(tc_fun(_1519487, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1519487, tc_HOL_Obool), tc_fun(_1519487, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1519487, tc_HOL_Obool), tc_fun(_1519487, tc_HOL_Obool)), _1519489), _1519491)), c_Wellfounded_Omax__ext(_1519487, _1519493)))), 38422 ^ _784416 : [(38423 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519487), 38421 ^ [_1519487, _1519489, _1519491, _1519493]), _1519489)))], (38425 ^ _784416) ^ [_1519892] : [hBOOL(hAPP(hAPP(c_member(_1519487), _1519892), _1519491)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1519487, _1519487)), hAPP(hAPP(c_Product__Type_OPair(_1519487, _1519487), 38421 ^ [_1519487, _1519489, _1519491, _1519493]), _1519892)), _1519493))]]], (38433 ^ _784416) ^ [] : [-(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))))], (38435 ^ _784416) ^ [_1520136, _1520138] : [c_Wellfounded_Owf(_1520136, _1520138), -(c_Wellfounded_Owf(tc_List_Olist(_1520136), c_List_Olex(_1520136, _1520138)))], (38441 ^ _784416) ^ [_1520223, _1520225, _1520227] : [c_Wellfounded_Owf(_1520223, _1520225), -(c_Wellfounded_Owf(tc_List_Olist(_1520223), hAPP(c_List_Olexn(_1520223, _1520225), _1520227)))], (38447 ^ _784416) ^ [_1520318, _1520320] : [-(c_List_Olex(_1520318, _1520320) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1520318), tc_List_Olist(_1520318)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1520318, _1520320)))], (38449 ^ _784416) ^ [_1520368, _1520370] : [-(hAPP(c_List_Olexn(_1520368, _1520370), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1520368), tc_List_Olist(_1520368)), tc_HOL_Obool)))], (38451 ^ _784416) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (38453 ^ _784416) ^ [_1520429, _1520431, _1520433, _1520435] : [38455 ^ _784416 : [(38456 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1520429, 38454 ^ [_1520429, _1520431, _1520433, _1520435])))], (38458 ^ _784416) ^ [] : [c_Wellfounded_Owf(_1520431, hAPP(_1520433, 38454 ^ [_1520429, _1520431, _1520433, _1520435]))]], -(c_Wellfounded_Owf(tc_prod(_1520435, _1520431), c_Recdef_Osame__fst(_1520435, _1520431, _1520429, _1520433)))], (38462 ^ _784416) ^ [_1520614] : [-(c_Nitpick_Ozero__frac(_1520614) = c_Nitpick_OAbs__Frac(_1520614, 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))))], (38464 ^ _784416) ^ [_1520642, _1520644, _1520646] : [-(hAPP(c_Relation_ORange(_1520642, _1520644), hAPP(c_Set_OCollect(tc_prod(_1520642, _1520644)), hAPP(c_Product__Type_Oprod_Oprod__case(_1520642, _1520644, tc_HOL_Obool), _1520646))) = hAPP(c_Set_OCollect(_1520644), hAPP(hAPP(c_COMBB(tc_fun(_1520642, tc_HOL_Obool), tc_HOL_Obool, _1520644), c_HOL_OEx(_1520642)), hAPP(c_COMBC(_1520642, _1520644, tc_HOL_Obool), _1520646))))], (38466 ^ _784416) ^ [_1520717, _1520719, _1520721, _1520723, _1520725] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1520717, _1520719)), hAPP(hAPP(c_Product__Type_OPair(_1520717, _1520719), _1520721), _1520723)), _1520725)), -(hBOOL(hAPP(hAPP(c_member(_1520719), _1520723), hAPP(c_Relation_ORange(_1520717, _1520719), _1520725))))], (38472 ^ _784416) ^ [_1520864, _1520866] : [-(hAPP(c_Relation_ORange(_1520864, _1520864), c_Relation_OId__on(_1520864, _1520866)) = _1520866)], (38474 ^ _784416) ^ [_1520898, _1520900, _1520902, _1520904] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1520898, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1520898, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1520900, _1520898), _1520902)), hAPP(c_Relation_ORange(_1520900, _1520898), _1520904))), hAPP(c_Relation_ORange(_1520900, _1520898), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1520900, _1520898), tc_HOL_Obool)), _1520902), _1520904)))))], (38476 ^ _784416) ^ [_1520998, _1521000, _1521002] : [hAPP(c_Relation_ORange(_1520998, _1521000), _1521002) = c_Orderings_Obot__class_Obot(tc_fun(_1521000, tc_HOL_Obool)), -(_1521002 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520998, _1521000), tc_HOL_Obool)))], (38482 ^ _784416) ^ [_1521111, _1521113, _1521115] : [_1521115 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521111, _1521113), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1521111, _1521113), _1521115) = c_Orderings_Obot__class_Obot(tc_fun(_1521113, tc_HOL_Obool)))], (38488 ^ _784416) ^ [_1521230, _1521232] : [-(hAPP(c_Relation_ORange(_1521230, _1521232), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521230, _1521232), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1521232, tc_HOL_Obool)))], (38490 ^ _784416) ^ [_1521274, _1521276, _1521278, _1521280] : [-(hAPP(c_Relation_ORange(_1521274, _1521276), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1521274, _1521276), tc_HOL_Obool)), _1521278), _1521280)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521276, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521274, _1521276), _1521278)), hAPP(c_Relation_ORange(_1521274, _1521276), _1521280)))], (38492 ^ _784416) ^ [_1521346, _1521348, _1521350] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1521346, _1521348)), _1521350)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521348), hAPP(c_Relation_ORange(_1521346, _1521348), _1521350))))], (38498 ^ _784416) ^ [_1521459, _1521461, _1521463] : [-(hAPP(c_Set_Oimage(tc_prod(_1521459, _1521461), _1521461, c_Product__Type_Osnd(_1521459, _1521461)), _1521463) = hAPP(c_Relation_ORange(_1521459, _1521461), _1521463))], (38500 ^ _784416) ^ [_1521526, _1521528, _1521530, _1521532] : [hBOOL(hAPP(hAPP(c_member(_1521526), _1521528), hAPP(c_Relation_ORange(_1521530, _1521526), _1521532))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1521530, _1521526)), hAPP(hAPP(c_Product__Type_OPair(_1521530, _1521526), 38503 ^ [_1521526, _1521528, _1521530, _1521532]), _1521528)), _1521532)))], (38507 ^ _784416) ^ [_1521683, _1521685, _1521687, _1521689] : [38508 ^ _784416 : [(38509 ^ _784416) ^ [_1521758] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1521687, _1521683)), hAPP(hAPP(c_Product__Type_OPair(_1521687, _1521683), _1521758), _1521685)), _1521689))]], -(hBOOL(hAPP(hAPP(c_member(_1521683), _1521685), hAPP(c_Relation_ORange(_1521687, _1521683), _1521689))))], (38513 ^ _784416) ^ [_1521843, _1521845, _1521847, _1521849, _1521851] : [-(hAPP(c_Relation_ORange(_1521843, _1521845), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1521843, _1521845)), hAPP(hAPP(c_Product__Type_OPair(_1521843, _1521845), _1521847), _1521849)), _1521851)) = hAPP(hAPP(c_Set_Oinsert(_1521845), _1521849), hAPP(c_Relation_ORange(_1521843, _1521845), _1521851)))], (38515 ^ _784416) ^ [_1521914, _1521916, _1521918, _1521920] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521914, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521916, _1521914), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1521916, _1521914), tc_HOL_Obool)), _1521918), _1521920))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1521914, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521916, _1521914), _1521918)), hAPP(c_Relation_ORange(_1521916, _1521914), _1521920)))))], (38517 ^ _784416) ^ [_1521996] : [-(c_Nitpick_Oone__frac(_1521996) = c_Nitpick_OAbs__Frac(_1521996, 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))))], (38519 ^ _784416) ^ [_1522024, _1522026] : [-(c_Nitpick_Onumber__of__frac(_1522024, _1522026) = c_Nitpick_OAbs__Frac(_1522024, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1522026), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (38521 ^ _784416) ^ [_1522082, _1522084, _1522086, _1522088] : [hBOOL(hAPP(c_Predicate_ORangeP(_1522082, _1522084, hAPP(hAPP(c_COMBC(_1522082, tc_fun(tc_prod(_1522082, _1522084), tc_HOL_Obool), tc_fun(_1522084, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522084, tc_fun(tc_fun(tc_prod(_1522082, _1522084), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1522082, _1522084), tc_HOL_Obool), tc_fun(_1522084, tc_HOL_Obool)), _1522082), c_COMBC(_1522084, tc_fun(tc_prod(_1522082, _1522084), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522084, tc_prod(_1522082, _1522084)), tc_fun(_1522084, tc_fun(tc_fun(tc_prod(_1522082, _1522084), tc_HOL_Obool), tc_HOL_Obool)), _1522082), hAPP(c_COMBB(tc_prod(_1522082, _1522084), tc_fun(tc_fun(tc_prod(_1522082, _1522084), tc_HOL_Obool), tc_HOL_Obool), _1522084), c_member(tc_prod(_1522082, _1522084)))), c_Product__Type_OPair(_1522082, _1522084)))), _1522086)), _1522088)), -(hBOOL(hAPP(hAPP(c_member(_1522084), _1522088), hAPP(c_Relation_ORange(_1522082, _1522084), _1522086))))], (38527 ^ _784416) ^ [_1522433, _1522435, _1522437, _1522439] : [hBOOL(hAPP(hAPP(c_member(_1522435), _1522439), hAPP(c_Relation_ORange(_1522433, _1522435), _1522437))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1522433, _1522435, hAPP(hAPP(c_COMBC(_1522433, tc_fun(tc_prod(_1522433, _1522435), tc_HOL_Obool), tc_fun(_1522435, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522435, tc_fun(tc_fun(tc_prod(_1522433, _1522435), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1522433, _1522435), tc_HOL_Obool), tc_fun(_1522435, tc_HOL_Obool)), _1522433), c_COMBC(_1522435, tc_fun(tc_prod(_1522433, _1522435), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522435, tc_prod(_1522433, _1522435)), tc_fun(_1522435, tc_fun(tc_fun(tc_prod(_1522433, _1522435), tc_HOL_Obool), tc_HOL_Obool)), _1522433), hAPP(c_COMBB(tc_prod(_1522433, _1522435), tc_fun(tc_fun(tc_prod(_1522433, _1522435), tc_HOL_Obool), tc_HOL_Obool), _1522435), c_member(tc_prod(_1522433, _1522435)))), c_Product__Type_OPair(_1522433, _1522435)))), _1522437)), _1522439)))], (38533 ^ _784416) ^ [_1522790, _1522792, _1522794, _1522796, _1522798] : [hBOOL(hAPP(hAPP(_1522790, _1522792), _1522794)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1522796, _1522798, _1522790), _1522794)))], (38539 ^ _784416) ^ [_1522916, _1522918, _1522920, _1522922] : [hBOOL(hAPP(c_Predicate_ORangeP(_1522916, _1522918, _1522920), _1522922)), -(hBOOL(hAPP(hAPP(_1522920, 38542 ^ [_1522916, _1522918, _1522920, _1522922]), _1522922)))], (38546 ^ _784416) ^ [_1523031, _1523033, _1523035, _1523037] : [38547 ^ _784416 : [(38548 ^ _784416) ^ [_1523085] : [hBOOL(hAPP(hAPP(_1523035, _1523085), _1523037))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1523031, _1523033, _1523035), _1523037)))], (38552 ^ _784416) ^ [_1523149, _1523151, _1523153] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1523149), _1523151), _1523153) = c_Nitpick_OAbs__Frac(_1523149, c_Nitpick_Onorm__frac(_1523151, _1523153)))], (38554 ^ _784416) ^ [_1523190, _1523192, _1523194, _1523196] : [hBOOL(hAPP(hAPP(c_member(_1523190), _1523192), hAPP(c_Relation_ORange(_1523194, _1523190), _1523196))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523194, _1523190)), hAPP(hAPP(c_Product__Type_OPair(_1523194, _1523190), 38557 ^ [_1523190, _1523192, _1523194, _1523196]), _1523192)), _1523196)))], (38561 ^ _784416) ^ [_1523355, _1523357, _1523359] : [c_Wellfounded_Owf(_1523355, _1523357), c_Wellfounded_Owf(_1523355, _1523359), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1523355, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1523355, _1523355), _1523357)), hAPP(c_Relation_ORange(_1523355, _1523355), _1523359)) = c_Orderings_Obot__class_Obot(tc_fun(_1523355, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1523355, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1523355, _1523355), tc_HOL_Obool)), _1523357), _1523359)))], (38575 ^ _784416) ^ [_1523626, _1523628, _1523630, _1523632, _1523634] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1523626, _1523628)), hAPP(hAPP(c_Product__Type_OPair(_1523626, _1523628), _1523630), _1523632)), _1523634)), -(hBOOL(hAPP(hAPP(c_member(_1523626), _1523630), hAPP(c_Relation_ODomain(_1523626, _1523628), _1523634))))], (38581 ^ _784416) ^ [_1523773, _1523775] : [-(hAPP(c_Relation_ODomain(_1523773, _1523773), c_Relation_OId__on(_1523773, _1523775)) = _1523775)], (38583 ^ _784416) ^ [_1523825, _1523827, _1523829] : [hAPP(c_Relation_ODomain(_1523825, _1523827), _1523829) = c_Orderings_Obot__class_Obot(tc_fun(_1523825, tc_HOL_Obool)), -(_1523829 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1523825, _1523827), tc_HOL_Obool)))], (38589 ^ _784416) ^ [_1523938, _1523940, _1523942] : [_1523942 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1523938, _1523940), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1523938, _1523940), _1523942) = c_Orderings_Obot__class_Obot(tc_fun(_1523938, tc_HOL_Obool)))], (38595 ^ _784416) ^ [_1524057, _1524059] : [-(hAPP(c_Relation_ODomain(_1524057, _1524059), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1524057, _1524059), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1524057, tc_HOL_Obool)))], (38597 ^ _784416) ^ [_1524101, _1524103, _1524105, _1524107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524101, _1524103), tc_HOL_Obool)), _1524105), _1524107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524101, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524101, _1524103), _1524105)), hAPP(c_Relation_ODomain(_1524101, _1524103), _1524107))))], (38603 ^ _784416) ^ [_1524252, _1524254, _1524256, _1524258] : [-(hAPP(c_Relation_ODomain(_1524252, _1524254), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1524252, _1524254), tc_HOL_Obool)), _1524256), _1524258)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1524252, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524252, _1524254), _1524256)), hAPP(c_Relation_ODomain(_1524252, _1524254), _1524258)))], (38605 ^ _784416) ^ [_1524324, _1524326, _1524328] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1524324, _1524326)), _1524328)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1524324), hAPP(c_Relation_ODomain(_1524324, _1524326), _1524328))))], (38611 ^ _784416) ^ [_1524437, _1524439, _1524441] : [-(hAPP(c_Set_Oimage(tc_prod(_1524437, _1524439), _1524437, c_Product__Type_Ofst(_1524437, _1524439)), _1524441) = hAPP(c_Relation_ODomain(_1524437, _1524439), _1524441))], (38613 ^ _784416) ^ [_1524504, _1524506, _1524508, _1524510] : [hBOOL(hAPP(hAPP(c_member(_1524504), _1524506), hAPP(c_Relation_ODomain(_1524504, _1524508), _1524510))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524504, _1524508)), hAPP(hAPP(c_Product__Type_OPair(_1524504, _1524508), _1524506), 38616 ^ [_1524504, _1524506, _1524508, _1524510])), _1524510)))], (38620 ^ _784416) ^ [_1524661, _1524663, _1524665, _1524667] : [38621 ^ _784416 : [(38622 ^ _784416) ^ [_1524736] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524661, _1524665)), hAPP(hAPP(c_Product__Type_OPair(_1524661, _1524665), _1524663), _1524736)), _1524667))]], -(hBOOL(hAPP(hAPP(c_member(_1524661), _1524663), hAPP(c_Relation_ODomain(_1524661, _1524665), _1524667))))], (38626 ^ _784416) ^ [_1524821, _1524823, _1524825, _1524827, _1524829] : [-(hAPP(c_Relation_ODomain(_1524821, _1524823), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1524821, _1524823)), hAPP(hAPP(c_Product__Type_OPair(_1524821, _1524823), _1524825), _1524827)), _1524829)) = hAPP(hAPP(c_Set_Oinsert(_1524821), _1524825), hAPP(c_Relation_ODomain(_1524821, _1524823), _1524829)))], (38628 ^ _784416) ^ [_1524892, _1524894, _1524896, _1524898] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524892, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524892, _1524894), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1524892, _1524894), tc_HOL_Obool)), _1524896), _1524898))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1524892, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524892, _1524894), _1524896)), hAPP(c_Relation_ODomain(_1524892, _1524894), _1524898)))))], (38630 ^ _784416) ^ [_1524974, _1524976, _1524978, _1524980] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524974, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1524974, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524974, _1524976), _1524978)), hAPP(c_Relation_ODomain(_1524974, _1524976), _1524980))), hAPP(c_Relation_ODomain(_1524974, _1524976), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1524974, _1524976), tc_HOL_Obool)), _1524978), _1524980)))))], (38632 ^ _784416) ^ [_1525056, _1525058] : [-(hAPP(c_Relation_OField(_1525056), _1525058) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1525056, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1525056, _1525056), _1525058)), hAPP(c_Relation_ORange(_1525056, _1525056), _1525058)))], (38634 ^ _784416) ^ [_1525109, _1525111, _1525113] : [-(hAPP(c_Relation_ODomain(_1525109, _1525111), hAPP(c_Set_OCollect(tc_prod(_1525109, _1525111)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525109, _1525111, tc_HOL_Obool), _1525113))) = hAPP(c_Set_OCollect(_1525109), hAPP(hAPP(c_COMBB(tc_fun(_1525111, tc_HOL_Obool), tc_HOL_Obool, _1525109), c_HOL_OEx(_1525111)), _1525113)))], (38636 ^ _784416) ^ [_1525198, _1525200, _1525202, _1525204] : [hBOOL(hAPP(c_Predicate_ODomainP(_1525198, _1525200, hAPP(hAPP(c_COMBC(_1525198, tc_fun(tc_prod(_1525198, _1525200), tc_HOL_Obool), tc_fun(_1525200, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525200, tc_fun(tc_fun(tc_prod(_1525198, _1525200), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525198, _1525200), tc_HOL_Obool), tc_fun(_1525200, tc_HOL_Obool)), _1525198), c_COMBC(_1525200, tc_fun(tc_prod(_1525198, _1525200), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525200, tc_prod(_1525198, _1525200)), tc_fun(_1525200, tc_fun(tc_fun(tc_prod(_1525198, _1525200), tc_HOL_Obool), tc_HOL_Obool)), _1525198), hAPP(c_COMBB(tc_prod(_1525198, _1525200), tc_fun(tc_fun(tc_prod(_1525198, _1525200), tc_HOL_Obool), tc_HOL_Obool), _1525200), c_member(tc_prod(_1525198, _1525200)))), c_Product__Type_OPair(_1525198, _1525200)))), _1525202)), _1525204)), -(hBOOL(hAPP(hAPP(c_member(_1525198), _1525204), hAPP(c_Relation_ODomain(_1525198, _1525200), _1525202))))], (38642 ^ _784416) ^ [_1525549, _1525551, _1525553, _1525555] : [hBOOL(hAPP(hAPP(c_member(_1525549), _1525555), hAPP(c_Relation_ODomain(_1525549, _1525551), _1525553))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1525549, _1525551, hAPP(hAPP(c_COMBC(_1525549, tc_fun(tc_prod(_1525549, _1525551), tc_HOL_Obool), tc_fun(_1525551, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525551, tc_fun(tc_fun(tc_prod(_1525549, _1525551), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525549, _1525551), tc_HOL_Obool), tc_fun(_1525551, tc_HOL_Obool)), _1525549), c_COMBC(_1525551, tc_fun(tc_prod(_1525549, _1525551), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525551, tc_prod(_1525549, _1525551)), tc_fun(_1525551, tc_fun(tc_fun(tc_prod(_1525549, _1525551), tc_HOL_Obool), tc_HOL_Obool)), _1525549), hAPP(c_COMBB(tc_prod(_1525549, _1525551), tc_fun(tc_fun(tc_prod(_1525549, _1525551), tc_HOL_Obool), tc_HOL_Obool), _1525551), c_member(tc_prod(_1525549, _1525551)))), c_Product__Type_OPair(_1525549, _1525551)))), _1525553)), _1525555)))], (38648 ^ _784416) ^ [_1525906, _1525908, _1525910, _1525912] : [hBOOL(hAPP(hAPP(c_member(_1525906), _1525908), hAPP(c_Relation_ODomain(_1525906, _1525910), _1525912))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1525906, _1525910)), hAPP(hAPP(c_Product__Type_OPair(_1525906, _1525910), _1525908), 38651 ^ [_1525906, _1525908, _1525910, _1525912])), _1525912)))], (38655 ^ _784416) ^ [_1526071, _1526073, _1526075, _1526077, _1526079, _1526081] : [-(hAPP(c_Set_Oimage(_1526071, tc_prod(_1526073, _1526075), hAPP(hAPP(c_COMBS(_1526071, _1526075, tc_prod(_1526073, _1526075)), hAPP(hAPP(c_COMBB(_1526073, tc_fun(_1526075, tc_prod(_1526073, _1526075)), _1526071), c_Product__Type_OPair(_1526073, _1526075)), _1526077)), _1526079)), _1526081) = hAPP(hAPP(c_Product__Type_OSigma(_1526073, _1526075), hAPP(c_Set_Oimage(_1526071, _1526073, _1526077), _1526081)), hAPP(hAPP(c_COMBB(tc_fun(_1526071, tc_HOL_Obool), tc_fun(_1526075, tc_HOL_Obool), _1526073), c_Set_Oimage(_1526071, _1526075, _1526079)), hAPP(hAPP(c_COMBC(_1526073, tc_fun(_1526071, tc_HOL_Obool), tc_fun(_1526071, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526071, tc_HOL_Obool), tc_fun(tc_fun(_1526071, tc_HOL_Obool), tc_fun(_1526071, tc_HOL_Obool)), _1526073), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1526071, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1526073, tc_HOL_Obool), tc_fun(_1526071, tc_HOL_Obool), _1526073), c_Set_Ovimage(_1526071, _1526073, _1526077)), hAPP(hAPP(c_COMBC(_1526073, tc_fun(_1526073, tc_HOL_Obool), tc_fun(_1526073, tc_HOL_Obool)), c_Set_Oinsert(_1526073)), c_Orderings_Obot__class_Obot(tc_fun(_1526073, tc_HOL_Obool)))))), _1526081))))], (38657 ^ _784416) ^ [_1526268, _1526270, _1526272, _1526274, _1526276] : [hBOOL(hAPP(hAPP(_1526268, _1526270), _1526272)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1526274, _1526276, _1526268), _1526270)))], (38663 ^ _784416) ^ [_1526373, _1526375, _1526377, _1526379, _1526381, _1526383] : [hBOOL(hAPP(hAPP(c_member(_1526373), _1526375), _1526377)), hBOOL(hAPP(hAPP(c_member(_1526379), _1526381), hAPP(_1526383, _1526375))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526373, _1526379)), hAPP(hAPP(c_Product__Type_OPair(_1526373, _1526379), _1526375), _1526381)), hAPP(hAPP(c_Product__Type_OSigma(_1526373, _1526379), _1526377), _1526383))))], (38673 ^ _784416) ^ [_1526608, _1526610, _1526612] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1526608, _1526610), c_Orderings_Obot__class_Obot(tc_fun(_1526608, tc_HOL_Obool))), _1526612) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1526608, _1526610), tc_HOL_Obool)))], (38675 ^ _784416) ^ [_1526657, _1526659, _1526661, _1526663, _1526665, _1526667] : [hBOOL(hAPP(hAPP(c_member(_1526657), _1526659), _1526661)), 38678 ^ _784416 : [(38679 ^ _784416) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1526663, _1526657), _1526665), hAPP(c_COMBK(tc_fun(_1526657, tc_HOL_Obool), _1526663), _1526661)) = hAPP(hAPP(c_Product__Type_OSigma(_1526663, _1526657), _1526667), hAPP(c_COMBK(tc_fun(_1526657, tc_HOL_Obool), _1526663), _1526661)), -(_1526665 = _1526667)], (38685 ^ _784416) ^ [] : [_1526665 = _1526667, -(hAPP(hAPP(c_Product__Type_OSigma(_1526663, _1526657), _1526665), hAPP(c_COMBK(tc_fun(_1526657, tc_HOL_Obool), _1526663), _1526661)) = hAPP(hAPP(c_Product__Type_OSigma(_1526663, _1526657), _1526667), hAPP(c_COMBK(tc_fun(_1526657, tc_HOL_Obool), _1526663), _1526661)))]]], (38691 ^ _784416) ^ [_1527010, _1527012, _1527014, _1527016] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1527010, _1527012)), hAPP(hAPP(c_Product__Type_OSigma(_1527010, _1527012), _1527014), hAPP(c_COMBK(tc_fun(_1527012, tc_HOL_Obool), _1527010), _1527016))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1527010), _1527014)), hAPP(c_Finite__Set_Ocard(_1527012), _1527016)))], (38693 ^ _784416) ^ [_1527081, _1527083, _1527085, _1527087, _1527089, _1527091] : [class_Groups_Ocomm__monoid__add(_1527081), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1527083, _1527081), hAPP(hAPP(c_COMBC(_1527083, tc_fun(_1527085, tc_HOL_Obool), _1527081), hAPP(hAPP(c_COMBB(tc_fun(_1527085, _1527081), tc_fun(tc_fun(_1527085, tc_HOL_Obool), _1527081), _1527083), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1527085, _1527081)), _1527087)), _1527089)), _1527091) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1527083, _1527085), _1527081), hAPP(c_Product__Type_Oprod_Oprod__case(_1527083, _1527085, _1527081), _1527087)), hAPP(hAPP(c_Product__Type_OSigma(_1527083, _1527085), _1527091), hAPP(c_COMBK(tc_fun(_1527085, tc_HOL_Obool), _1527083), _1527089))))], (38699 ^ _784416) ^ [_1527326, _1527328, _1527330] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1527326, _1527328), _1527330), hAPP(c_COMBK(tc_fun(_1527328, tc_HOL_Obool), _1527326), c_Orderings_Obot__class_Obot(tc_fun(_1527328, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527326, _1527328), tc_HOL_Obool)))], (38711 ^ _784416) ^ [_1527567, _1527569, _1527571, _1527573] : [38712 ^ _784416 : [(38713 ^ _784416) ^ [] : [_1527571 = c_Orderings_Obot__class_Obot(tc_fun(_1527567, tc_HOL_Obool))], (38715 ^ _784416) ^ [] : [_1527573 = c_Orderings_Obot__class_Obot(tc_fun(_1527569, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1527567, _1527569), _1527571), hAPP(c_COMBK(tc_fun(_1527569, tc_HOL_Obool), _1527567), _1527573)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527567, _1527569), tc_HOL_Obool)))], (38701 ^ _784416) ^ [_1527405, _1527407, _1527409, _1527411] : [hAPP(hAPP(c_Product__Type_OSigma(_1527405, _1527407), _1527409), hAPP(c_COMBK(tc_fun(_1527407, tc_HOL_Obool), _1527405), _1527411)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527405, _1527407), tc_HOL_Obool)), -(_1527409 = c_Orderings_Obot__class_Obot(tc_fun(_1527405, tc_HOL_Obool))), -(_1527411 = c_Orderings_Obot__class_Obot(tc_fun(_1527407, tc_HOL_Obool)))], (38719 ^ _784416) ^ [_1527760, _1527762, _1527764] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1527760, _1527762), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1527760, _1527762), c_Orderings_Otop__class_Otop(tc_fun(_1527760, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1527762, tc_HOL_Obool), _1527760), _1527764))) = hAPP(hAPP(c_Product__Type_OSigma(_1527760, _1527762), c_Orderings_Otop__class_Otop(tc_fun(_1527760, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1527762, tc_HOL_Obool), _1527760), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1527762, tc_HOL_Obool)), _1527764))))], (38721 ^ _784416) ^ [_1527852, _1527854, _1527856] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1527852, _1527854), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1527852, _1527854), _1527856), hAPP(c_COMBK(tc_fun(_1527854, tc_HOL_Obool), _1527852), c_Orderings_Otop__class_Otop(tc_fun(_1527854, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1527852, _1527854), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1527852, tc_HOL_Obool)), _1527856)), hAPP(c_COMBK(tc_fun(_1527854, tc_HOL_Obool), _1527852), c_Orderings_Otop__class_Otop(tc_fun(_1527854, tc_HOL_Obool)))))], (38723 ^ _784416) ^ [_1527944, _1527946, _1527948, _1527950, _1527952, _1527954] : [class_Groups_Ocomm__monoid__mult(_1527944), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1527946, _1527944), hAPP(hAPP(c_COMBC(_1527946, tc_fun(_1527948, tc_HOL_Obool), _1527944), hAPP(hAPP(c_COMBB(tc_fun(_1527948, _1527944), tc_fun(tc_fun(_1527948, tc_HOL_Obool), _1527944), _1527946), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1527948, _1527944)), _1527950)), _1527952)), _1527954) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1527946, _1527948), _1527944), hAPP(c_Product__Type_Oprod_Oprod__case(_1527946, _1527948, _1527944), _1527950)), hAPP(hAPP(c_Product__Type_OSigma(_1527946, _1527948), _1527954), hAPP(c_COMBK(tc_fun(_1527948, tc_HOL_Obool), _1527946), _1527952))))], (38729 ^ _784416) ^ [_1528189, _1528191, _1528193, _1528195, _1528197] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1528189, _1528191), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1528189, tc_HOL_Obool)), _1528193), _1528195)), _1528197) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528189, _1528191), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1528189, _1528191), _1528193), _1528197)), hAPP(hAPP(c_Product__Type_OSigma(_1528189, _1528191), _1528195), _1528197)))], (38731 ^ _784416) ^ [_1528272, _1528274, _1528276, _1528278, _1528280] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1528272, _1528274), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1528272, tc_HOL_Obool)), _1528276), _1528278)), hAPP(c_COMBK(tc_fun(_1528274, tc_HOL_Obool), _1528272), _1528280)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528272, _1528274), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1528272, _1528274), _1528276), hAPP(c_COMBK(tc_fun(_1528274, tc_HOL_Obool), _1528272), _1528280))), hAPP(hAPP(c_Product__Type_OSigma(_1528272, _1528274), _1528278), hAPP(c_COMBK(tc_fun(_1528274, tc_HOL_Obool), _1528272), _1528280))))], (38733 ^ _784416) ^ [_1528382, _1528384, _1528386, _1528388, _1528390] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1528382, _1528384), _1528386), hAPP(hAPP(c_COMBS(_1528382, tc_fun(_1528384, tc_HOL_Obool), tc_fun(_1528384, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1528384, tc_HOL_Obool), tc_fun(tc_fun(_1528384, tc_HOL_Obool), tc_fun(_1528384, tc_HOL_Obool)), _1528382), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1528384, tc_HOL_Obool))), _1528388)), _1528390)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528382, _1528384), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1528382, _1528384), _1528386), _1528388)), hAPP(hAPP(c_Product__Type_OSigma(_1528382, _1528384), _1528386), _1528390)))], (38735 ^ _784416) ^ [_1528497, _1528499, _1528501, _1528503, _1528505, _1528507, _1528509, _1528511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528497, _1528499), tc_HOL_Obool)), _1528501), hAPP(hAPP(c_Product__Type_OSigma(_1528497, _1528499), _1528503), hAPP(c_COMBK(tc_fun(_1528499, tc_HOL_Obool), _1528497), _1528505)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528499, _1528507), tc_HOL_Obool)), _1528509), hAPP(hAPP(c_Product__Type_OSigma(_1528499, _1528507), _1528505), hAPP(c_COMBK(tc_fun(_1528507, tc_HOL_Obool), _1528499), _1528511)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1528497, _1528507), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1528497, _1528499, _1528507), _1528501), _1528509)), hAPP(hAPP(c_Product__Type_OSigma(_1528497, _1528507), _1528503), hAPP(c_COMBK(tc_fun(_1528507, tc_HOL_Obool), _1528497), _1528511)))))], (38745 ^ _784416) ^ [_1528856, _1528858, _1528860, _1528862] : [-(hAPP(c_Set_Oimage(tc_prod(_1528856, _1528858), tc_prod(_1528858, _1528856), hAPP(c_Product__Type_Oprod_Oprod__case(_1528856, _1528858, tc_prod(_1528858, _1528856)), hAPP(c_COMBC(_1528858, _1528856, tc_prod(_1528858, _1528856)), c_Product__Type_OPair(_1528858, _1528856)))), hAPP(hAPP(c_Product__Type_OSigma(_1528856, _1528858), _1528860), hAPP(c_COMBK(tc_fun(_1528858, tc_HOL_Obool), _1528856), _1528862))) = hAPP(hAPP(c_Product__Type_OSigma(_1528858, _1528856), _1528862), hAPP(c_COMBK(tc_fun(_1528856, tc_HOL_Obool), _1528858), _1528860)))], (38747 ^ _784416) ^ [_1528957, _1528959, _1528961, _1528963] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1528957), _1528959)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1528961), _1528963)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1528957, _1528961)), hAPP(hAPP(c_Product__Type_OSigma(_1528957, _1528961), _1528959), hAPP(c_COMBK(tc_fun(_1528961, tc_HOL_Obool), _1528957), _1528963)))))], (38757 ^ _784416) ^ [_1529160, _1529162, _1529164] : [c_Equiv__Relations_Oequiv(_1529160, _1529162, _1529164), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529160, _1529160), tc_HOL_Obool)), _1529164), hAPP(hAPP(c_Product__Type_OSigma(_1529160, _1529160), _1529162), hAPP(c_COMBK(tc_fun(_1529160, tc_HOL_Obool), _1529160), _1529162)))))], (38763 ^ _784416) ^ [_1529303, _1529305, _1529307, _1529309, _1529311] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529303, _1529305), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1529303, tc_HOL_Obool)), _1529307), _1529309)), _1529311) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1529303, _1529305), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529303, _1529305), _1529307), _1529311)), hAPP(hAPP(c_Product__Type_OSigma(_1529303, _1529305), _1529309), _1529311)))], (38765 ^ _784416) ^ [_1529386, _1529388, _1529390, _1529392, _1529394] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529386, _1529388), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1529386, tc_HOL_Obool)), _1529390), _1529392)), hAPP(c_COMBK(tc_fun(_1529388, tc_HOL_Obool), _1529386), _1529394)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1529386, _1529388), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529386, _1529388), _1529390), hAPP(c_COMBK(tc_fun(_1529388, tc_HOL_Obool), _1529386), _1529394))), hAPP(hAPP(c_Product__Type_OSigma(_1529386, _1529388), _1529392), hAPP(c_COMBK(tc_fun(_1529388, tc_HOL_Obool), _1529386), _1529394))))], (38767 ^ _784416) ^ [_1529496, _1529498, _1529500, _1529502, _1529504] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529496, _1529498), _1529500), hAPP(hAPP(c_COMBS(_1529496, tc_fun(_1529498, tc_HOL_Obool), tc_fun(_1529498, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529498, tc_HOL_Obool), tc_fun(tc_fun(_1529498, tc_HOL_Obool), tc_fun(_1529498, tc_HOL_Obool)), _1529496), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1529498, tc_HOL_Obool))), _1529502)), _1529504)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1529496, _1529498), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529496, _1529498), _1529500), _1529502)), hAPP(hAPP(c_Product__Type_OSigma(_1529496, _1529498), _1529500), _1529504)))], (38769 ^ _784416) ^ [_1529611, _1529613] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529611, _1529611), tc_HOL_Obool)), c_Relation_OId__on(_1529611, _1529613)), hAPP(hAPP(c_Product__Type_OSigma(_1529611, _1529611), _1529613), hAPP(c_COMBK(tc_fun(_1529611, tc_HOL_Obool), _1529611), _1529613)))))], (38771 ^ _784416) ^ [_1529670, _1529672, _1529674, _1529676, _1529678] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529670, _1529672), _1529674), hAPP(hAPP(c_COMBS(_1529670, tc_fun(_1529672, tc_HOL_Obool), tc_fun(_1529672, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529672, tc_HOL_Obool), tc_fun(tc_fun(_1529672, tc_HOL_Obool), tc_fun(_1529672, tc_HOL_Obool)), _1529670), c_Groups_Ominus__class_Ominus(tc_fun(_1529672, tc_HOL_Obool))), _1529676)), _1529678)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1529670, _1529672), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529670, _1529672), _1529674), _1529676)), hAPP(hAPP(c_Product__Type_OSigma(_1529670, _1529672), _1529674), _1529678)))], (38773 ^ _784416) ^ [_1529785, _1529787, _1529789, _1529791, _1529793] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529785, _1529787), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1529785, tc_HOL_Obool)), _1529789), _1529791)), hAPP(c_COMBK(tc_fun(_1529787, tc_HOL_Obool), _1529785), _1529793)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1529785, _1529787), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529785, _1529787), _1529789), hAPP(c_COMBK(tc_fun(_1529787, tc_HOL_Obool), _1529785), _1529793))), hAPP(hAPP(c_Product__Type_OSigma(_1529785, _1529787), _1529791), hAPP(c_COMBK(tc_fun(_1529787, tc_HOL_Obool), _1529785), _1529793))))], (38775 ^ _784416) ^ [_1529895, _1529897, _1529899, _1529901, _1529903] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529895, _1529897), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1529895, tc_HOL_Obool)), _1529899), _1529901)), _1529903) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1529895, _1529897), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529895, _1529897), _1529899), _1529903)), hAPP(hAPP(c_Product__Type_OSigma(_1529895, _1529897), _1529901), _1529903)))], (38777 ^ _784416) ^ [_1529999, _1530001, _1530003, _1530005] : [hBOOL(hAPP(c_Predicate_ODomainP(_1529999, _1530001, _1530003), _1530005)), -(hBOOL(hAPP(hAPP(_1530003, _1530005), 38780 ^ [_1529999, _1530001, _1530003, _1530005])))], (38784 ^ _784416) ^ [_1530114, _1530116, _1530118, _1530120] : [38785 ^ _784416 : [(38786 ^ _784416) ^ [_1530168] : [hBOOL(hAPP(hAPP(_1530118, _1530120), _1530168))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1530114, _1530116, _1530118), _1530120)))], (38790 ^ _784416) ^ [_1530232, _1530234] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1530232, _1530234), c_Orderings_Otop__class_Otop(tc_fun(_1530232, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1530234, tc_HOL_Obool), _1530232), c_Orderings_Otop__class_Otop(tc_fun(_1530234, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1530232, _1530234), tc_HOL_Obool)))], (38792 ^ _784416) ^ [_1530293, _1530295, _1530297, _1530299, _1530301, _1530303] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530293, _1530295)), hAPP(hAPP(c_Product__Type_OPair(_1530293, _1530295), _1530297), _1530299)), hAPP(hAPP(c_Product__Type_OSigma(_1530293, _1530295), _1530301), _1530303))), 38795 ^ _784416 : [(38796 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530293), _1530297), _1530301)))], (38798 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530295), _1530299), hAPP(_1530303, _1530297))))]]], (38800 ^ _784416) ^ [_1530498, _1530500, _1530502, _1530504, _1530506, _1530508] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530498, _1530500)), hAPP(hAPP(c_Product__Type_OPair(_1530498, _1530500), _1530502), _1530504)), hAPP(hAPP(c_Product__Type_OSigma(_1530498, _1530500), _1530506), _1530508))), -(hBOOL(hAPP(hAPP(c_member(_1530500), _1530504), hAPP(_1530508, _1530502))))], (38806 ^ _784416) ^ [_1530659, _1530661, _1530663, _1530665, _1530667, _1530669] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530659, _1530661)), hAPP(hAPP(c_Product__Type_OPair(_1530659, _1530661), _1530663), _1530665)), hAPP(hAPP(c_Product__Type_OSigma(_1530659, _1530661), _1530667), _1530669))), -(hBOOL(hAPP(hAPP(c_member(_1530659), _1530663), _1530667)))], (38812 ^ _784416) ^ [_1530841, _1530843, _1530845, _1530847, _1530849, _1530851] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530841, _1530843)), hAPP(hAPP(c_Product__Type_OPair(_1530841, _1530843), _1530845), _1530847)), hAPP(hAPP(c_Product__Type_OSigma(_1530841, _1530843), _1530849), _1530851))), 38815 ^ _784416 : [(38816 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530841), _1530845), _1530849)))], (38818 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530843), _1530847), hAPP(_1530851, _1530845))))]]], (38820 ^ _784416) ^ [_1531038, _1531040, _1531042, _1531044, _1531046, _1531048] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531038, _1531040)), hAPP(hAPP(c_Product__Type_OPair(_1531038, _1531040), _1531042), _1531044)), hAPP(hAPP(c_Product__Type_OSigma(_1531038, _1531040), _1531046), _1531048)))), hBOOL(hAPP(hAPP(c_member(_1531038), _1531042), _1531046)), hBOOL(hAPP(hAPP(c_member(_1531040), _1531044), hAPP(_1531048, _1531042)))], (38830 ^ _784416) ^ [_1531275, _1531277, _1531279, _1531281] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1531275, _1531277)), hAPP(hAPP(c_Product__Type_OSigma(_1531275, _1531277), hAPP(hAPP(c_Set_Oinsert(_1531275), _1531279), c_Orderings_Obot__class_Obot(tc_fun(_1531275, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1531277, tc_HOL_Obool), _1531275), _1531281))) = hAPP(c_Finite__Set_Ocard(_1531277), _1531281))], (38832 ^ _784416) ^ [_1531348, _1531350, _1531352, _1531354, _1531356, _1531358] : [hBOOL(hAPP(hAPP(c_member(_1531348), _1531350), _1531352)), 38835 ^ _784416 : [(38836 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531354, _1531348), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531354, _1531348), _1531356), hAPP(c_COMBK(tc_fun(_1531348, tc_HOL_Obool), _1531354), _1531352))), hAPP(hAPP(c_Product__Type_OSigma(_1531354, _1531348), _1531358), hAPP(c_COMBK(tc_fun(_1531348, tc_HOL_Obool), _1531354), _1531352)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531354, tc_HOL_Obool)), _1531356), _1531358)))], (38842 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531354, tc_HOL_Obool)), _1531356), _1531358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531354, _1531348), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531354, _1531348), _1531356), hAPP(c_COMBK(tc_fun(_1531348, tc_HOL_Obool), _1531354), _1531352))), hAPP(hAPP(c_Product__Type_OSigma(_1531354, _1531348), _1531358), hAPP(c_COMBK(tc_fun(_1531348, tc_HOL_Obool), _1531354), _1531352)))))]]], (38848 ^ _784416) ^ [_1531770, _1531772, _1531774, _1531776, _1531778, _1531780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531770, _1531772), tc_HOL_Obool)), _1531774), hAPP(hAPP(c_Product__Type_OSigma(_1531770, _1531772), _1531776), hAPP(c_COMBK(tc_fun(_1531772, tc_HOL_Obool), _1531770), _1531778)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531772, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1531770, _1531772, _1531774), _1531780)), _1531778)))], (38854 ^ _784416) ^ [_1531951, _1531953, _1531955, _1531957] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1531951, _1531953)), hAPP(hAPP(c_Product__Type_OSigma(_1531951, _1531953), _1531955), hAPP(c_COMBK(tc_fun(_1531953, tc_HOL_Obool), _1531951), _1531957)))), -(_1531957 = c_Orderings_Obot__class_Obot(tc_fun(_1531953, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1531951), _1531955)))], (38864 ^ _784416) ^ [_1532115, _1532117, _1532119, _1532121] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1532115, _1532117)), hAPP(hAPP(c_Product__Type_OSigma(_1532115, _1532117), _1532119), hAPP(c_COMBK(tc_fun(_1532117, tc_HOL_Obool), _1532115), _1532121)))), -(_1532119 = c_Orderings_Obot__class_Obot(tc_fun(_1532115, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1532117), _1532121)))], (38874 ^ _784416) ^ [_1532279, _1532281, _1532283, _1532285] : [-(hAPP(c_Set_OCollect(tc_prod(_1532279, _1532281)), hAPP(c_Product__Type_Oprod_Oprod__case(_1532279, _1532281, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1532279, tc_fun(_1532281, tc_HOL_Obool), tc_fun(_1532281, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1532281, tc_HOL_Obool), tc_fun(_1532281, tc_HOL_Obool)), _1532279), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1532281)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532279), c_fconj), _1532283))), _1532285))) = hAPP(hAPP(c_Product__Type_OSigma(_1532279, _1532281), hAPP(c_Set_OCollect(_1532279), _1532283)), hAPP(hAPP(c_COMBB(tc_fun(_1532281, tc_HOL_Obool), tc_fun(_1532281, tc_HOL_Obool), _1532279), c_Set_OCollect(_1532281)), _1532285)))], (38876 ^ _784416) ^ [_1532404, _1532406, _1532408, _1532410] : [-(hAPP(c_Set_OCollect(tc_prod(_1532404, _1532406)), hAPP(c_Product__Type_Oprod_Oprod__case(_1532404, _1532406, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1532404, tc_fun(_1532406, tc_HOL_Obool), tc_fun(_1532406, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1532406, tc_HOL_Obool), tc_fun(_1532406, tc_HOL_Obool)), _1532404), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1532406)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532404), c_fconj), _1532408))), _1532410))) = hAPP(hAPP(c_Product__Type_OSigma(_1532404, _1532406), hAPP(c_Set_OCollect(_1532404), _1532408)), hAPP(c_COMBK(tc_fun(_1532406, tc_HOL_Obool), _1532404), hAPP(c_Set_OCollect(_1532406), _1532410))))], (38878 ^ _784416) ^ [_1532540, _1532542, _1532544, _1532546] : [_1532540 = c_Orderings_Obot__class_Obot(tc_fun(_1532542, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1532544, _1532542), _1532544, c_Product__Type_Ofst(_1532544, _1532542)), hAPP(hAPP(c_Product__Type_OSigma(_1532544, _1532542), _1532546), hAPP(c_COMBK(tc_fun(_1532542, tc_HOL_Obool), _1532544), _1532540))) = c_Orderings_Obot__class_Obot(tc_fun(_1532544, tc_HOL_Obool)))], (38884 ^ _784416) ^ [_1532697, _1532699, _1532701, _1532703] : [-(_1532697 = c_Orderings_Obot__class_Obot(tc_fun(_1532699, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1532701, _1532699), _1532701, c_Product__Type_Ofst(_1532701, _1532699)), hAPP(hAPP(c_Product__Type_OSigma(_1532701, _1532699), _1532703), hAPP(c_COMBK(tc_fun(_1532699, tc_HOL_Obool), _1532701), _1532697))) = _1532703)], (38890 ^ _784416) ^ [_1532790, _1532792, _1532794, _1532796] : [_1532790 = c_Orderings_Obot__class_Obot(tc_fun(_1532792, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1532792, _1532794), _1532794, c_Product__Type_Osnd(_1532792, _1532794)), hAPP(hAPP(c_Product__Type_OSigma(_1532792, _1532794), _1532790), hAPP(c_COMBK(tc_fun(_1532794, tc_HOL_Obool), _1532792), _1532796))) = c_Orderings_Obot__class_Obot(tc_fun(_1532794, tc_HOL_Obool)))], (38896 ^ _784416) ^ [_1532947, _1532949, _1532951, _1532953] : [-(_1532947 = c_Orderings_Obot__class_Obot(tc_fun(_1532949, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1532949, _1532951), _1532951, c_Product__Type_Osnd(_1532949, _1532951)), hAPP(hAPP(c_Product__Type_OSigma(_1532949, _1532951), _1532947), hAPP(c_COMBK(tc_fun(_1532951, tc_HOL_Obool), _1532949), _1532953))) = _1532953)], (38902 ^ _784416) ^ [_1533025, _1533027, _1533029, _1533031, _1533033, _1533035] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1533025, _1533027), hAPP(hAPP(c_Set_Oinsert(_1533025), _1533029), _1533031)), hAPP(c_COMBK(tc_fun(_1533027, tc_HOL_Obool), _1533025), hAPP(hAPP(c_Set_Oinsert(_1533027), _1533033), _1533035))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1533025, _1533027)), hAPP(hAPP(c_Product__Type_OPair(_1533025, _1533027), _1533029), _1533033)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1533025, _1533027), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1533025, _1533027), _1533031), hAPP(c_COMBK(tc_fun(_1533027, tc_HOL_Obool), _1533025), hAPP(hAPP(c_Set_Oinsert(_1533027), _1533033), _1533035)))), hAPP(hAPP(c_Product__Type_OSigma(_1533025, _1533027), hAPP(hAPP(c_Set_Oinsert(_1533025), _1533029), _1533031)), hAPP(c_COMBK(tc_fun(_1533027, tc_HOL_Obool), _1533025), _1533035)))))], (38904 ^ _784416) ^ [_1533178, _1533180, _1533182, _1533184] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1533178), _1533180)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533178, _1533178), tc_HOL_Obool)), _1533182), hAPP(hAPP(c_Product__Type_OSigma(_1533178, _1533178), _1533180), hAPP(c_COMBK(tc_fun(_1533178, tc_HOL_Obool), _1533178), _1533180)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1533178, tc_HOL_Obool)), _1533184), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1533178), _1533180), _1533182))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1533178), _1533184)))], (38918 ^ _784416) ^ [_1533485, _1533487, _1533489, _1533491, _1533493, _1533495] : [-(hAPP(c_Set_Ovimage(_1533485, tc_prod(_1533487, _1533489), _1533491), hAPP(hAPP(c_Product__Type_OSigma(_1533487, _1533489), _1533493), hAPP(c_COMBK(tc_fun(_1533489, tc_HOL_Obool), _1533487), _1533495))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533485, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1533485, _1533487, hAPP(c_Fun_Ocomp(tc_prod(_1533487, _1533489), _1533487, _1533485, c_Product__Type_Ofst(_1533487, _1533489)), _1533491)), _1533493)), hAPP(c_Set_Ovimage(_1533485, _1533489, hAPP(c_Fun_Ocomp(tc_prod(_1533487, _1533489), _1533489, _1533485, c_Product__Type_Osnd(_1533487, _1533489)), _1533491)), _1533495)))], (38920 ^ _784416) ^ [_1533599, _1533601, _1533603, _1533605, _1533607, _1533609, _1533611, _1533613] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1533599, _1533601), tc_fun(tc_prod(_1533603, _1533605), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1533599, _1533601), _1533607), hAPP(c_COMBK(tc_fun(_1533601, tc_HOL_Obool), _1533599), _1533609))), hAPP(c_Product__Type_Oprod_Oprod__case(_1533599, _1533601, tc_fun(tc_prod(_1533603, _1533605), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1533599, tc_fun(_1533601, tc_fun(_1533603, tc_fun(_1533605, tc_HOL_Obool))), tc_fun(_1533601, tc_fun(tc_prod(_1533603, _1533605), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1533603, tc_fun(_1533605, tc_HOL_Obool)), tc_fun(tc_prod(_1533603, _1533605), tc_HOL_Obool)), tc_fun(tc_fun(_1533601, tc_fun(_1533603, tc_fun(_1533605, tc_HOL_Obool))), tc_fun(_1533601, tc_fun(tc_prod(_1533603, _1533605), tc_HOL_Obool))), _1533599), c_COMBB(tc_fun(_1533603, tc_fun(_1533605, tc_HOL_Obool)), tc_fun(tc_prod(_1533603, _1533605), tc_HOL_Obool), _1533601)), hAPP(hAPP(c_COMBB(tc_fun(_1533603, tc_HOL_Obool), tc_fun(tc_fun(_1533603, tc_fun(_1533605, tc_HOL_Obool)), tc_fun(tc_prod(_1533603, _1533605), tc_HOL_Obool)), _1533599), c_Product__Type_OSigma(_1533603, _1533605)), _1533611))), hAPP(hAPP(c_COMBB(tc_fun(_1533605, tc_HOL_Obool), tc_fun(_1533603, tc_fun(_1533605, tc_HOL_Obool)), _1533601), c_COMBK(tc_fun(_1533605, tc_HOL_Obool), _1533603)), _1533613)))) = hAPP(hAPP(c_Product__Type_OSigma(_1533603, _1533605), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533599, tc_fun(_1533603, tc_HOL_Obool)), _1533607), _1533611)), hAPP(c_COMBK(tc_fun(_1533605, tc_HOL_Obool), _1533603), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533601, tc_fun(_1533605, tc_HOL_Obool)), _1533609), _1533613))))], (38922 ^ _784416) ^ [_1533873, _1533875, _1533877, _1533879] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1533873, _1533875), _1533877), _1533879) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533873, tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool)), _1533877), hAPP(hAPP(c_COMBS(_1533873, tc_fun(_1533875, tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool)), tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533875, tc_HOL_Obool), tc_fun(tc_fun(_1533875, tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool)), tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool)), _1533873), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1533875, tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool))), _1533879)), hAPP(hAPP(c_COMBC(_1533873, tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool), tc_fun(_1533875, tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1533875, tc_fun(tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool), tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool), tc_fun(_1533875, tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool))), _1533873), c_COMBC(_1533875, tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool), tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1533875, tc_prod(_1533873, _1533875)), tc_fun(_1533875, tc_fun(tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool), tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool))), _1533873), hAPP(c_COMBB(tc_prod(_1533873, _1533875), tc_fun(tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool), tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool)), _1533875), c_Set_Oinsert(tc_prod(_1533873, _1533875)))), c_Product__Type_OPair(_1533873, _1533875)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1533873, _1533875), tc_HOL_Obool))))))], (38924 ^ _784416) ^ [_1534153, _1534155, _1534157] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1534153), _1534155)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534153, _1534153), tc_HOL_Obool)), _1534157), hAPP(hAPP(c_Product__Type_OSigma(_1534153, _1534153), _1534155), hAPP(c_COMBK(tc_fun(_1534153, tc_HOL_Obool), _1534153), _1534155)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1534153, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1534153), _1534155), _1534157))))], (38934 ^ _784416) ^ [_1534386, _1534388, _1534390, _1534392, _1534394, _1534396, _1534398] : [class_Rings_Osemiring__0(_1534386), c_Fun_Oinj__on(tc_prod(_1534388, _1534390), _1534386, hAPP(c_Product__Type_Oprod_Oprod__case(_1534388, _1534390, _1534386), hAPP(hAPP(c_COMBC(_1534388, tc_fun(_1534390, _1534386), tc_fun(_1534390, _1534386)), hAPP(hAPP(c_COMBB(tc_fun(_1534386, _1534386), tc_fun(tc_fun(_1534390, _1534386), tc_fun(_1534390, _1534386)), _1534388), c_COMBB(_1534386, _1534386, _1534390)), hAPP(hAPP(c_COMBB(_1534386, tc_fun(_1534386, _1534386), _1534388), c_Groups_Otimes__class_Otimes(_1534386)), _1534392))), _1534394)), hAPP(hAPP(c_Product__Type_OSigma(_1534388, _1534390), _1534396), hAPP(c_COMBK(tc_fun(_1534390, tc_HOL_Obool), _1534388), _1534398))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1534386), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1534388, _1534386), _1534392), _1534396)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1534390, _1534386), _1534394), _1534398)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1534386, _1534386), c_Fun_Oid(_1534386)), hAPP(c_Set_OCollect(_1534386), hAPP(hAPP(c_COMBB(tc_fun(_1534388, tc_HOL_Obool), tc_HOL_Obool, _1534386), c_HOL_OEx(_1534388)), hAPP(hAPP(c_COMBB(tc_fun(_1534388, tc_fun(_1534390, tc_HOL_Obool)), tc_fun(_1534388, tc_HOL_Obool), _1534386), hAPP(c_COMBB(tc_fun(_1534390, tc_HOL_Obool), tc_HOL_Obool, _1534388), c_HOL_OEx(_1534390))), hAPP(hAPP(c_COMBC(_1534386, tc_fun(_1534388, tc_fun(_1534390, tc_HOL_Obool)), tc_fun(_1534388, tc_fun(_1534390, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1534388, tc_fun(tc_fun(_1534390, tc_HOL_Obool), tc_fun(_1534390, tc_HOL_Obool))), tc_fun(tc_fun(_1534388, tc_fun(_1534390, tc_HOL_Obool)), tc_fun(_1534388, tc_fun(_1534390, tc_HOL_Obool))), _1534386), c_COMBS(_1534388, tc_fun(_1534390, tc_HOL_Obool), tc_fun(_1534390, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1534388, tc_fun(_1534390, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1534388, tc_fun(tc_fun(_1534390, tc_HOL_Obool), tc_fun(_1534390, tc_HOL_Obool))), _1534386), hAPP(c_COMBB(tc_fun(_1534390, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1534390, tc_HOL_Obool), tc_fun(_1534390, tc_HOL_Obool)), _1534388), c_COMBS(_1534390, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1534388, tc_fun(_1534390, tc_HOL_Obool)), tc_fun(_1534388, tc_fun(_1534390, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1534386), hAPP(c_COMBB(tc_fun(_1534390, tc_HOL_Obool), tc_fun(_1534390, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1534388), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534390), c_fconj))), hAPP(hAPP(c_COMBC(_1534386, tc_fun(_1534388, tc_fun(_1534390, _1534386)), tc_fun(_1534388, tc_fun(_1534390, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1534390, _1534386), tc_fun(_1534390, tc_HOL_Obool)), tc_fun(tc_fun(_1534388, tc_fun(_1534390, _1534386)), tc_fun(_1534388, tc_fun(_1534390, tc_HOL_Obool))), _1534386), c_COMBB(tc_fun(_1534390, _1534386), tc_fun(_1534390, tc_HOL_Obool), _1534388)), hAPP(hAPP(c_COMBB(tc_fun(_1534386, tc_HOL_Obool), tc_fun(tc_fun(_1534390, _1534386), tc_fun(_1534390, tc_HOL_Obool)), _1534386), c_COMBB(_1534386, tc_HOL_Obool, _1534390)), c_fequal))), hAPP(hAPP(c_COMBC(_1534388, tc_fun(_1534390, _1534386), tc_fun(_1534390, _1534386)), hAPP(hAPP(c_COMBB(tc_fun(_1534386, _1534386), tc_fun(tc_fun(_1534390, _1534386), tc_fun(_1534390, _1534386)), _1534388), c_COMBB(_1534386, _1534386, _1534390)), hAPP(hAPP(c_COMBB(_1534386, tc_fun(_1534386, _1534386), _1534388), c_Groups_Otimes__class_Otimes(_1534386)), _1534392))), _1534394)))))), hAPP(hAPP(c_COMBC(_1534388, tc_fun(_1534390, tc_HOL_Obool), tc_fun(_1534390, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1534390, tc_HOL_Obool), tc_fun(_1534390, tc_HOL_Obool)), _1534388), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534390)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534388), c_fconj), hAPP(hAPP(c_COMBC(_1534388, tc_fun(_1534388, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534388)), _1534396)))), hAPP(hAPP(c_COMBC(_1534390, tc_fun(_1534390, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534390)), _1534398))))))))], (38945 ^ _784416) ^ [_1535661, _1535663, _1535665, _1535667] : [-(c_Fun_Oinj__on(_1535661, tc_prod(_1535663, _1535661), 38943 ^ [_1535661, _1535663, _1535665, _1535667], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535663, tc_fun(_1535661, tc_HOL_Obool)), _1535665), _1535667)))], (38947 ^ _784416) ^ [_1535715, _1535717, _1535719, _1535721] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1535717, _1535715), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1535715, tc_prod(_1535717, _1535715), 38943 ^ [_1535715, _1535717, _1535719, _1535721]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1535717, tc_fun(_1535715, tc_HOL_Obool)), _1535719), _1535721))), hAPP(hAPP(c_Product__Type_OSigma(_1535717, _1535715), _1535719), _1535721))))], (38949 ^ _784416) ^ [_1535801, _1535803, _1535805, _1535807, _1535809, _1535811] : [class_Groups_Ocomm__monoid__mult(_1535801), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535803), _1535805)), 38959 ^ _784416 : [(38960 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1535803), 38958 ^ [_1535801, _1535803, _1535805, _1535807, _1535809, _1535811]), _1535805)))], (38962 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1535807), hAPP(_1535809, 38958 ^ [_1535801, _1535803, _1535805, _1535807, _1535809, _1535811])))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1535801, _1535803, c_Groups_Otimes__class_Otimes(_1535801)), hAPP(hAPP(c_COMBS(_1535803, tc_fun(_1535807, tc_HOL_Obool), _1535801), hAPP(hAPP(c_COMBC(_1535803, _1535801, tc_fun(tc_fun(_1535807, tc_HOL_Obool), _1535801)), hAPP(hAPP(c_COMBB(tc_fun(_1535807, _1535801), tc_fun(_1535801, tc_fun(tc_fun(_1535807, tc_HOL_Obool), _1535801)), _1535803), c_Finite__Set_Ofold__image(_1535801, _1535807, c_Groups_Otimes__class_Otimes(_1535801))), _1535811)), c_Groups_Oone__class_Oone(_1535801))), _1535809)), c_Groups_Oone__class_Oone(_1535801)), _1535805) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1535801, tc_prod(_1535803, _1535807), c_Groups_Otimes__class_Otimes(_1535801)), hAPP(c_Product__Type_Oprod_Oprod__case(_1535803, _1535807, _1535801), _1535811)), c_Groups_Oone__class_Oone(_1535801)), hAPP(hAPP(c_Product__Type_OSigma(_1535803, _1535807), _1535805), _1535809)))], (38966 ^ _784416) ^ [_1536358, _1536360] : [-(hAPP(c_Set_Oimage(_1536358, _1536358, c_Fun_Oid(_1536358)), _1536360) = _1536360)], (38968 ^ _784416) ^ [_1536392, _1536394] : [-(c_Product__Type_Oapfst(_1536392, _1536392, _1536394, c_Fun_Oid(_1536392)) = c_Fun_Oid(tc_prod(_1536392, _1536394)))], (38970 ^ _784416) ^ [_1536429, _1536431] : [-(c_Fun_Oinj__on(_1536429, _1536429, c_Fun_Oid(_1536429), _1536431))], (38972 ^ _784416) ^ [_1536458, _1536460] : [-(hAPP(c_Set_Ovimage(_1536458, _1536458, c_Fun_Oid(_1536458)), _1536460) = _1536460)], (38974 ^ _784416) ^ [_1536492, _1536494] : [-(hAPP(c_Fun_Oid(_1536492), _1536494) = _1536494)], (38976 ^ _784416) ^ [_1536522, _1536524] : [-(hAPP(c_Fun_Oid(_1536522), _1536524) = _1536524)], (38978 ^ _784416) ^ [_1536552, _1536554, _1536556] : [-(hAPP(c_Fun_Ocomp(_1536552, _1536552, _1536554, c_Fun_Oid(_1536552)), _1536556) = _1536556)], (38980 ^ _784416) ^ [_1536589, _1536591, _1536593] : [-(hAPP(c_Fun_Ocomp(_1536589, _1536591, _1536589, _1536593), c_Fun_Oid(_1536589)) = _1536593)], (38982 ^ _784416) ^ [_1536626, _1536628, _1536630, _1536632, _1536634, _1536636, _1536638] : [hAPP(c_Fun_Ocomp(_1536626, _1536628, _1536630, _1536632), _1536634) = hAPP(c_Fun_Ocomp(_1536628, _1536628, _1536630, c_Fun_Oid(_1536628)), _1536636), -(hAPP(_1536632, hAPP(_1536634, _1536638)) = hAPP(_1536636, _1536638))], (38988 ^ _784416) ^ [_1536767, _1536769] : [-(c_Product__Type_Oapsnd(_1536767, _1536767, _1536769, c_Fun_Oid(_1536767)) = c_Fun_Oid(tc_prod(_1536769, _1536767)))], (38990 ^ _784416) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (38992 ^ _784416) ^ [_1536822] : [-(hAPP(c_Set_Oimage(_1536822, _1536822, c_Fun_Oid(_1536822)), c_Orderings_Otop__class_Otop(tc_fun(_1536822, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1536822, tc_HOL_Obool)))], (38994 ^ _784416) ^ [_1536864] : [-(c_Hilbert__Choice_Oinv__into(_1536864, _1536864, c_Orderings_Otop__class_Otop(tc_fun(_1536864, tc_HOL_Obool)), c_Fun_Oid(_1536864)) = c_Fun_Oid(_1536864))], (38996 ^ _784416) ^ [_1536901, _1536903, _1536905, _1536907] : [c_Finite__Set_Ofolding(_1536901, _1536903, _1536905, _1536907), -(hAPP(_1536907, c_Orderings_Obot__class_Obot(tc_fun(_1536901, tc_HOL_Obool))) = c_Fun_Oid(_1536903))], (39002 ^ _784416) ^ [_1537006, _1537008] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1537006, _1537008, tc_prod(_1537006, _1537008)), c_Product__Type_OPair(_1537006, _1537008)) = c_Fun_Oid(tc_prod(_1537006, _1537008)))], (39004 ^ _784416) ^ [_1537049, _1537051, _1537053, _1537055] : [class_Groups_Ocomm__monoid__add(_1537049), c_Fun_Oinj__on(_1537051, _1537049, _1537053, _1537055), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1537051, _1537049), _1537053), _1537055) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1537049, _1537049), c_Fun_Oid(_1537049)), hAPP(c_Set_Oimage(_1537051, _1537049, _1537053), _1537055)))], (39014 ^ _784416) ^ [_1537242, _1537244, _1537246, _1537248] : [class_Groups_Ocomm__monoid__mult(_1537242), c_Fun_Oinj__on(_1537244, _1537242, _1537246, _1537248), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1537244, _1537242), _1537246), _1537248) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1537242, _1537242), c_Fun_Oid(_1537242)), hAPP(c_Set_Oimage(_1537244, _1537242, _1537246), _1537248)))], (39024 ^ _784416) ^ [_1537453, _1537455, _1537457] : [hAPP(c_Set_Oimage(_1537453, _1537455, _1537457), c_Orderings_Otop__class_Otop(tc_fun(_1537453, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1537455, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1537453, _1537455, _1537455, _1537457), c_Hilbert__Choice_Oinv__into(_1537453, _1537455, c_Orderings_Otop__class_Otop(tc_fun(_1537453, tc_HOL_Obool)), _1537457)) = c_Fun_Oid(_1537455))], (39030 ^ _784416) ^ [_1537602, _1537604, _1537606] : [hAPP(c_Fun_Ocomp(_1537602, _1537604, _1537604, _1537606), c_Hilbert__Choice_Oinv__into(_1537602, _1537604, c_Orderings_Otop__class_Otop(tc_fun(_1537602, tc_HOL_Obool)), _1537606)) = c_Fun_Oid(_1537604), -(hAPP(c_Set_Oimage(_1537602, _1537604, _1537606), c_Orderings_Otop__class_Otop(tc_fun(_1537602, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1537604, tc_HOL_Obool)))], (39036 ^ _784416) ^ [_1537757, _1537759, _1537761] : [c_Fun_Oinj__on(_1537757, _1537759, _1537761, c_Orderings_Otop__class_Otop(tc_fun(_1537757, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1537759, _1537757, _1537757, c_Hilbert__Choice_Oinv__into(_1537757, _1537759, c_Orderings_Otop__class_Otop(tc_fun(_1537757, tc_HOL_Obool)), _1537761)), _1537761) = c_Fun_Oid(_1537757))], (39042 ^ _784416) ^ [_1537908, _1537910, _1537912] : [c_Fun_Oinj__on(_1537908, _1537910, _1537912, c_Orderings_Otop__class_Otop(tc_fun(_1537908, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1537910, _1537908, _1537908, c_Hilbert__Choice_Oinv__into(_1537908, _1537910, c_Orderings_Otop__class_Otop(tc_fun(_1537908, tc_HOL_Obool)), _1537912)), _1537912) = c_Fun_Oid(_1537908))], (39048 ^ _784416) ^ [_1538037, _1538039, _1538041] : [hAPP(c_Fun_Ocomp(_1538039, _1538037, _1538037, c_Hilbert__Choice_Oinv__into(_1538037, _1538039, c_Orderings_Otop__class_Otop(tc_fun(_1538037, tc_HOL_Obool)), _1538041)), _1538041) = c_Fun_Oid(_1538037), -(c_Fun_Oinj__on(_1538037, _1538039, _1538041, c_Orderings_Otop__class_Otop(tc_fun(_1538037, tc_HOL_Obool))))], (39054 ^ _784416) ^ [_1538172, _1538174, _1538176, _1538178, _1538180, _1538182] : [class_Groups_Ocomm__monoid__mult(_1538172), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538174), _1538176)), 39064 ^ _784416 : [(39065 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538174), 39063 ^ [_1538172, _1538174, _1538176, _1538178, _1538180, _1538182]), _1538176)))], (39067 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538178), hAPP(_1538180, 39063 ^ [_1538172, _1538174, _1538176, _1538178, _1538180, _1538182])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1538174, _1538172), hAPP(hAPP(c_COMBS(_1538174, tc_fun(_1538178, tc_HOL_Obool), _1538172), hAPP(hAPP(c_COMBB(tc_fun(_1538178, _1538172), tc_fun(tc_fun(_1538178, tc_HOL_Obool), _1538172), _1538174), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1538178, _1538172)), _1538182)), _1538180)), _1538176) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1538174, _1538178), _1538172), hAPP(c_Product__Type_Oprod_Oprod__case(_1538174, _1538178, _1538172), _1538182)), hAPP(hAPP(c_Product__Type_OSigma(_1538174, _1538178), _1538176), _1538180)))], (39071 ^ _784416) ^ [_1538649, _1538651, _1538653, _1538655, _1538657, _1538659] : [class_Groups_Ocomm__monoid__add(_1538649), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538651), _1538653)), 39081 ^ _784416 : [(39082 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538651), 39080 ^ [_1538649, _1538651, _1538653, _1538655, _1538657, _1538659]), _1538653)))], (39084 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538655), hAPP(_1538657, 39080 ^ [_1538649, _1538651, _1538653, _1538655, _1538657, _1538659])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538651, _1538649), hAPP(hAPP(c_COMBS(_1538651, tc_fun(_1538655, tc_HOL_Obool), _1538649), hAPP(hAPP(c_COMBB(tc_fun(_1538655, _1538649), tc_fun(tc_fun(_1538655, tc_HOL_Obool), _1538649), _1538651), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538655, _1538649)), _1538659)), _1538657)), _1538653) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1538651, _1538655), _1538649), hAPP(c_Product__Type_Oprod_Oprod__case(_1538651, _1538655, _1538649), _1538659)), hAPP(hAPP(c_Product__Type_OSigma(_1538651, _1538655), _1538653), _1538657)))], (39088 ^ _784416) ^ [_1539126, _1539128, _1539130, _1539132] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539126), _1539128)), 39094 ^ _784416 : [(39095 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539126), 39093 ^ [_1539126, _1539128, _1539130, _1539132]), _1539128)))], (39097 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539130), hAPP(_1539132, 39093 ^ [_1539126, _1539128, _1539130, _1539132])))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1539126, _1539130)), hAPP(hAPP(c_Product__Type_OSigma(_1539126, _1539130), _1539128), _1539132)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539126, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1539130, tc_HOL_Obool), tc_Nat_Onat, _1539126), c_Finite__Set_Ocard(_1539130)), _1539132)), _1539128))], (39101 ^ _784416) ^ [_1539463, _1539465, _1539467, _1539469] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539463), _1539465)), 39107 ^ _784416 : [(39108 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539463), 39106 ^ [_1539463, _1539465, _1539467, _1539469]), _1539465)))], (39110 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539467), hAPP(_1539469, 39106 ^ [_1539463, _1539465, _1539467, _1539469])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1539463, _1539467)), hAPP(hAPP(c_Product__Type_OSigma(_1539463, _1539467), _1539465), _1539469))))], (39114 ^ _784416) ^ [_1539750, _1539752, _1539754, _1539756, _1539758] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539750, _1539752)), _1539754), hAPP(hAPP(c_Product__Type_OSigma(_1539750, _1539752), _1539756), _1539758))), 39118 ^ _784416 : [(39119 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539750), 39117 ^ [_1539750, _1539752, _1539754, _1539756, _1539758]), _1539756)))], (39122 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539752), 39120 ^ [_1539750, _1539752, _1539754, _1539756, _1539758]), hAPP(_1539758, 39117 ^ [_1539750, _1539752, _1539754, _1539756, _1539758]))))], (39124 ^ _784416) ^ [] : [-(_1539754 = hAPP(hAPP(c_Product__Type_OPair(_1539750, _1539752), 39117 ^ [_1539750, _1539752, _1539754, _1539756, _1539758]), 39120 ^ [_1539750, _1539752, _1539754, _1539756, _1539758]))]]], (39126 ^ _784416) ^ [_1540052, _1540054, _1540056, _1540058, _1540060, _1540062] : [hAPP(c_Set_Oimage(_1540052, _1540054, _1540056), c_Orderings_Otop__class_Otop(tc_fun(_1540052, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1540054, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1540058, _1540060, _1540062), c_Orderings_Otop__class_Otop(tc_fun(_1540058, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1540060, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1540052, _1540058), tc_prod(_1540054, _1540060), c_Product__Type_Omap__pair(_1540052, _1540054, _1540058, _1540060, _1540056, _1540062)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1540052, _1540058), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1540054, _1540060), tc_HOL_Obool)))], (39136 ^ _784416) ^ [_1540337, _1540339, _1540341, _1540343, _1540345, _1540347, _1540349, _1540351, _1540353] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540337, _1540339)), hAPP(hAPP(c_Product__Type_OPair(_1540337, _1540339), _1540341), _1540343)), _1540345)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540347, _1540349)), hAPP(hAPP(c_Product__Type_OPair(_1540347, _1540349), hAPP(_1540351, _1540341)), hAPP(_1540353, _1540343))), hAPP(c_Set_Oimage(tc_prod(_1540337, _1540339), tc_prod(_1540347, _1540349), c_Product__Type_Omap__pair(_1540337, _1540347, _1540339, _1540349, _1540351, _1540353)), _1540345))))], (39142 ^ _784416) ^ [_1540556, _1540558, _1540560] : [-(hAPP(c_Product__Type_Omap__pair(_1540556, _1540556, _1540558, _1540558, c_COMBI(_1540556), c_COMBI(_1540558)), _1540560) = _1540560)], (39144 ^ _784416) ^ [_1540597, _1540599, _1540601, _1540603, _1540605, _1540607, _1540609, _1540611] : [-(hAPP(c_Product__Type_Omap__pair(_1540597, _1540599, _1540601, _1540603, _1540605, _1540607), hAPP(hAPP(c_Product__Type_OPair(_1540597, _1540601), _1540609), _1540611)) = hAPP(hAPP(c_Product__Type_OPair(_1540599, _1540603), hAPP(_1540605, _1540609)), hAPP(_1540607, _1540611)))], (39146 ^ _784416) ^ [_1540668, _1540670, _1540672, _1540674, _1540676, _1540678, _1540680] : [-(hAPP(c_Product__Type_Ofst(_1540668, _1540670), hAPP(c_Product__Type_Omap__pair(_1540672, _1540668, _1540674, _1540670, _1540676, _1540678), _1540680)) = hAPP(_1540676, hAPP(c_Product__Type_Ofst(_1540672, _1540674), _1540680)))], (39148 ^ _784416) ^ [_1540728, _1540730, _1540732, _1540734, _1540736, _1540738, _1540740] : [-(hAPP(c_Product__Type_Osnd(_1540728, _1540730), hAPP(c_Product__Type_Omap__pair(_1540732, _1540728, _1540734, _1540730, _1540736, _1540738), _1540740)) = hAPP(_1540738, hAPP(c_Product__Type_Osnd(_1540732, _1540734), _1540740)))], (39150 ^ _784416) ^ [_1540788, _1540790, _1540792, _1540794, _1540796, _1540798] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1540788, _1540790), _1540790, tc_prod(_1540792, _1540794), c_Product__Type_Osnd(_1540788, _1540790)), c_Product__Type_Omap__pair(_1540792, _1540788, _1540794, _1540790, _1540796, _1540798)) = hAPP(c_Fun_Ocomp(_1540794, _1540790, tc_prod(_1540792, _1540794), _1540798), c_Product__Type_Osnd(_1540792, _1540794)))], (39152 ^ _784416) ^ [_1540859, _1540861, _1540863, _1540865, _1540867, _1540869] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1540859, _1540861), _1540859, tc_prod(_1540863, _1540865), c_Product__Type_Ofst(_1540859, _1540861)), c_Product__Type_Omap__pair(_1540863, _1540859, _1540865, _1540861, _1540867, _1540869)) = hAPP(c_Fun_Ocomp(_1540863, _1540859, tc_prod(_1540863, _1540865), _1540867), c_Product__Type_Ofst(_1540863, _1540865)))], (39154 ^ _784416) ^ [_1540930, _1540932, _1540934, _1540936, _1540938, _1540940, _1540942, _1540944, _1540946, _1540948, _1540950] : [-(hAPP(c_Product__Type_Omap__pair(_1540930, _1540932, _1540934, _1540936, _1540938, _1540940), hAPP(c_Product__Type_Omap__pair(_1540942, _1540930, _1540944, _1540934, _1540946, _1540948), _1540950)) = hAPP(c_Product__Type_Omap__pair(_1540942, _1540932, _1540944, _1540936, hAPP(c_Fun_Ocomp(_1540930, _1540932, _1540942, _1540938), _1540946), hAPP(c_Fun_Ocomp(_1540934, _1540936, _1540944, _1540940), _1540948)), _1540950))], (39156 ^ _784416) ^ [_1541019, _1541021, _1541023, _1541025, _1541027, _1541029, _1541031, _1541033, _1541035, _1541037] : [-(c_Product__Type_Omap__pair(_1541019, _1541021, _1541023, _1541025, hAPP(c_Fun_Ocomp(_1541027, _1541021, _1541019, _1541029), _1541031), hAPP(c_Fun_Ocomp(_1541033, _1541025, _1541023, _1541035), _1541037)) = hAPP(c_Fun_Ocomp(tc_prod(_1541027, _1541033), tc_prod(_1541021, _1541025), tc_prod(_1541019, _1541023), c_Product__Type_Omap__pair(_1541027, _1541021, _1541033, _1541025, _1541029, _1541035)), c_Product__Type_Omap__pair(_1541019, _1541027, _1541023, _1541033, _1541031, _1541037)))], (39158 ^ _784416) ^ [_1541114, _1541116, _1541118, _1541120, _1541122, _1541124, _1541126, _1541128, _1541130, _1541132] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1541114, _1541116), tc_prod(_1541118, _1541120), tc_prod(_1541122, _1541124), c_Product__Type_Omap__pair(_1541114, _1541118, _1541116, _1541120, _1541126, _1541128)), c_Product__Type_Omap__pair(_1541122, _1541114, _1541124, _1541116, _1541130, _1541132)) = c_Product__Type_Omap__pair(_1541122, _1541118, _1541124, _1541120, hAPP(c_Fun_Ocomp(_1541114, _1541118, _1541122, _1541126), _1541130), hAPP(c_Fun_Ocomp(_1541116, _1541120, _1541124, _1541128), _1541132)))], (39160 ^ _784416) ^ [_1541209, _1541211] : [-(c_Product__Type_Omap__pair(_1541209, _1541209, _1541211, _1541211, c_COMBI(_1541209), c_COMBI(_1541211)) = c_Fun_Oid(tc_prod(_1541209, _1541211)))], (39162 ^ _784416) ^ [_1541250, _1541252, _1541254, _1541256] : [-(c_Product__Type_Oapfst(_1541250, _1541252, _1541254, _1541256) = c_Product__Type_Omap__pair(_1541250, _1541252, _1541254, _1541254, _1541256, c_Fun_Oid(_1541254)))], (39164 ^ _784416) ^ [_1541293, _1541295, _1541297, _1541299] : [-(c_Product__Type_Oapsnd(_1541293, _1541295, _1541297, _1541299) = c_Product__Type_Omap__pair(_1541297, _1541297, _1541293, _1541295, c_Fun_Oid(_1541297), _1541299))], (39166 ^ _784416) ^ [_1541336, _1541338] : [-(c_Product__Type_Omap__pair(_1541336, _1541336, _1541338, _1541338, c_Fun_Oid(_1541336), c_Fun_Oid(_1541338)) = c_Fun_Oid(tc_prod(_1541336, _1541338)))], (39168 ^ _784416) ^ [_1541377, _1541379, _1541381, _1541383, _1541385, _1541387] : [-(c_Product__Type_Omap__pair(_1541377, _1541379, _1541381, _1541383, _1541385, _1541387) = hAPP(c_Product__Type_Oprod_Oprod__case(_1541377, _1541381, tc_prod(_1541379, _1541383)), hAPP(hAPP(c_COMBC(_1541377, tc_fun(_1541381, _1541383), tc_fun(_1541381, tc_prod(_1541379, _1541383))), hAPP(hAPP(c_COMBB(tc_fun(_1541383, tc_prod(_1541379, _1541383)), tc_fun(tc_fun(_1541381, _1541383), tc_fun(_1541381, tc_prod(_1541379, _1541383))), _1541377), c_COMBB(_1541383, tc_prod(_1541379, _1541383), _1541381)), hAPP(hAPP(c_COMBB(_1541379, tc_fun(_1541383, tc_prod(_1541379, _1541383)), _1541377), c_Product__Type_OPair(_1541379, _1541383)), _1541385))), _1541387)))], (39170 ^ _784416) ^ [_1541500, _1541502, _1541504, _1541506, _1541508, _1541510, _1541512, _1541514, _1541516, _1541518] : [hAPP(c_Set_Oimage(_1541500, _1541502, _1541504), _1541506) = _1541508, hAPP(c_Set_Oimage(_1541510, _1541512, _1541514), _1541516) = _1541518, -(hAPP(c_Set_Oimage(tc_prod(_1541500, _1541510), tc_prod(_1541502, _1541512), c_Product__Type_Omap__pair(_1541500, _1541502, _1541510, _1541512, _1541504, _1541514)), hAPP(hAPP(c_Product__Type_OSigma(_1541500, _1541510), _1541506), hAPP(c_COMBK(tc_fun(_1541510, tc_HOL_Obool), _1541500), _1541516))) = hAPP(hAPP(c_Product__Type_OSigma(_1541502, _1541512), _1541508), hAPP(c_COMBK(tc_fun(_1541512, tc_HOL_Obool), _1541502), _1541518)))], (39180 ^ _784416) ^ [_1541801, _1541803, _1541805, _1541807] : [c_Wellfounded_Owf(_1541801, _1541803), c_Fun_Oinj__on(_1541801, _1541805, _1541807, c_Orderings_Otop__class_Otop(tc_fun(_1541801, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1541805, hAPP(c_Set_Oimage(tc_prod(_1541801, _1541801), tc_prod(_1541805, _1541805), c_Product__Type_Omap__pair(_1541801, _1541805, _1541801, _1541805, _1541807, _1541807)), _1541803)))], (39190 ^ _784416) ^ [_1541992, _1541994, _1541996, _1541998, _1542000, _1542002, _1542004, _1542006] : [c_Fun_Oinj__on(_1541992, _1541994, _1541996, _1541998), c_Fun_Oinj__on(_1542000, _1542002, _1542004, _1542006), -(c_Fun_Oinj__on(tc_prod(_1541992, _1542000), tc_prod(_1541994, _1542002), c_Product__Type_Omap__pair(_1541992, _1541994, _1542000, _1542002, _1541996, _1542004), hAPP(hAPP(c_Product__Type_OSigma(_1541992, _1542000), _1541998), hAPP(c_COMBK(tc_fun(_1542000, tc_HOL_Obool), _1541992), _1542006))))], (39200 ^ _784416) ^ [_1542219, _1542221, _1542223, _1542225, _1542227, _1542229, _1542231, _1542233] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542219, _1542221)), _1542223), hAPP(c_Set_Oimage(tc_prod(_1542225, _1542227), tc_prod(_1542219, _1542221), c_Product__Type_Omap__pair(_1542225, _1542219, _1542227, _1542221, _1542229, _1542231)), _1542233))), 39205 ^ _784416 : [(39206 ^ _784416) ^ [] : [-(_1542223 = hAPP(hAPP(c_Product__Type_OPair(_1542219, _1542221), hAPP(_1542229, 39203 ^ [_1542219, _1542221, _1542223, _1542225, _1542227, _1542229, _1542231, _1542233])), hAPP(_1542231, 39204 ^ [_1542219, _1542221, _1542223, _1542225, _1542227, _1542229, _1542231, _1542233])))], (39208 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542225, _1542227)), hAPP(hAPP(c_Product__Type_OPair(_1542225, _1542227), 39203 ^ [_1542219, _1542221, _1542223, _1542225, _1542227, _1542229, _1542231, _1542233]), 39204 ^ [_1542219, _1542221, _1542223, _1542225, _1542227, _1542229, _1542231, _1542233])), _1542233)))]]], (39210 ^ _784416) ^ [_1542570, _1542572, _1542574] : [c_Relation_Orefl__on(_1542570, _1542572, _1542574), 39213 ^ _784416 : [(39214 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542570, _1542570), tc_HOL_Obool)), _1542574), hAPP(hAPP(c_Product__Type_OSigma(_1542570, _1542570), _1542572), hAPP(c_COMBK(tc_fun(_1542570, tc_HOL_Obool), _1542570), _1542572)))))], (39216 ^ _784416) ^ [_1542752] : [hBOOL(hAPP(hAPP(c_member(_1542570), _1542752), _1542572)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542570, _1542570)), hAPP(hAPP(c_Product__Type_OPair(_1542570, _1542570), _1542752), _1542752)), _1542574)))]]], (39222 ^ _784416) ^ [_1542887, _1542889, _1542891] : [-(c_Relation_Orefl__on(_1542887, _1542889, _1542891)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542887, _1542887), tc_HOL_Obool)), _1542891), hAPP(hAPP(c_Product__Type_OSigma(_1542887, _1542887), _1542889), hAPP(c_COMBK(tc_fun(_1542887, tc_HOL_Obool), _1542887), _1542889)))), 39228 ^ _784416 : [(39229 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1542887), 39227 ^ [_1542887, _1542889, _1542891]), _1542889)))], (39231 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542887, _1542887)), hAPP(hAPP(c_Product__Type_OPair(_1542887, _1542887), 39227 ^ [_1542887, _1542889, _1542891]), 39227 ^ [_1542887, _1542889, _1542891])), _1542891))]]], (39235 ^ _784416) ^ [_1543236, _1543238, _1543240] : [39237 ^ _784416 : [(39238 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39236 ^ [_1543236, _1543238, _1543240]), _1543236)))], (39240 ^ _784416) ^ [] : [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(_1543238, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 39236 ^ [_1543236, _1543238, _1543240]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1543238, 39236 ^ [_1543236, _1543238, _1543240])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1543238, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1543240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1543240), hAPP(_1543238, _1543236))), 39250 ^ _784416 : [(39251 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 39249 ^ [_1543236, _1543238, _1543240]), _1543236)))], (39253 ^ _784416) ^ [] : [-(hAPP(_1543238, 39249 ^ [_1543236, _1543238, _1543240]) = _1543240)]]], (39255 ^ _784416) ^ [_1543686, _1543688] : [-(c_Relation_Orefl__on(_1543686, _1543688, c_Relation_OId__on(_1543686, _1543688)))], (39257 ^ _784416) ^ [_1543715] : [-(c_Relation_Orefl__on(_1543715, c_Orderings_Obot__class_Obot(tc_fun(_1543715, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1543715, _1543715), tc_HOL_Obool))))], (39259 ^ _784416) ^ [_1543752, _1543754, _1543756, _1543758, _1543760] : [c_Relation_Orefl__on(_1543752, _1543754, _1543756), c_Relation_Orefl__on(_1543752, _1543758, _1543760), -(c_Relation_Orefl__on(_1543752, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1543752, tc_HOL_Obool)), _1543754), _1543758), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1543752, _1543752), tc_HOL_Obool)), _1543756), _1543760)))], (39269 ^ _784416) ^ [_1543949, _1543951, _1543953, _1543955, _1543957] : [c_Relation_Orefl__on(_1543949, _1543951, _1543953), c_Relation_Orefl__on(_1543949, _1543955, _1543957), -(c_Relation_Orefl__on(_1543949, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1543949, tc_HOL_Obool)), _1543951), _1543955), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1543949, _1543949), tc_HOL_Obool)), _1543953), _1543957)))], (39279 ^ _784416) ^ [_1544146, _1544148, _1544150, _1544152] : [c_Relation_Orefl__on(_1544146, _1544148, _1544150), hBOOL(hAPP(hAPP(c_member(_1544146), _1544152), _1544148)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1544146, _1544146)), hAPP(hAPP(c_Product__Type_OPair(_1544146, _1544146), _1544152), _1544152)), _1544150)))], (39289 ^ _784416) ^ [_1544337, _1544339, _1544341, _1544343, _1544345] : [c_Relation_Orefl__on(_1544337, _1544339, _1544341), hBOOL(hAPP(hAPP(c_member(tc_prod(_1544337, _1544337)), hAPP(hAPP(c_Product__Type_OPair(_1544337, _1544337), _1544343), _1544345)), _1544341)), -(hBOOL(hAPP(hAPP(c_member(_1544337), _1544343), _1544339)))], (39299 ^ _784416) ^ [_1544532, _1544534, _1544536, _1544538, _1544540] : [c_Relation_Orefl__on(_1544532, _1544534, _1544536), hBOOL(hAPP(hAPP(c_member(tc_prod(_1544532, _1544532)), hAPP(hAPP(c_Product__Type_OPair(_1544532, _1544532), _1544538), _1544540)), _1544536)), -(hBOOL(hAPP(hAPP(c_member(_1544532), _1544540), _1544534)))], (39309 ^ _784416) ^ [_1544742, _1544744] : [c_Predicate_Oreflp(_1544742, _1544744), -(c_Relation_Orefl__on(_1544742, c_Orderings_Otop__class_Otop(tc_fun(_1544742, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1544742, _1544742)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544742, _1544742, tc_HOL_Obool), _1544744))))], (39315 ^ _784416) ^ [_1544857, _1544859] : [c_Relation_Orefl__on(_1544857, c_Orderings_Otop__class_Otop(tc_fun(_1544857, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1544857, _1544857)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544857, _1544857, tc_HOL_Obool), _1544859))), -(c_Predicate_Oreflp(_1544857, _1544859))], (39321 ^ _784416) ^ [_1544978, _1544980, _1544982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1544978, _1544978), tc_HOL_Obool)), _1544980), hAPP(hAPP(c_Product__Type_OSigma(_1544978, _1544978), _1544982), hAPP(c_COMBK(tc_fun(_1544978, tc_HOL_Obool), _1544978), _1544982)))), 39327 ^ _784416 : [(39328 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1544978), 39326 ^ [_1544978, _1544980, _1544982]), _1544982)))], (39330 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544978, _1544978)), hAPP(hAPP(c_Product__Type_OPair(_1544978, _1544978), 39326 ^ [_1544978, _1544980, _1544982]), 39326 ^ [_1544978, _1544980, _1544982])), _1544980))]], -(c_Relation_Orefl__on(_1544978, _1544982, _1544980))], (39334 ^ _784416) ^ [_1545325, _1545327, _1545329] : [39336 ^ _784416 : [(39337 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39335 ^ [_1545325, _1545327, _1545329]), _1545325)))], (39339 ^ _784416) ^ [] : [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(_1545327, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 39335 ^ [_1545325, _1545327, _1545329]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1545327, 39335 ^ [_1545325, _1545327, _1545329])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1545327, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1545329)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1545329), hAPP(_1545327, _1545325))), 39349 ^ _784416 : [(39350 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 39348 ^ [_1545325, _1545327, _1545329]), _1545325)))], (39352 ^ _784416) ^ [] : [-(hAPP(_1545327, 39348 ^ [_1545325, _1545327, _1545329]) = _1545329)]]], (39354 ^ _784416) ^ [_1545775, _1545777, _1545779] : [c_Predicate_Oreflp(_1545775, _1545777), -(hBOOL(hAPP(hAPP(_1545777, _1545779), _1545779)))], (39360 ^ _784416) ^ [_1545879, _1545881] : [c_Wellfounded_OwfP(_1545879, _1545881), -(c_Wellfounded_Owf(_1545879, hAPP(c_Set_OCollect(tc_prod(_1545879, _1545879)), hAPP(c_Product__Type_Oprod_Oprod__case(_1545879, _1545879, tc_HOL_Obool), _1545881))))], (39366 ^ _784416) ^ [_1545982, _1545984] : [c_Wellfounded_Owf(_1545982, hAPP(c_Set_OCollect(tc_prod(_1545982, _1545982)), hAPP(c_Product__Type_Oprod_Oprod__case(_1545982, _1545982, tc_HOL_Obool), _1545984))), -(c_Wellfounded_OwfP(_1545982, _1545984))], (39372 ^ _784416) ^ [_1546091, _1546093, _1546095] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1546091), _1546093)), 39378 ^ _784416 : [(39379 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1546091), 39377 ^ [_1546091, _1546093, _1546095]), _1546093)))], (39381 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1546095, 39377 ^ [_1546091, _1546093, _1546095])))]], -(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(_1546091, tc_Nat_Onat), _1546095), _1546093))))], (39385 ^ _784416) ^ [_1546352, _1546354] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1546352), c_Int_OInteg)), hBOOL(hAPP(_1546354, hAPP(c_Int_ORep__Integ, 39390 ^ [_1546352, _1546354]))), -(hBOOL(hAPP(_1546354, _1546352)))], (39396 ^ _784416) ^ [_1546534] : [-(c_Wellfounded_OwfP(_1546534, hAPP(c_COMBK(tc_fun(_1546534, tc_HOL_Obool), _1546534), hAPP(c_COMBK(tc_HOL_Obool, _1546534), c_fFalse))))], (39398 ^ _784416) ^ [_1546587, _1546589] : [c_Wellfounded_OwfP(_1546587, _1546589), 39401 ^ _784416 : [(39402 ^ _784416) ^ [_1546651] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1546587, _1546589), _1546651)))]]], (39404 ^ _784416) ^ [_1546679, _1546681] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1546679, _1546681), 39405 ^ [_1546679, _1546681])), -(c_Wellfounded_OwfP(_1546679, _1546681))], (39411 ^ _784416) ^ [_1546797, _1546799, _1546801] : [c_Wellfounded_OwfP(_1546797, _1546799), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1546797, _1546799), _1546801)))], (39417 ^ _784416) ^ [_1546886, _1546888, _1546890] : [c_Wellfounded_OwfP(_1546886, _1546888), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1546886, tc_fun(_1546886, tc_HOL_Obool))), _1546890), _1546888)), -(c_Wellfounded_OwfP(_1546886, _1546890))], (39427 ^ _784416) ^ [_1547045, _1547047] : [c_Wellfounded_Owf(_1547045, _1547047), -(c_Wellfounded_OwfP(_1547045, c_FunDef_Oin__rel(_1547045, _1547045, _1547047)))], (39433 ^ _784416) ^ [_1547145, _1547147] : [c_Wellfounded_OwfP(_1547145, hAPP(hAPP(c_COMBC(_1547145, tc_fun(tc_prod(_1547145, _1547145), tc_HOL_Obool), tc_fun(_1547145, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547145, tc_fun(tc_fun(tc_prod(_1547145, _1547145), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1547145, _1547145), tc_HOL_Obool), tc_fun(_1547145, tc_HOL_Obool)), _1547145), c_COMBC(_1547145, tc_fun(tc_prod(_1547145, _1547145), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547145, tc_prod(_1547145, _1547145)), tc_fun(_1547145, tc_fun(tc_fun(tc_prod(_1547145, _1547145), tc_HOL_Obool), tc_HOL_Obool)), _1547145), hAPP(c_COMBB(tc_prod(_1547145, _1547145), tc_fun(tc_fun(tc_prod(_1547145, _1547145), tc_HOL_Obool), tc_HOL_Obool), _1547145), c_member(tc_prod(_1547145, _1547145)))), c_Product__Type_OPair(_1547145, _1547145)))), _1547147)), -(c_Wellfounded_Owf(_1547145, _1547147))], (39439 ^ _784416) ^ [_1547454, _1547456] : [c_Wellfounded_Owf(_1547454, _1547456), -(c_Wellfounded_OwfP(_1547454, hAPP(hAPP(c_COMBC(_1547454, tc_fun(tc_prod(_1547454, _1547454), tc_HOL_Obool), tc_fun(_1547454, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547454, tc_fun(tc_fun(tc_prod(_1547454, _1547454), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1547454, _1547454), tc_HOL_Obool), tc_fun(_1547454, tc_HOL_Obool)), _1547454), c_COMBC(_1547454, tc_fun(tc_prod(_1547454, _1547454), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547454, tc_prod(_1547454, _1547454)), tc_fun(_1547454, tc_fun(tc_fun(tc_prod(_1547454, _1547454), tc_HOL_Obool), tc_HOL_Obool)), _1547454), hAPP(c_COMBB(tc_prod(_1547454, _1547454), tc_fun(tc_fun(tc_prod(_1547454, _1547454), tc_HOL_Obool), tc_HOL_Obool), _1547454), c_member(tc_prod(_1547454, _1547454)))), c_Product__Type_OPair(_1547454, _1547454)))), _1547456)))], (39445 ^ _784416) ^ [_1547769, _1547771] : [c_Wellfounded_OwfP(_1547769, _1547771), -(c_Wellfounded_Oacyclic(_1547769, hAPP(c_Set_OCollect(tc_prod(_1547769, _1547769)), hAPP(c_Product__Type_Oprod_Oprod__case(_1547769, _1547769, tc_HOL_Obool), _1547771))))], (39451 ^ _784416) ^ [_1547876] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1547876), c_Int_OInteg)), -(_1547876 = hAPP(c_Int_ORep__Integ, 39454 ^ [_1547876]))], (39458 ^ _784416) ^ [_1547980, _1547982, _1547984, _1547986] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1547980), _1547982))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1547984), hAPP(c_Set_Oimage(_1547980, _1547984, _1547986), _1547982))), 39466 ^ _784416 : [(39467 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1547980), 39465 ^ [_1547980, _1547982, _1547984, _1547986]), _1547982)))], (39469 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1547980), hAPP(c_Set_OCollect(_1547980), hAPP(hAPP(c_COMBS(_1547980, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547980), c_fconj), hAPP(hAPP(c_COMBC(_1547980, tc_fun(_1547980, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547980)), _1547982))), hAPP(hAPP(c_COMBC(_1547980, _1547984, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1547984, tc_fun(_1547984, tc_HOL_Obool), _1547980), c_fequal), _1547986)), hAPP(_1547986, 39465 ^ [_1547980, _1547982, _1547984, _1547986]))))))]]], (39471 ^ _784416) ^ [_1548445, _1548447, _1548449] : [c_Wellfounded_Oacyclic(_1548445, _1548447), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1548445, _1548445), tc_HOL_Obool)), _1548449), _1548447)), -(c_Wellfounded_Oacyclic(_1548445, _1548449))], (39481 ^ _784416) ^ [_1548604, _1548606] : [c_Wellfounded_Owf(_1548604, _1548606), -(c_Wellfounded_Oacyclic(_1548604, _1548606))], (39487 ^ _784416) ^ [_1548681, _1548683] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1548681, _1548681)), _1548683)), 39490 ^ _784416 : [(39491 ^ _784416) ^ [] : [c_Wellfounded_Owf(_1548681, _1548683), -(c_Wellfounded_Oacyclic(_1548681, _1548683))], (39497 ^ _784416) ^ [] : [c_Wellfounded_Oacyclic(_1548681, _1548683), -(c_Wellfounded_Owf(_1548681, _1548683))]]], (39503 ^ _784416) ^ [_1548902, _1548904] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1548902, _1548902)), _1548904)), c_Wellfounded_Oacyclic(_1548902, _1548904), -(c_Wellfounded_Owf(_1548902, _1548904))], (39513 ^ _784416) ^ [_1549060, _1549062] : [c_Nitpick_Owf_H(_1549060, _1549062), 39516 ^ _784416 : [(39517 ^ _784416) ^ [] : [-(c_Wellfounded_Oacyclic(_1549060, _1549062))], (39519 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1549060, _1549060)), _1549062))), -(c_Nitpick_Ounknown(tc_HOL_Obool))]]], (39525 ^ _784416) ^ [_1549180, _1549182] : [-(c_Nitpick_Owf_H(_1549180, _1549182)), c_Wellfounded_Oacyclic(_1549180, _1549182), 39530 ^ _784416 : [(39531 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1549180, _1549180)), _1549182))], (39533 ^ _784416) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)]]], (39553 ^ _784416) ^ [_1549994, _1549996, _1549998] : [-(c_Relation_Orefl__on(_1549994, _1549996, _1549998)), 39557 ^ _784416 : [(39558 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549994, _1549994)), 39556 ^ [_1549994, _1549996, _1549998]), _1549998)))], (39560 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1549994, _1549994, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1549994, tc_fun(_1549994, tc_HOL_Obool), tc_fun(_1549994, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1549994, tc_HOL_Obool), tc_fun(_1549994, tc_HOL_Obool)), _1549994), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1549994)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549994), c_fconj), hAPP(hAPP(c_COMBC(_1549994, tc_fun(_1549994, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549994)), _1549996)))), hAPP(hAPP(c_COMBC(_1549994, tc_fun(_1549994, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549994)), _1549996))), 39556 ^ [_1549994, _1549996, _1549998]))]], 39562 ^ _784416 : [(39563 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1549994), 39561 ^ [_1549994, _1549996, _1549998]), _1549996)))], (39565 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1549994, _1549994)), hAPP(hAPP(c_Product__Type_OPair(_1549994, _1549994), 39561 ^ [_1549994, _1549996, _1549998]), 39561 ^ [_1549994, _1549996, _1549998])), _1549998))]]], (39537 ^ _784416) ^ [_1549375, _1549377, _1549379] : [c_Relation_Orefl__on(_1549375, _1549377, _1549379), 39540 ^ _784416 : [(39541 ^ _784416) ^ [_1549586] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1549375, _1549375)), _1549586), _1549379)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1549375, _1549375, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1549375, tc_fun(_1549375, tc_HOL_Obool), tc_fun(_1549375, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1549375, tc_HOL_Obool), tc_fun(_1549375, tc_HOL_Obool)), _1549375), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1549375)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549375), c_fconj), hAPP(hAPP(c_COMBC(_1549375, tc_fun(_1549375, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549375)), _1549377)))), hAPP(hAPP(c_COMBC(_1549375, tc_fun(_1549375, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549375)), _1549377))), _1549586)))], (39547 ^ _784416) ^ [_1549859] : [hBOOL(hAPP(hAPP(c_member(_1549375), _1549859), _1549377)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549375, _1549375)), hAPP(hAPP(c_Product__Type_OPair(_1549375, _1549375), _1549859), _1549859)), _1549379)))]]], (39569 ^ _784416) ^ [_1550635, _1550637] : [39571 ^ _784416 : [(39572 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39570 ^ [_1550635, _1550637]), c_Int_OInteg)))], (39574 ^ _784416) ^ [] : [hBOOL(hAPP(_1550635, hAPP(c_Int_OAbs__Integ, 39570 ^ [_1550635, _1550637])))]], -(hBOOL(hAPP(_1550635, _1550637)))], (39578 ^ _784416) ^ [_1550804, _1550806, _1550808] : [hBOOL(hAPP(hAPP(c_member(_1550806), _1550804), c_Orderings_Obot__class_Obot(tc_fun(_1550806, tc_HOL_Obool)))), -(hBOOL(hAPP(_1550808, _1550804)))], (39594 ^ _784416) ^ [_1551112, _1551114, _1551116] : [39596 ^ _784416 : [(39597 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1551112), 39595 ^ [_1551112, _1551114, _1551116]), _1551116)))], (39599 ^ _784416) ^ [] : [hBOOL(hAPP(_1551114, 39595 ^ [_1551112, _1551114, _1551116]))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1551112, _1551114), _1551116)))], (39584 ^ _784416) ^ [_1550929, _1550931, _1550933] : [hBOOL(hAPP(c_Predicate_OPowp(_1550929, _1550931), _1550933)), 39587 ^ _784416 : [(39588 ^ _784416) ^ [_1551013] : [hBOOL(hAPP(hAPP(c_member(_1550929), _1551013), _1550933)), -(hBOOL(hAPP(_1550931, _1551013)))]]], (39613 ^ _784416) ^ [_1551689, _1551691, _1551693, _1551695] : [39615 ^ _784416 : [(39616 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1551689, _1551689)), 39614 ^ [_1551689, _1551691, _1551693, _1551695]), _1551693)))], (39618 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1551689, _1551689, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1551689, tc_fun(_1551689, _1551691), tc_fun(_1551689, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1551691, tc_HOL_Obool), tc_fun(tc_fun(_1551689, _1551691), tc_fun(_1551689, tc_HOL_Obool)), _1551689), c_COMBB(_1551691, tc_HOL_Obool, _1551689)), hAPP(hAPP(c_COMBB(_1551691, tc_fun(_1551691, tc_HOL_Obool), _1551689), c_fequal), _1551695))), _1551695)), 39614 ^ [_1551689, _1551691, _1551693, _1551695]))]], -(c_Equiv__Relations_Ocongruent(_1551689, _1551691, _1551693, _1551695))], (39603 ^ _784416) ^ [_1551313, _1551315, _1551317, _1551319] : [c_Equiv__Relations_Ocongruent(_1551313, _1551315, _1551317, _1551319), 39606 ^ _784416 : [(39607 ^ _784416) ^ [_1551458] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1551313, _1551313)), _1551458), _1551317)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1551313, _1551313, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1551313, tc_fun(_1551313, _1551315), tc_fun(_1551313, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1551315, tc_HOL_Obool), tc_fun(tc_fun(_1551313, _1551315), tc_fun(_1551313, tc_HOL_Obool)), _1551313), c_COMBB(_1551315, tc_HOL_Obool, _1551313)), hAPP(hAPP(c_COMBB(_1551315, tc_fun(_1551315, tc_HOL_Obool), _1551313), c_fequal), _1551319))), _1551319)), _1551458)))]]], (39623 ^ _784416) ^ [_1552062] : [-(_1552062 = hAPP(c_Int_OAbs__Integ, 39621 ^ [_1552062]))], (39625 ^ _784416) ^ [_1552090] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39621 ^ [_1552090]), c_Int_OInteg)))], (39627 ^ _784416) ^ [_1552125, _1552127, _1552129, _1552131] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1552125), _1552127)), 39633 ^ _784416 : [(39634 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1552125), 39632 ^ [_1552125, _1552127, _1552129, _1552131]), _1552127)))], (39636 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1552129), hAPP(_1552131, 39632 ^ [_1552125, _1552127, _1552129, _1552131])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1552129), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1552125, tc_fun(_1552129, tc_HOL_Obool)), _1552127), _1552131))))], (39640 ^ _784416) ^ [_1552412, _1552414] : [39642 ^ _784416 : [(39643 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 39641 ^ [_1552412, _1552414]), _1552412)))], (39645 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1552414), 39641 ^ [_1552412, _1552414]))]], -(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)), _1552414), _1552412))], (39649 ^ _784416) ^ [_1552587, _1552589, _1552591] : [c_Wellfounded_OwfP(_1552587, hAPP(_1552589, 39650 ^ [_1552587, _1552589, _1552591])), 39657 ^ _784416 : [(39658 ^ _784416) ^ [] : [hAPP(_1552589, 39655 ^ [_1552587, _1552589, _1552591]) = hAPP(_1552589, 39656 ^ [_1552587, _1552589, _1552591])], (39660 ^ _784416) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1552587, tc_HOL_Obool)), c_Predicate_ODomainP(_1552587, _1552587, hAPP(_1552589, 39655 ^ [_1552587, _1552589, _1552591]))), c_Predicate_ORangeP(_1552587, _1552587, hAPP(_1552589, 39656 ^ [_1552587, _1552589, _1552591]))) = c_Orderings_Obot__class_Obot(tc_fun(_1552587, tc_HOL_Obool))]], -(c_Wellfounded_OwfP(_1552587, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1552591, tc_fun(_1552587, tc_fun(_1552587, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1552591, tc_HOL_Obool))), _1552589)))], (39664 ^ _784416) ^ [_1553027, _1553029, _1553031] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1553027), c_Map_Odom(_1553027, _1553029, _1553031))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1553027), c_Orderings_Otop__class_Otop(tc_fun(_1553027, tc_HOL_Obool))))), -(hAPP(_1553031, 39671 ^ [_1553027, _1553029, _1553031]) = c_Option_Ooption_ONone(_1553029))], (39675 ^ _784416) ^ [_1553179, _1553181, _1553183, _1553185, _1553187, _1553189] : [39678 ^ _784416 : [(39679 ^ _784416) ^ [] : [-(_1553179 = hAPP(hAPP(c_Product__Type_OPair(_1553181, _1553183), 39676 ^ [_1553179, _1553181, _1553183, _1553185, _1553187, _1553189]), 39677 ^ [_1553179, _1553181, _1553183, _1553185, _1553187, _1553189]))], (39681 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1553185), _1553187), hAPP(hAPP(_1553189, 39676 ^ [_1553179, _1553181, _1553183, _1553185, _1553187, _1553189]), 39677 ^ [_1553179, _1553181, _1553183, _1553185, _1553187, _1553189])))]], -(hBOOL(hAPP(hAPP(c_member(_1553185), _1553187), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1553181, _1553183, tc_fun(_1553185, tc_HOL_Obool)), _1553189), _1553179))))], (39685 ^ _784416) ^ [_1553504, _1553506, _1553508, _1553510, _1553512, _1553514] : [hBOOL(hAPP(hAPP(c_member(_1553504), _1553506), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1553508, _1553510, tc_fun(_1553504, tc_HOL_Obool)), _1553512), _1553514))), 39690 ^ _784416 : [(39691 ^ _784416) ^ [] : [-(_1553514 = hAPP(hAPP(c_Product__Type_OPair(_1553508, _1553510), 39688 ^ [_1553504, _1553506, _1553508, _1553510, _1553512, _1553514]), 39689 ^ [_1553504, _1553506, _1553508, _1553510, _1553512, _1553514]))], (39693 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553504), _1553506), hAPP(hAPP(_1553512, 39688 ^ [_1553504, _1553506, _1553508, _1553510, _1553512, _1553514]), 39689 ^ [_1553504, _1553506, _1553508, _1553510, _1553512, _1553514]))))]]], (39695 ^ _784416) ^ [_1553773, _1553775, _1553777, _1553779] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1553773, tc_Nat_Onat), _1553775), _1553777) = hAPP(c_Nat_OSuc, _1553779), 39699 ^ _784416 : [(39700 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553773), 39698 ^ [_1553773, _1553775, _1553777, _1553779]), _1553777)))], (39702 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1553775, 39698 ^ [_1553773, _1553775, _1553777, _1553779]))))]]], (39704 ^ _784416) ^ [_1553955, _1553957, _1553959] : [-(c_Hilbert__Choice_OEps(tc_prod(_1553955, _1553957), hAPP(c_Product__Type_Oprod_Oprod__case(_1553955, _1553957, tc_HOL_Obool), _1553959)) = c_Hilbert__Choice_OEps(tc_prod(_1553955, _1553957), hAPP(hAPP(c_COMBS(tc_prod(_1553955, _1553957), _1553957, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1553955, tc_fun(_1553957, tc_HOL_Obool), tc_prod(_1553955, _1553957)), _1553959), c_Product__Type_Ofst(_1553955, _1553957))), c_Product__Type_Osnd(_1553955, _1553957))))], (39706 ^ _784416) ^ [_1554036, _1554038] : [-(c_Hilbert__Choice_OEps(_1554036, hAPP(c_fequal, _1554038)) = _1554038)], (39708 ^ _784416) ^ [_1554067, _1554069] : [-(c_Hilbert__Choice_OEps(_1554067, hAPP(hAPP(c_COMBC(_1554067, _1554067, tc_HOL_Obool), c_fequal), _1554069)) = _1554069)], (39710 ^ _784416) ^ [_1554120, _1554122] : [hBOOL(hAPP(_1554120, c_Hilbert__Choice_OEps(_1554122, _1554120))), -(hBOOL(hAPP(_1554120, 39713 ^ [_1554120, _1554122])))], (39717 ^ _784416) ^ [_1554219, _1554221] : [39718 ^ _784416 : [(39719 ^ _784416) ^ [_1554265] : [hBOOL(hAPP(_1554219, _1554265))]], -(hBOOL(hAPP(_1554219, c_Hilbert__Choice_OEps(_1554221, _1554219))))], (39723 ^ _784416) ^ [_1554325, _1554327] : [39724 ^ _784416 : [(39725 ^ _784416) ^ [_1554371] : [hBOOL(hAPP(_1554325, _1554371))]], -(hBOOL(hAPP(_1554325, c_Hilbert__Choice_OEps(_1554327, _1554325))))], (39729 ^ _784416) ^ [_1554429, _1554431, _1554433] : [hBOOL(hAPP(_1554429, _1554431)), -(hBOOL(hAPP(_1554429, c_Hilbert__Choice_OEps(_1554433, _1554429))))], (39735 ^ _784416) ^ [_1554522, _1554524] : [39736 ^ _784416 : [(39737 ^ _784416) ^ [_1554568] : [hBOOL(hAPP(_1554522, _1554568))]], -(hBOOL(hAPP(_1554522, c_Hilbert__Choice_OEps(_1554524, _1554522))))], (39741 ^ _784416) ^ [_1554626, _1554628, _1554630] : [39742 ^ _784416 : [(39743 ^ _784416) ^ [_1554680] : [hBOOL(hAPP(_1554626, _1554680))]], _1554628 = c_Hilbert__Choice_OEps(_1554630, _1554626), -(hBOOL(hAPP(_1554626, _1554628)))], (39751 ^ _784416) ^ [_1554786, _1554788, _1554790] : [-(c_Hilbert__Choice_OEps(tc_prod(_1554786, _1554788), _1554790) = c_Hilbert__Choice_OEps(tc_prod(_1554786, _1554788), hAPP(c_Product__Type_Oprod_Oprod__case(_1554786, _1554788, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1554788, tc_prod(_1554786, _1554788)), tc_fun(_1554788, tc_HOL_Obool), _1554786), hAPP(c_COMBB(tc_prod(_1554786, _1554788), tc_HOL_Obool, _1554788), _1554790)), c_Product__Type_OPair(_1554786, _1554788)))))], (39753 ^ _784416) ^ [_1554864, _1554866, _1554868, _1554870] : [-(c_Hilbert__Choice_OEps(tc_prod(_1554864, _1554866), hAPP(c_Product__Type_Oprod_Oprod__case(_1554864, _1554866, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1554864, tc_fun(_1554866, tc_HOL_Obool), tc_fun(_1554866, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1554866, tc_HOL_Obool), tc_fun(_1554866, tc_HOL_Obool)), _1554864), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1554866)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1554864), c_fconj), hAPP(c_fequal, _1554868)))), hAPP(c_fequal, _1554870)))) = hAPP(hAPP(c_Product__Type_OPair(_1554864, _1554866), _1554868), _1554870))], (39755 ^ _784416) ^ [_1554970, _1554972, _1554974, _1554976, _1554978] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1554970, _1554972, _1554974, _1554976), _1554978) = c_Hilbert__Choice_OEps(_1554970, hAPP(hAPP(c_COMBS(_1554970, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1554970), c_fconj), hAPP(hAPP(c_COMBC(_1554970, tc_fun(_1554970, tc_HOL_Obool), tc_HOL_Obool), c_member(_1554970)), _1554974))), hAPP(hAPP(c_COMBC(_1554970, _1554972, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1554972, tc_fun(_1554972, tc_HOL_Obool), _1554970), c_fequal), _1554976)), _1554978))))], (39757 ^ _784416) ^ [_1555070, _1555072, _1555074, _1555076] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1555070, _1555072, c_Orderings_Otop__class_Otop(tc_fun(_1555070, tc_HOL_Obool)), _1555074), _1555076) = c_Hilbert__Choice_OEps(_1555070, hAPP(hAPP(c_COMBC(_1555070, _1555072, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1555072, tc_fun(_1555072, tc_HOL_Obool), _1555070), c_fequal), _1555074)), _1555076)))], (39759 ^ _784416) ^ [_1555138, _1555140, _1555142] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1555138, _1555140) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1555142, _1555140), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1555142), _1555138)), -(_1555138 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1555142), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1555140), 39766 ^ [_1555138, _1555140, _1555142])))], (39770 ^ _784416) ^ [_1555335, _1555337] : [39772 ^ _784416 : [(39773 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1555335, tc_HOL_Obool)), 39771 ^ [_1555335, _1555337]), hAPP(c_Relation_OImage(_1555335, _1555335, _1555337), 39771 ^ [_1555335, _1555337]))))], (39775 ^ _784416) ^ [] : [39771 ^ [_1555335, _1555337] = c_Orderings_Obot__class_Obot(tc_fun(_1555335, tc_HOL_Obool))]], -(c_Wellfounded_Owf(_1555335, _1555337))], (39779 ^ _784416) ^ [_1555532, _1555534, _1555536, _1555538, _1555540, _1555542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1555532, tc_HOL_Obool)), _1555534), _1555536)), 39785 ^ _784416 : [(39786 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1555532), 39784 ^ [_1555532, _1555534, _1555536, _1555538, _1555540, _1555542]), _1555534)))], (39788 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1555538, tc_HOL_Obool)), hAPP(_1555540, 39784 ^ [_1555532, _1555534, _1555536, _1555538, _1555540, _1555542])), hAPP(_1555542, 39784 ^ [_1555532, _1555534, _1555536, _1555538, _1555540, _1555542])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555532, _1555538), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1555532, _1555538), _1555534), _1555540)), hAPP(hAPP(c_Product__Type_OSigma(_1555532, _1555538), _1555536), _1555542))))], (39792 ^ _784416) ^ [_1555923, _1555925, _1555927] : [39794 ^ _784416 : [(39795 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1555923, _1555923)), hAPP(hAPP(c_Product__Type_OPair(_1555923, _1555923), 39793 ^ [_1555923, _1555925, _1555927]), _1555925)), _1555927)))], (39797 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1555923), 39793 ^ [_1555923, _1555925, _1555927]), c_Wellfounded_Oacc(_1555923, _1555927)))]], -(hBOOL(hAPP(hAPP(c_member(_1555923), _1555925), c_Wellfounded_Oacc(_1555923, _1555927))))], (39801 ^ _784416) ^ [_1556160, _1556162, _1556164] : [-(hBOOL(hAPP(hAPP(c_member(_1556160), _1556162), c_Wellfounded_Oacc(_1556160, _1556164)))), 39805 ^ _784416 : [(39806 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1556160, _1556160)), hAPP(hAPP(c_Product__Type_OPair(_1556160, _1556160), 39804 ^ [_1556160, _1556162, _1556164]), _1556162)), _1556164)))], (39808 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1556160), 39804 ^ [_1556160, _1556162, _1556164]), c_Wellfounded_Oacc(_1556160, _1556164)))]]], (39810 ^ _784416) ^ [_1556387, _1556389, _1556391, _1556393] : [class_Groups_Ocomm__monoid__mult(_1556387), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556389), _1556391)), 39820 ^ _784416 : [(39821 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1556389), 39819 ^ [_1556387, _1556389, _1556391, _1556393]), _1556391)))], (39823 ^ _784416) ^ [] : [hAPP(_1556393, 39819 ^ [_1556387, _1556389, _1556391, _1556393]) = c_Groups_Oone__class_Oone(_1556387)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1556387, _1556389, c_Groups_Otimes__class_Otimes(_1556387)), _1556393), c_Groups_Oone__class_Oone(_1556387)), _1556391) = c_Groups_Oone__class_Oone(_1556387))], (39827 ^ _784416) ^ [_1556728, _1556730] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1556728), _1556730)), 39833 ^ _784416 : [(39834 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1556728), 39832 ^ [_1556728, _1556730]), _1556730)))], (39836 ^ _784416) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1556728), _1556730) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39840 ^ _784416) ^ [_1556949, _1556951, _1556953, _1556955] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1556949, tc_HOL_Obool), tc_fun(_1556949, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1556949, tc_HOL_Obool), tc_fun(_1556949, tc_HOL_Obool)), _1556951), _1556953)), c_Wellfounded_Omax__ext(_1556949, _1556955))), 39843 ^ _784416 : [(39844 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1556949), _1556951)))], (39846 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1556949), _1556953)))], (39848 ^ _784416) ^ [] : [_1556953 = c_Orderings_Obot__class_Obot(tc_fun(_1556949, tc_HOL_Obool))], (39850 ^ _784416) ^ [_1557243] : [hBOOL(hAPP(hAPP(c_member(_1556949), _1557243), _1556951)), 39854 ^ _784416 : [(39855 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1556949), 39853 ^ [_1556949, _1556951, _1556953, _1556955, _1557243]), _1556953)))], (39857 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1556949, _1556949)), hAPP(hAPP(c_Product__Type_OPair(_1556949, _1556949), _1557243), 39853 ^ [_1556949, _1556951, _1556953, _1556955, _1557243])), _1556955)))]]]]], (39859 ^ _784416) ^ [_1557455, _1557457, _1557459, _1557461] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1557455, tc_HOL_Obool), tc_fun(_1557455, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1557455, tc_HOL_Obool), tc_fun(_1557455, tc_HOL_Obool)), _1557457), _1557459)), c_Wellfounded_Omax__ext(_1557455, _1557461)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557455), _1557457)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557455), _1557459)), -(_1557459 = c_Orderings_Obot__class_Obot(tc_fun(_1557455, tc_HOL_Obool))), 39873 ^ _784416 : [(39874 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1557455), 39872 ^ [_1557455, _1557457, _1557459, _1557461]), _1557457)))], (39876 ^ _784416) ^ [_1557860] : [hBOOL(hAPP(hAPP(c_member(_1557455), _1557860), _1557459)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1557455, _1557455)), hAPP(hAPP(c_Product__Type_OPair(_1557455, _1557455), 39872 ^ [_1557455, _1557457, _1557459, _1557461]), _1557860)), _1557461))]]], (39884 ^ _784416) ^ [_1558088, _1558090, _1558092] : [39886 ^ _784416 : [(39887 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 39885 ^ [_1558088, _1558090, _1558092]), _1558088)))], (39889 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1558090, 39885 ^ [_1558088, _1558090, _1558092])))], (39891 ^ _784416) ^ [] : [hBOOL(hAPP(_1558090, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 39885 ^ [_1558088, _1558090, _1558092]), _1558088)))]], hBOOL(hAPP(_1558090, _1558092)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1558092), _1558088)), -(hBOOL(hAPP(_1558090, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (39903 ^ _784416) ^ [_1558450, _1558452, _1558454, _1558456, _1558458, _1558460] : [class_Groups_Oab__semigroup__mult(_1558450), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558452), _1558454)), 39913 ^ _784416 : [(39914 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558452), 39912 ^ [_1558450, _1558452, _1558454, _1558456, _1558458, _1558460]), _1558454)))], (39916 ^ _784416) ^ [] : [hAPP(_1558456, 39912 ^ [_1558450, _1558452, _1558454, _1558456, _1558458, _1558460]) = hAPP(_1558458, 39912 ^ [_1558450, _1558452, _1558454, _1558456, _1558458, _1558460])]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1558450, _1558452, c_Groups_Otimes__class_Otimes(_1558450)), _1558456), _1558460), _1558454) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1558450, _1558452, c_Groups_Otimes__class_Otimes(_1558450)), _1558458), _1558460), _1558454))], (39920 ^ _784416) ^ [_1558855, _1558857, _1558859] : [class_Orderings_Olinorder(_1558855), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558855), _1558857)), 39930 ^ _784416 : [(39931 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558855), 39929 ^ [_1558855, _1558857, _1558859]), _1558857)))], (39933 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1558855), _1558859), 39929 ^ [_1558855, _1558857, _1558859]))]], hBOOL(hAPP(hAPP(c_member(_1558855), _1558859), _1558857)), -(c_Big__Operators_Olinorder__class_OMin(_1558855, _1558857) = _1558859)], (39941 ^ _784416) ^ [_1559227, _1559229, _1559231] : [class_Orderings_Olinorder(_1559227), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559227), _1559229)), 39951 ^ _784416 : [(39952 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559227), 39950 ^ [_1559227, _1559229, _1559231]), _1559229)))], (39954 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1559227), 39950 ^ [_1559227, _1559229, _1559231]), _1559231))]], hBOOL(hAPP(hAPP(c_member(_1559227), _1559231), _1559229)), -(c_Big__Operators_Olinorder__class_OMax(_1559227, _1559229) = _1559231)], (39962 ^ _784416) ^ [_1559599, _1559601, _1559603] : [c_Wellfounded_Owf(_1559599, _1559601), hBOOL(hAPP(hAPP(c_member(tc_prod(_1559599, _1559599)), hAPP(hAPP(c_Product__Type_OPair(_1559599, _1559599), hAPP(_1559603, hAPP(c_Nat_OSuc, 39965 ^ [_1559599, _1559601, _1559603]))), hAPP(_1559603, 39965 ^ [_1559599, _1559601, _1559603]))), _1559601))], (39969 ^ _784416) ^ [_1559800, _1559802, _1559804, _1559806, _1559808, _1559810, _1559812, _1559814] : [class_Groups_Ocomm__monoid__add(_1559800), c_Fun_Oinj__on(_1559802, _1559804, _1559806, _1559808), _1559810 = hAPP(c_Set_Oimage(_1559802, _1559804, _1559806), _1559808), 39983 ^ _784416 : [(39984 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559802), 39982 ^ [_1559800, _1559802, _1559804, _1559806, _1559808, _1559810, _1559812, _1559814]), _1559808)))], (39986 ^ _784416) ^ [] : [hAPP(_1559812, 39982 ^ [_1559800, _1559802, _1559804, _1559806, _1559808, _1559810, _1559812, _1559814]) = hAPP(_1559814, hAPP(_1559806, 39982 ^ [_1559800, _1559802, _1559804, _1559806, _1559808, _1559810, _1559812, _1559814]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1559804, _1559800), _1559814), _1559810) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1559802, _1559800), _1559812), _1559808))], (39990 ^ _784416) ^ [_1560292, _1560294, _1560296, _1560298, _1560300, _1560302, _1560304] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1560292, _1560294, _1560296, _1560298), _1560300), _1560302), _1560304) = hAPP(hAPP(_1560302, hAPP(c_Product__Type_Ofst(_1560294, _1560296), hAPP(_1560300, _1560304))), hAPP(c_Product__Type_Osnd(_1560294, _1560296), hAPP(_1560300, _1560304))))], (39992 ^ _784416) ^ [_1560365, _1560367, _1560369, _1560371, _1560373, _1560375, _1560377, _1560379, _1560381] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1560365, _1560367, _1560369, _1560371), hAPP(hAPP(c_Product__Type_Oscomp(_1560365, _1560373, _1560375, tc_prod(_1560367, _1560369)), _1560377), _1560379)), _1560381) = hAPP(hAPP(c_Product__Type_Oscomp(_1560365, _1560373, _1560375, _1560371), _1560377), hAPP(hAPP(c_COMBC(_1560373, tc_fun(_1560367, tc_fun(_1560369, _1560371)), tc_fun(_1560375, _1560371)), hAPP(hAPP(c_COMBB(tc_fun(_1560375, tc_prod(_1560367, _1560369)), tc_fun(tc_fun(_1560367, tc_fun(_1560369, _1560371)), tc_fun(_1560375, _1560371)), _1560373), c_Product__Type_Oscomp(_1560375, _1560367, _1560369, _1560371)), _1560379)), _1560381)))], (39994 ^ _784416) ^ [_1560492, _1560494, _1560496, _1560498] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1560492, _1560494, _1560496, tc_prod(_1560494, _1560496)), _1560498), c_Product__Type_OPair(_1560494, _1560496)) = _1560498)], (39996 ^ _784416) ^ [_1560538, _1560540, _1560542, _1560544, _1560546] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1560538, _1560540, _1560538, _1560542), hAPP(c_Product__Type_OPair(_1560540, _1560538), _1560544)), _1560546) = hAPP(_1560546, _1560544))], (39998 ^ _784416) ^ [_1560589, _1560591, _1560593, _1560595, _1560597, _1560599, _1560601] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1560589, _1560591, _1560593, _1560595), _1560597), _1560599), _1560601) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1560591, _1560593, _1560595), _1560599), hAPP(_1560597, _1560601)))], (40000 ^ _784416) ^ [_1560651, _1560653, _1560655, _1560657, _1560659, _1560661, _1560663] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1560651, _1560653, _1560655, _1560657), _1560659), _1560661), _1560663) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1560653, _1560655, _1560657), _1560661), hAPP(_1560659, _1560663)))], (40002 ^ _784416) ^ [_1560731, _1560733, _1560735, _1560737, _1560739] : [_1560731 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1560733, _1560735, _1560731, _1560737), _1560739) = hAPP(c_Product__Type_OPair(_1560733, _1560735), _1560739))], (40008 ^ _784416) ^ [_1560836, _1560838, _1560840, _1560842, _1560844] : [-(_1560836 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1560838, _1560840, _1560836, _1560842), _1560844) = hAPP(hAPP(c_Product__Type_Oscomp(_1560840, _1560838, _1560840, tc_prod(_1560838, _1560840)), hAPP(_1560842, _1560844)), c_Random_Oiterate(_1560838, _1560840, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1560836), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1560842)))], (40014 ^ _784416) ^ [_1560916, _1560918, _1560920, _1560922, _1560924, _1560926, _1560928, _1560930] : [class_Groups_Ocomm__monoid__add(_1560916), class_Orderings_Oord(_1560918), _1560920 = _1560922, _1560924 = _1560926, 40032 ^ _784416 : [(40033 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1560918), _1560922), 40031 ^ [_1560916, _1560918, _1560920, _1560922, _1560924, _1560926, _1560928, _1560930])))], (40035 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1560918), 40031 ^ [_1560916, _1560918, _1560920, _1560922, _1560924, _1560926, _1560928, _1560930]), _1560926)))], (40037 ^ _784416) ^ [] : [hAPP(_1560928, 40031 ^ [_1560916, _1560918, _1560920, _1560922, _1560924, _1560926, _1560928, _1560930]) = hAPP(_1560930, 40031 ^ [_1560916, _1560918, _1560920, _1560922, _1560924, _1560926, _1560928, _1560930])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560918, _1560916), _1560928), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1560918, _1560920), _1560924)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560918, _1560916), _1560930), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1560918, _1560922), _1560926)))], (40041 ^ _784416) ^ [_1561560, _1561562] : [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), _1561560), _1561562)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1561560), _1561562)))], (40047 ^ _784416) ^ [_1561665, _1561667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1561665), _1561667)), -(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), _1561665), _1561667)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (40053 ^ _784416) ^ [_1561776, _1561778] : [c_Wellfounded_Owf(_1561776, _1561778), -(c_Wellfounded_Owf(_1561776, c_Transitive__Closure_Otrancl(_1561776, _1561778)))], (40059 ^ _784416) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (40061 ^ _784416) ^ [_1561892, _1561894] : [c_Wellfounded_Oacyclic(_1561892, _1561894), 40064 ^ _784416 : [(40065 ^ _784416) ^ [_1561977] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561892, _1561892)), hAPP(hAPP(c_Product__Type_OPair(_1561892, _1561892), _1561977), _1561977)), c_Transitive__Closure_Otrancl(_1561892, _1561894)))]]], (40067 ^ _784416) ^ [_1562020, _1562022] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562020, _1562020)), hAPP(hAPP(c_Product__Type_OPair(_1562020, _1562020), 40068 ^ [_1562020, _1562022]), 40068 ^ [_1562020, _1562022])), c_Transitive__Closure_Otrancl(_1562020, _1562022)))), -(c_Wellfounded_Oacyclic(_1562020, _1562022))], (40074 ^ _784416) ^ [_1562094, _1562096, _1562098, _1562100] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562094, _1562094)), hAPP(hAPP(c_Product__Type_OPair(_1562094, _1562094), _1562096), _1562098)), _1562100)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562094, _1562094)), hAPP(hAPP(c_Product__Type_OPair(_1562094, _1562094), _1562096), _1562098)), c_Transitive__Closure_Otrancl(_1562094, _1562100))))], (40080 ^ _784416) ^ [_1562257, _1562259] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1562257, _1562257), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1562257, _1562259)), hAPP(hAPP(c_Product__Type_OSigma(_1562257, _1562257), hAPP(c_Relation_OField(_1562257), _1562259)), hAPP(c_COMBK(tc_fun(_1562257, tc_HOL_Obool), _1562257), hAPP(c_Relation_OField(_1562257), _1562259))))))], (40082 ^ _784416) ^ [_1562326, _1562328, _1562330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1562326, _1562326), tc_HOL_Obool)), _1562328), _1562330)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1562326, _1562326), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1562326, _1562326, _1562326), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1562326, _1562326), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1562326, _1562328)), _1562330)), _1562328)), _1562330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1562326, _1562326), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1562326, _1562328)), _1562330)))], (40092 ^ _784416) ^ [_1562597, _1562599, _1562601] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562597, _1562597)), _1562599), _1562601)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562597, _1562597)), _1562599), c_Transitive__Closure_Otrancl(_1562597, _1562601))))], (40098 ^ _784416) ^ [_1562722] : [-(c_Transitive__Closure_Otrancl(_1562722, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1562722, _1562722), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1562722, _1562722), tc_HOL_Obool)))], (40100 ^ _784416) ^ [_1562764, _1562766] : [-(hAPP(c_Relation_ODomain(_1562764, _1562764), c_Transitive__Closure_Otrancl(_1562764, _1562766)) = hAPP(c_Relation_ODomain(_1562764, _1562764), _1562766))], (40102 ^ _784416) ^ [_1562804, _1562806] : [-(hAPP(c_Relation_ORange(_1562804, _1562804), c_Transitive__Closure_Otrancl(_1562804, _1562806)) = hAPP(c_Relation_ORange(_1562804, _1562804), _1562806))], (40104 ^ _784416) ^ [_1562859, _1562861] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1562859, _1562859)), c_Transitive__Closure_Otrancl(_1562859, _1562861))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1562859, _1562859)), _1562861)))], (40110 ^ _784416) ^ [_1562966, _1562968] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1562966, _1562966)), _1562968)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1562966, _1562966)), c_Transitive__Closure_Otrancl(_1562966, _1562968))))], (40116 ^ _784416) ^ [_1563079, _1563081, _1563083, _1563085, _1563087] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563079, _1563079)), hAPP(hAPP(c_Product__Type_OPair(_1563079, _1563079), _1563081), _1563083)), c_Transitive__Closure_Otrancl(_1563079, _1563085))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1563079, _1563079)), hAPP(hAPP(c_Product__Type_OPair(_1563079, _1563079), _1563083), _1563087)), c_Transitive__Closure_Otrancl(_1563079, _1563085))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563079, _1563079)), hAPP(hAPP(c_Product__Type_OPair(_1563079, _1563079), _1563081), _1563087)), c_Transitive__Closure_Otrancl(_1563079, _1563085))))], (40126 ^ _784416) ^ [_1563352, _1563354, _1563356, _1563358, _1563360] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563352, _1563352)), hAPP(hAPP(c_Product__Type_OPair(_1563352, _1563352), _1563354), _1563356)), c_Transitive__Closure_Otrancl(_1563352, _1563358))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1563352, _1563352)), hAPP(hAPP(c_Product__Type_OPair(_1563352, _1563352), _1563356), _1563360)), _1563358)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563352, _1563352)), hAPP(hAPP(c_Product__Type_OPair(_1563352, _1563352), _1563354), _1563360)), c_Transitive__Closure_Otrancl(_1563352, _1563358))))], (40136 ^ _784416) ^ [_1563619, _1563621, _1563623, _1563625, _1563627] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563619, _1563619)), hAPP(hAPP(c_Product__Type_OPair(_1563619, _1563619), _1563621), _1563623)), _1563625)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1563619, _1563619)), hAPP(hAPP(c_Product__Type_OPair(_1563619, _1563619), _1563623), _1563627)), c_Transitive__Closure_Otrancl(_1563619, _1563625))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563619, _1563619)), hAPP(hAPP(c_Product__Type_OPair(_1563619, _1563619), _1563621), _1563627)), c_Transitive__Closure_Otrancl(_1563619, _1563625))))], (40146 ^ _784416) ^ [_1563886, _1563888, _1563890, _1563892, _1563894] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563886, _1563886)), hAPP(hAPP(c_Product__Type_OPair(_1563886, _1563886), _1563888), _1563890)), _1563892)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1563886, _1563886)), hAPP(hAPP(c_Product__Type_OPair(_1563886, _1563886), _1563890), _1563894)), _1563892)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563886, _1563886)), hAPP(hAPP(c_Product__Type_OPair(_1563886, _1563886), _1563888), _1563894)), c_Transitive__Closure_Otrancl(_1563886, _1563892))))], (40156 ^ _784416) ^ [_1564147, _1564149, _1564151, _1564153] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564147, _1564147)), _1564149), c_Transitive__Closure_Otrancl(_1564147, _1564151))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564147, _1564147), tc_HOL_Obool)), _1564151), _1564153)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564147, _1564147)), _1564149), c_Transitive__Closure_Otrancl(_1564147, _1564153))))], (40166 ^ _784416) ^ [_1564362, _1564364] : [-(c_Transitive__Closure_Otrancl(_1564362, _1564364) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1564362, _1564362), tc_HOL_Obool)), _1564364), hAPP(hAPP(c_Relation_Orel__comp(_1564362, _1564362, _1564362), c_Transitive__Closure_Otrancl(_1564362, _1564364)), _1564364)))], (40168 ^ _784416) ^ [_1564417, _1564419, _1564421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564417, _1564417), tc_HOL_Obool)), _1564419), hAPP(hAPP(c_Product__Type_OSigma(_1564417, _1564417), _1564421), hAPP(c_COMBK(tc_fun(_1564417, tc_HOL_Obool), _1564417), _1564421)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564417, _1564417), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1564417, _1564419)), hAPP(hAPP(c_Product__Type_OSigma(_1564417, _1564417), _1564421), hAPP(c_COMBK(tc_fun(_1564417, tc_HOL_Obool), _1564417), _1564421)))))], (40174 ^ _784416) ^ [_1564635, _1564637] : [40175 ^ _784416 : [(40176 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1564635), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (40178 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1564637), _1564635))]], -(c_Random_Olog(_1564635, _1564637) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (40182 ^ _784416) ^ [_1564770, _1564772] : [-(c_Random_Olog(_1564770, _1564772) = 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(_1564770, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1564772), _1564770)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1564770), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1564772), _1564770)))], (40192 ^ _784416) ^ [_1564852, _1564854, _1564856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1564852), _1564854)), -(c_Random_Ominus__shift(_1564856, _1564852, _1564854) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1564856), _1564852)), _1564854))], (40198 ^ _784416) ^ [_1564967, _1564969, _1564971] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1564967), _1564969))), -(c_Random_Ominus__shift(_1564971, _1564967, _1564969) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1564967), _1564969))], (40204 ^ _784416) ^ [_1565031, _1565033] : [_1565031 = _1565033, -(c_Random_Oinc__shift(_1565031, _1565033) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (40210 ^ _784416) ^ [_1565108, _1565110] : [-(_1565108 = _1565110), -(c_Random_Oinc__shift(_1565108, _1565110) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1565110), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (40216 ^ _784416) ^ [_1565155, _1565157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1565155)), -(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(_1565155), _1565157))), _1565155)))], (40222 ^ _784416) ^ [_1565262, _1565264, _1565266, _1565268] : [-(c_Transitive__Closure_Otrancl(_1565262, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1565262, _1565262)), hAPP(hAPP(c_Product__Type_OPair(_1565262, _1565262), _1565264), _1565266)), _1565268)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1565262, _1565262), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1565262, _1565268)), hAPP(c_Set_OCollect(tc_prod(_1565262, _1565262)), hAPP(c_Product__Type_Oprod_Oprod__case(_1565262, _1565262, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1565262, tc_fun(_1565262, tc_HOL_Obool), tc_fun(_1565262, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1565262, tc_HOL_Obool), tc_fun(_1565262, tc_HOL_Obool)), _1565262), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1565262)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1565262), c_fconj), hAPP(hAPP(c_COMBC(_1565262, tc_fun(tc_prod(_1565262, _1565262), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1565262, _1565262), tc_fun(tc_fun(tc_prod(_1565262, _1565262), tc_HOL_Obool), tc_HOL_Obool), _1565262), c_member(tc_prod(_1565262, _1565262))), hAPP(hAPP(c_COMBC(_1565262, _1565262, tc_prod(_1565262, _1565262)), c_Product__Type_OPair(_1565262, _1565262)), _1565264))), c_Transitive__Closure_Ortrancl(_1565262, _1565268))))), hAPP(hAPP(c_COMBC(_1565262, tc_fun(tc_prod(_1565262, _1565262), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1565262, _1565262), tc_fun(tc_fun(tc_prod(_1565262, _1565262), tc_HOL_Obool), tc_HOL_Obool), _1565262), c_member(tc_prod(_1565262, _1565262))), hAPP(c_Product__Type_OPair(_1565262, _1565262), _1565266))), c_Transitive__Closure_Ortrancl(_1565262, _1565268)))))))], (40224 ^ _784416) ^ [_1565530, _1565532, _1565534, _1565536] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565530, tc_fun(_1565530, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1565530, tc_fun(tc_prod(_1565530, _1565530), tc_HOL_Obool), tc_fun(_1565530, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565530, tc_fun(tc_fun(tc_prod(_1565530, _1565530), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1565530, _1565530), tc_HOL_Obool), tc_fun(_1565530, tc_HOL_Obool)), _1565530), c_COMBC(_1565530, tc_fun(tc_prod(_1565530, _1565530), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565530, tc_prod(_1565530, _1565530)), tc_fun(_1565530, tc_fun(tc_fun(tc_prod(_1565530, _1565530), tc_HOL_Obool), tc_HOL_Obool)), _1565530), hAPP(c_COMBB(tc_prod(_1565530, _1565530), tc_fun(tc_fun(tc_prod(_1565530, _1565530), tc_HOL_Obool), tc_HOL_Obool), _1565530), c_member(tc_prod(_1565530, _1565530)))), c_Product__Type_OPair(_1565530, _1565530)))), _1565532)), c_fequal), _1565534), _1565536)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565530, _1565530)), hAPP(hAPP(c_Product__Type_OPair(_1565530, _1565530), _1565534), _1565536)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1565530, _1565530), tc_HOL_Obool)), _1565532), c_Relation_OId(_1565530)))))], (40230 ^ _784416) ^ [_1565951, _1565953, _1565955, _1565957] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565951, _1565951)), hAPP(hAPP(c_Product__Type_OPair(_1565951, _1565951), _1565955), _1565957)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1565951, _1565951), tc_HOL_Obool)), _1565953), c_Relation_OId(_1565951)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565951, tc_fun(_1565951, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1565951, tc_fun(tc_prod(_1565951, _1565951), tc_HOL_Obool), tc_fun(_1565951, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565951, tc_fun(tc_fun(tc_prod(_1565951, _1565951), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1565951, _1565951), tc_HOL_Obool), tc_fun(_1565951, tc_HOL_Obool)), _1565951), c_COMBC(_1565951, tc_fun(tc_prod(_1565951, _1565951), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565951, tc_prod(_1565951, _1565951)), tc_fun(_1565951, tc_fun(tc_fun(tc_prod(_1565951, _1565951), tc_HOL_Obool), tc_HOL_Obool)), _1565951), hAPP(c_COMBB(tc_prod(_1565951, _1565951), tc_fun(tc_fun(tc_prod(_1565951, _1565951), tc_HOL_Obool), tc_HOL_Obool), _1565951), c_member(tc_prod(_1565951, _1565951)))), c_Product__Type_OPair(_1565951, _1565951)))), _1565953)), c_fequal), _1565955), _1565957)))], (40236 ^ _784416) ^ [_1566378, _1566380, _1566382] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566378, _1566378)), _1566380), _1566382)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566378, _1566378)), _1566380), c_Transitive__Closure_Ortrancl(_1566378, _1566382))))], (40242 ^ _784416) ^ [_1566503, _1566505, _1566507] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566503, _1566503)), hAPP(hAPP(c_Product__Type_OPair(_1566503, _1566503), _1566505), _1566505)), c_Transitive__Closure_Ortrancl(_1566503, _1566507))))], (40244 ^ _784416) ^ [_1566552, _1566554] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566552, _1566552)), hAPP(hAPP(c_Product__Type_OPair(_1566552, _1566552), _1566554), _1566554)), c_Relation_OId(_1566552))))], (40246 ^ _784416) ^ [_1566598, _1566600, _1566602, _1566604] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566598, _1566598)), hAPP(hAPP(c_Product__Type_OPair(_1566598, _1566598), _1566600), _1566602)), c_Transitive__Closure_Otrancl(_1566598, _1566604))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566598, _1566598)), hAPP(hAPP(c_Product__Type_OPair(_1566598, _1566598), _1566600), _1566602)), c_Transitive__Closure_Ortrancl(_1566598, _1566604))))], (40252 ^ _784416) ^ [_1566767, _1566769, _1566771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566767, _1566767), tc_HOL_Obool)), _1566769), _1566771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566767, _1566767), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1566767, _1566769)), c_Transitive__Closure_Ortrancl(_1566767, _1566771))))], (40258 ^ _784416) ^ [_1566910, _1566912, _1566914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566910, _1566910), tc_HOL_Obool)), _1566912), _1566914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566910, _1566910), tc_HOL_Obool)), _1566914), c_Transitive__Closure_Ortrancl(_1566910, _1566912))), -(c_Transitive__Closure_Ortrancl(_1566910, _1566914) = c_Transitive__Closure_Ortrancl(_1566910, _1566912))], (40268 ^ _784416) ^ [_1567113, _1567115, _1567117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1567113, _1567113), tc_HOL_Obool)), _1567115), c_Transitive__Closure_Ortrancl(_1567113, _1567117))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1567113, _1567113), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1567113, _1567115)), c_Transitive__Closure_Ortrancl(_1567113, _1567117))))], (40274 ^ _784416) ^ [_1567262, _1567264, _1567266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1567262, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1567262, _1567262, _1567264), _1567266)), _1567266)), -(hAPP(c_Relation_OImage(_1567262, _1567262, c_Transitive__Closure_Ortrancl(_1567262, _1567264)), _1567266) = _1567266)], (40280 ^ _784416) ^ [_1567395, _1567397, _1567399] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1567395, _1567395), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1567395, _1567395), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1567395, _1567397)), c_Transitive__Closure_Ortrancl(_1567395, _1567399))), c_Transitive__Closure_Ortrancl(_1567395, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1567395, _1567395), tc_HOL_Obool)), _1567397), _1567399)))))], (40282 ^ _784416) ^ [_1567472, _1567474, _1567476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1567472, _1567472), tc_HOL_Obool)), c_Relation_OId(_1567472)), _1567474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1567472, _1567472), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1567472, _1567472, _1567472), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1567472, _1567472), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1567472, _1567476)), _1567474)), _1567476)), _1567474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1567472, _1567472), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1567472, _1567476)), _1567474)))], (40292 ^ _784416) ^ [_1567747, _1567749] : [-(hAPP(c_Relation_OImage(_1567747, _1567747, c_Relation_OId(_1567747)), _1567749) = _1567749)], (40294 ^ _784416) ^ [_1567781, _1567783, _1567785] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1567781, _1567781, _1567783), c_Relation_OId(_1567781)), _1567785) = _1567785)], (40296 ^ _784416) ^ [_1567820, _1567822, _1567824] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1567820, _1567822, _1567822), _1567824), c_Relation_OId(_1567822)) = _1567824)], (40298 ^ _784416) ^ [_1567859, _1567861] : [-(c_Relation_Orefl__on(_1567859, c_Orderings_Otop__class_Otop(tc_fun(_1567859, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1567859, _1567861)))], (40300 ^ _784416) ^ [_1567893, _1567895] : [-(c_Transitive__Closure_Ortrancl(_1567893, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1567893, _1567893), tc_HOL_Obool)), _1567895), c_Relation_OId(_1567893))) = c_Transitive__Closure_Ortrancl(_1567893, _1567895))], (40302 ^ _784416) ^ [_1567940, _1567942] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1567940, _1567940, _1567940), _1567942), c_Transitive__Closure_Ortrancl(_1567940, _1567942)) = hAPP(hAPP(c_Relation_Orel__comp(_1567940, _1567940, _1567940), c_Transitive__Closure_Ortrancl(_1567940, _1567942)), _1567942))], (40304 ^ _784416) ^ [_1567991, _1567993] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1567991, _1567991, _1567991), c_Transitive__Closure_Ortrancl(_1567991, _1567993)), c_Transitive__Closure_Ortrancl(_1567991, _1567993)) = c_Transitive__Closure_Ortrancl(_1567991, _1567993))], (40306 ^ _784416) ^ [_1568035, _1568037] : [-(c_Transitive__Closure_Ortrancl(_1568035, _1568037) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568035, _1568035), tc_HOL_Obool)), c_Relation_OId(_1568035)), hAPP(hAPP(c_Relation_Orel__comp(_1568035, _1568035, _1568035), c_Transitive__Closure_Ortrancl(_1568035, _1568037)), _1568037)))], (40308 ^ _784416) ^ [_1568092, _1568094, _1568096, _1568098] : [40309 ^ _784416 : [(40310 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568092, _1568092)), _1568094), c_Transitive__Closure_Ortrancl(_1568092, _1568096)))], (40312 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568092, _1568092)), _1568094), c_Transitive__Closure_Ortrancl(_1568092, _1568098)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568092, _1568092)), _1568094), c_Transitive__Closure_Ortrancl(_1568092, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568092, _1568092), tc_HOL_Obool)), _1568096), _1568098)))))], (40316 ^ _784416) ^ [_1568317, _1568319] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568317, _1568317), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1568317, _1568319)), c_Relation_OId(_1568317)) = c_Transitive__Closure_Ortrancl(_1568317, _1568319))], (40318 ^ _784416) ^ [_1568364, _1568366] : [-(c_Transitive__Closure_Ortrancl(_1568364, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568364, _1568364), tc_HOL_Obool)), _1568366), c_Relation_OId(_1568364))) = c_Transitive__Closure_Ortrancl(_1568364, _1568366))], (40320 ^ _784416) ^ [_1568411, _1568413, _1568415] : [-(c_Transitive__Closure_Ortrancl(_1568411, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568411, _1568411), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1568411, _1568413)), c_Transitive__Closure_Ortrancl(_1568411, _1568415))) = c_Transitive__Closure_Ortrancl(_1568411, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568411, _1568411), tc_HOL_Obool)), _1568413), _1568415)))], (40322 ^ _784416) ^ [_1568478, _1568480] : [-(c_Transitive__Closure_Ortrancl(_1568478, c_Transitive__Closure_Ortrancl(_1568478, _1568480)) = c_Transitive__Closure_Ortrancl(_1568478, _1568480))], (40324 ^ _784416) ^ [_1568512, _1568514, _1568516, _1568518, _1568520] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568512, _1568512)), hAPP(hAPP(c_Product__Type_OPair(_1568512, _1568512), _1568514), _1568516)), c_Transitive__Closure_Ortrancl(_1568512, _1568518))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1568512, _1568512)), hAPP(hAPP(c_Product__Type_OPair(_1568512, _1568512), _1568516), _1568520)), c_Transitive__Closure_Ortrancl(_1568512, _1568518))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568512, _1568512)), hAPP(hAPP(c_Product__Type_OPair(_1568512, _1568512), _1568514), _1568520)), c_Transitive__Closure_Ortrancl(_1568512, _1568518))))], (40334 ^ _784416) ^ [_1568785, _1568787, _1568789, _1568791, _1568793] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568785, _1568785)), hAPP(hAPP(c_Product__Type_OPair(_1568785, _1568785), _1568787), _1568789)), c_Transitive__Closure_Ortrancl(_1568785, _1568791))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1568785, _1568785)), hAPP(hAPP(c_Product__Type_OPair(_1568785, _1568785), _1568789), _1568793)), _1568791)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568785, _1568785)), hAPP(hAPP(c_Product__Type_OPair(_1568785, _1568785), _1568787), _1568793)), c_Transitive__Closure_Ortrancl(_1568785, _1568791))))], (40344 ^ _784416) ^ [_1569052, _1569054, _1569056, _1569058, _1569060] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569052, _1569052)), hAPP(hAPP(c_Product__Type_OPair(_1569052, _1569052), _1569054), _1569056)), _1569058)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1569052, _1569052)), hAPP(hAPP(c_Product__Type_OPair(_1569052, _1569052), _1569056), _1569060)), c_Transitive__Closure_Ortrancl(_1569052, _1569058))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569052, _1569052)), hAPP(hAPP(c_Product__Type_OPair(_1569052, _1569052), _1569054), _1569060)), c_Transitive__Closure_Ortrancl(_1569052, _1569058))))], (40354 ^ _784416) ^ [_1569319, _1569321] : [-(hAPP(c_Relation_ORange(_1569319, _1569319), c_Transitive__Closure_Ortrancl(_1569319, _1569321)) = c_Orderings_Otop__class_Otop(tc_fun(_1569319, tc_HOL_Obool)))], (40356 ^ _784416) ^ [_1569358] : [-(c_Transitive__Closure_Ortrancl(_1569358, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1569358, _1569358), tc_HOL_Obool))) = c_Relation_OId(_1569358))], (40358 ^ _784416) ^ [_1569394, _1569396] : [-(hAPP(c_Relation_ODomain(_1569394, _1569394), c_Transitive__Closure_Ortrancl(_1569394, _1569396)) = c_Orderings_Otop__class_Otop(tc_fun(_1569394, tc_HOL_Obool)))], (40360 ^ _784416) ^ [_1569433, _1569435] : [-(c_Transitive__Closure_Ortrancl(_1569433, c_Transitive__Closure_Otrancl(_1569433, _1569435)) = c_Transitive__Closure_Ortrancl(_1569433, _1569435))], (40362 ^ _784416) ^ [_1569467, _1569469] : [-(c_Transitive__Closure_Otrancl(_1569467, c_Transitive__Closure_Ortrancl(_1569467, _1569469)) = c_Transitive__Closure_Ortrancl(_1569467, _1569469))], (40364 ^ _784416) ^ [_1569501, _1569503] : [-(c_Transitive__Closure_Otrancl(_1569501, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1569501, _1569501), tc_HOL_Obool)), _1569503), c_Relation_OId(_1569501))) = c_Transitive__Closure_Ortrancl(_1569501, _1569503))], (40366 ^ _784416) ^ [_1569548, _1569550] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1569548, _1569548), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1569548, _1569550)), c_Relation_OId(_1569548)) = c_Transitive__Closure_Ortrancl(_1569548, _1569550))], (40368 ^ _784416) ^ [_1569595, _1569597] : [-(c_Transitive__Closure_Otrancl(_1569595, _1569597) = hAPP(hAPP(c_Relation_Orel__comp(_1569595, _1569595, _1569595), c_Transitive__Closure_Ortrancl(_1569595, _1569597)), _1569597))], (40370 ^ _784416) ^ [_1569636, _1569638] : [-(c_Transitive__Closure_Otrancl(_1569636, _1569638) = hAPP(hAPP(c_Relation_Orel__comp(_1569636, _1569636, _1569636), _1569638), c_Transitive__Closure_Ortrancl(_1569636, _1569638)))], (40372 ^ _784416) ^ [_1569695, _1569697, _1569699] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569695, _1569695)), hAPP(hAPP(c_Product__Type_OPair(_1569695, _1569695), _1569697), _1569699)), c_Relation_OId(_1569695))), -(_1569697 = _1569699)], (40378 ^ _784416) ^ [_1569812, _1569814, _1569816] : [_1569814 = _1569816, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569812, _1569812)), hAPP(hAPP(c_Product__Type_OPair(_1569812, _1569812), _1569814), _1569816)), c_Relation_OId(_1569812))))], (40384 ^ _784416) ^ [_1569935, _1569937, _1569939, _1569941, _1569943] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569935, _1569935)), hAPP(hAPP(c_Product__Type_OPair(_1569935, _1569935), _1569937), _1569939)), c_Transitive__Closure_Ortrancl(_1569935, _1569941))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1569935, _1569935)), hAPP(hAPP(c_Product__Type_OPair(_1569935, _1569935), _1569939), _1569943)), c_Transitive__Closure_Otrancl(_1569935, _1569941))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569935, _1569935)), hAPP(hAPP(c_Product__Type_OPair(_1569935, _1569935), _1569937), _1569943)), c_Transitive__Closure_Otrancl(_1569935, _1569941))))], (40394 ^ _784416) ^ [_1570208, _1570210, _1570212, _1570214, _1570216] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570208, _1570208)), hAPP(hAPP(c_Product__Type_OPair(_1570208, _1570208), _1570210), _1570212)), c_Transitive__Closure_Otrancl(_1570208, _1570214))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570208, _1570208)), hAPP(hAPP(c_Product__Type_OPair(_1570208, _1570208), _1570212), _1570216)), c_Transitive__Closure_Ortrancl(_1570208, _1570214))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570208, _1570208)), hAPP(hAPP(c_Product__Type_OPair(_1570208, _1570208), _1570210), _1570216)), c_Transitive__Closure_Otrancl(_1570208, _1570214))))], (40404 ^ _784416) ^ [_1570481, _1570483, _1570485, _1570487, _1570489] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570481, _1570481)), hAPP(hAPP(c_Product__Type_OPair(_1570481, _1570481), _1570483), _1570485)), c_Transitive__Closure_Ortrancl(_1570481, _1570487))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570481, _1570481)), hAPP(hAPP(c_Product__Type_OPair(_1570481, _1570481), _1570485), _1570489)), _1570487)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570481, _1570481)), hAPP(hAPP(c_Product__Type_OPair(_1570481, _1570481), _1570483), _1570489)), c_Transitive__Closure_Otrancl(_1570481, _1570487))))], (40414 ^ _784416) ^ [_1570748, _1570750, _1570752, _1570754] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570748, _1570748)), hAPP(hAPP(c_Product__Type_OPair(_1570748, _1570748), _1570750), _1570752)), c_Transitive__Closure_Ortrancl(_1570748, _1570754))), -(_1570750 = _1570752), 40421 ^ _784416 : [(40422 ^ _784416) ^ [] : [_1570750 = _1570752], (40424 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570748, _1570748)), hAPP(hAPP(c_Product__Type_OPair(_1570748, _1570748), _1570750), _1570752)), c_Transitive__Closure_Otrancl(_1570748, _1570754))))]]], (40426 ^ _784416) ^ [_1571010, _1571012, _1571014, _1571016, _1571018] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571010, _1571010)), hAPP(hAPP(c_Product__Type_OPair(_1571010, _1571010), _1571012), _1571014)), _1571016)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571010, _1571010)), hAPP(hAPP(c_Product__Type_OPair(_1571010, _1571010), _1571014), _1571018)), c_Transitive__Closure_Ortrancl(_1571010, _1571016))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571010, _1571010)), hAPP(hAPP(c_Product__Type_OPair(_1571010, _1571010), _1571012), _1571018)), c_Transitive__Closure_Otrancl(_1571010, _1571016))))], (40436 ^ _784416) ^ [_1571298, _1571300, _1571302, _1571304] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571298, _1571298)), hAPP(hAPP(c_Product__Type_OPair(_1571298, _1571298), _1571300), _1571302)), c_Transitive__Closure_Ortrancl(_1571298, _1571304))), -(_1571300 = _1571302), 40443 ^ _784416 : [(40444 ^ _784416) ^ [] : [_1571300 = _1571302], (40446 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571298, _1571298)), hAPP(hAPP(c_Product__Type_OPair(_1571298, _1571298), _1571300), _1571302)), c_Transitive__Closure_Otrancl(_1571298, _1571304))))]]], (40448 ^ _784416) ^ [_1571556, _1571558, _1571560, _1571562] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571556, _1571556)), hAPP(hAPP(c_Product__Type_OPair(_1571556, _1571556), _1571558), _1571560)), c_Transitive__Closure_Ortrancl(_1571556, _1571562)))), 40449 ^ _784416 : [(40450 ^ _784416) ^ [] : [_1571558 = _1571560], (40452 ^ _784416) ^ [] : [-(_1571558 = _1571560), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571556, _1571556)), hAPP(hAPP(c_Product__Type_OPair(_1571556, _1571556), _1571558), _1571560)), c_Transitive__Closure_Otrancl(_1571556, _1571562)))]]], (40460 ^ _784416) ^ [_1571822] : [-(hAPP(c_Relation_ODomain(_1571822, _1571822), c_Relation_OId(_1571822)) = c_Orderings_Otop__class_Otop(tc_fun(_1571822, tc_HOL_Obool)))], (40462 ^ _784416) ^ [_1571858] : [-(hAPP(c_Relation_ORange(_1571858, _1571858), c_Relation_OId(_1571858)) = c_Orderings_Otop__class_Otop(tc_fun(_1571858, tc_HOL_Obool)))], (40464 ^ _784416) ^ [_1571894] : [-(c_Relation_Orefl__on(_1571894, c_Orderings_Otop__class_Otop(tc_fun(_1571894, tc_HOL_Obool)), c_Relation_OId(_1571894)))], (40466 ^ _784416) ^ [] : [-(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))))], (40468 ^ _784416) ^ [_1571942, _1571944, _1571946, _1571948] : [-(hBOOL(hAPP(hAPP(c_member(_1571942), _1571944), hAPP(c_Relation_ODomain(_1571942, _1571942), _1571946)))), 40471 ^ _784416 : [(40472 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571942, _1571942)), hAPP(hAPP(c_Product__Type_OPair(_1571942, _1571942), _1571944), _1571948)), c_Transitive__Closure_Ortrancl(_1571942, _1571946))), -(_1571944 = _1571948)], (40478 ^ _784416) ^ [] : [_1571944 = _1571948, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571942, _1571942)), hAPP(hAPP(c_Product__Type_OPair(_1571942, _1571942), _1571944), _1571948)), c_Transitive__Closure_Ortrancl(_1571942, _1571946))))]]], (40484 ^ _784416) ^ [_1572238, _1572240, _1572242, _1572244] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572238, _1572238)), hAPP(hAPP(c_Product__Type_OPair(_1572238, _1572238), _1572240), _1572242)), c_Transitive__Closure_Ortrancl(_1572238, _1572244))), hBOOL(hAPP(hAPP(c_member(_1572238), _1572242), c_Wellfounded_Oacc(_1572238, _1572244))), -(hBOOL(hAPP(hAPP(c_member(_1572238), _1572240), c_Wellfounded_Oacc(_1572238, _1572244))))], (40494 ^ _784416) ^ [_1572459, _1572461, _1572463, _1572465] : [hBOOL(hAPP(hAPP(c_member(_1572459), _1572461), c_Wellfounded_Oacc(_1572459, _1572463))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1572459, _1572459)), hAPP(hAPP(c_Product__Type_OPair(_1572459, _1572459), _1572465), _1572461)), c_Transitive__Closure_Ortrancl(_1572459, _1572463))), -(hBOOL(hAPP(hAPP(c_member(_1572459), _1572465), c_Wellfounded_Oacc(_1572459, _1572463))))], (40504 ^ _784416) ^ [_1572701, _1572703, _1572705, _1572707] : [c_Wellfounded_Owf(_1572701, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1572701, _1572701)), hAPP(hAPP(c_Product__Type_OPair(_1572701, _1572701), _1572703), _1572705)), _1572707)), 40507 ^ _784416 : [(40508 ^ _784416) ^ [] : [-(c_Wellfounded_Owf(_1572701, _1572707))], (40510 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572701, _1572701)), hAPP(hAPP(c_Product__Type_OPair(_1572701, _1572701), _1572705), _1572703)), c_Transitive__Closure_Ortrancl(_1572701, _1572707)))]]], (40512 ^ _784416) ^ [_1572896, _1572898, _1572900, _1572902] : [-(c_Wellfounded_Owf(_1572896, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1572896, _1572896)), hAPP(hAPP(c_Product__Type_OPair(_1572896, _1572896), _1572898), _1572900)), _1572902))), c_Wellfounded_Owf(_1572896, _1572902), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572896, _1572896)), hAPP(hAPP(c_Product__Type_OPair(_1572896, _1572896), _1572900), _1572898)), c_Transitive__Closure_Ortrancl(_1572896, _1572902))))], (40522 ^ _784416) ^ [_1573143, _1573145, _1573147, _1573149] : [c_Wellfounded_Oacyclic(_1573143, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1573143, _1573143)), hAPP(hAPP(c_Product__Type_OPair(_1573143, _1573143), _1573145), _1573147)), _1573149)), 40525 ^ _784416 : [(40526 ^ _784416) ^ [] : [-(c_Wellfounded_Oacyclic(_1573143, _1573149))], (40528 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573143, _1573143)), hAPP(hAPP(c_Product__Type_OPair(_1573143, _1573143), _1573147), _1573145)), c_Transitive__Closure_Ortrancl(_1573143, _1573149)))]]], (40530 ^ _784416) ^ [_1573338, _1573340, _1573342, _1573344] : [-(c_Wellfounded_Oacyclic(_1573338, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1573338, _1573338)), hAPP(hAPP(c_Product__Type_OPair(_1573338, _1573338), _1573340), _1573342)), _1573344))), c_Wellfounded_Oacyclic(_1573338, _1573344), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573338, _1573338)), hAPP(hAPP(c_Product__Type_OPair(_1573338, _1573338), _1573342), _1573340)), c_Transitive__Closure_Ortrancl(_1573338, _1573344))))], (40540 ^ _784416) ^ [_1573564, _1573566] : [-(c_Relation_Orefl__on(_1573564, c_Orderings_Otop__class_Otop(tc_fun(_1573564, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573564, _1573564), tc_HOL_Obool)), _1573566), c_Relation_OId(_1573564))))], (40542 ^ _784416) ^ [_1573611] : [-(c_Relation_OId(_1573611) = hAPP(c_Set_OCollect(tc_prod(_1573611, _1573611)), hAPP(hAPP(c_COMBB(tc_fun(_1573611, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1573611, _1573611)), c_HOL_OEx(_1573611)), hAPP(hAPP(c_COMBC(tc_prod(_1573611, _1573611), tc_fun(_1573611, tc_prod(_1573611, _1573611)), tc_fun(_1573611, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1573611, _1573611), tc_HOL_Obool), tc_fun(tc_fun(_1573611, tc_prod(_1573611, _1573611)), tc_fun(_1573611, tc_HOL_Obool)), tc_prod(_1573611, _1573611)), c_COMBB(tc_prod(_1573611, _1573611), tc_HOL_Obool, _1573611)), c_fequal)), hAPP(hAPP(c_COMBS(_1573611, _1573611, tc_prod(_1573611, _1573611)), c_Product__Type_OPair(_1573611, _1573611)), c_COMBI(_1573611))))))], (40544 ^ _784416) ^ [_1573740, _1573742] : [-(c_Relation_Oirrefl(_1573740, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1573740, _1573740), tc_HOL_Obool)), _1573742), c_Relation_OId(_1573740))))], (40546 ^ _784416) ^ [_1573796, _1573798] : [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), _1573796), _1573798)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1573796), _1573798)))], (40552 ^ _784416) ^ [_1573901, _1573903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1573901), _1573903)), -(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), _1573901), _1573903)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (40558 ^ _784416) ^ [_1574012, _1574014, _1574016, _1574018, _1574020] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574012, _1574012)), hAPP(hAPP(c_Product__Type_OPair(_1574012, _1574012), _1574014), _1574016)), c_Transitive__Closure_Ortrancl(_1574012, _1574018))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1574012, _1574012), tc_HOL_Obool)), _1574018), hAPP(hAPP(c_Product__Type_OSigma(_1574012, _1574012), _1574020), hAPP(c_COMBK(tc_fun(_1574012, tc_HOL_Obool), _1574012), _1574020)))), -(_1574014 = _1574016), -(hBOOL(hAPP(hAPP(c_member(_1574012), _1574014), _1574020)))], (40572 ^ _784416) ^ [_1574286, _1574288, _1574290] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1574286, _1574286), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1574286, _1574286), _1574288)), c_Transitive__Closure_Ortrancl(_1574286, _1574288)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1574286, _1574286), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1574286, _1574286)), hAPP(hAPP(c_Product__Type_OPair(_1574286, _1574286), _1574290), _1574290)), c_Transitive__Closure_Otrancl(_1574286, _1574288)))], (40578 ^ _784416) ^ [_1574472, _1574474, _1574476, _1574478, _1574480] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574472, _1574472)), hAPP(hAPP(c_Product__Type_OPair(_1574472, _1574472), hAPP(_1574474, hAPP(c_Nat_OSuc, 40579 ^ [_1574472, _1574474, _1574476, _1574478, _1574480]))), hAPP(_1574474, 40579 ^ [_1574472, _1574474, _1574476, _1574478, _1574480]))), c_Transitive__Closure_Ortrancl(_1574472, _1574476))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574472, _1574472)), hAPP(hAPP(c_Product__Type_OPair(_1574472, _1574472), hAPP(_1574474, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1574478), _1574480))), hAPP(_1574474, _1574478))), c_Transitive__Closure_Ortrancl(_1574472, _1574476))))], (40585 ^ _784416) ^ [_1574783, _1574785, _1574787] : [c_Relation_Ototal__on(_1574783, _1574785, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1574783, _1574783), tc_HOL_Obool)), _1574787), c_Relation_OId(_1574783))), -(c_Relation_Ototal__on(_1574783, _1574785, _1574787))], (40591 ^ _784416) ^ [_1574894, _1574896, _1574898] : [c_Relation_Ototal__on(_1574894, _1574896, _1574898), -(c_Relation_Ototal__on(_1574894, _1574896, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1574894, _1574894), tc_HOL_Obool)), _1574898), c_Relation_OId(_1574894))))], (40597 ^ _784416) ^ [_1575011] : [-(hAPP(c_Relation_Oconverse(_1575011, _1575011), c_Relation_OId(_1575011)) = c_Relation_OId(_1575011))], (40599 ^ _784416) ^ [_1575044, _1575046] : [-(c_Transitive__Closure_Ortrancl(_1575044, hAPP(c_Relation_Oconverse(_1575044, _1575044), _1575046)) = hAPP(c_Relation_Oconverse(_1575044, _1575044), c_Transitive__Closure_Ortrancl(_1575044, _1575046)))], (40601 ^ _784416) ^ [_1575087, _1575089] : [-(c_Transitive__Closure_Otrancl(_1575087, hAPP(c_Relation_Oconverse(_1575087, _1575087), _1575089)) = hAPP(c_Relation_Oconverse(_1575087, _1575087), c_Transitive__Closure_Otrancl(_1575087, _1575089)))], (40603 ^ _784416) ^ [_1575154, _1575156, _1575158, _1575160, _1575162] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575154, _1575156)), hAPP(hAPP(c_Product__Type_OPair(_1575154, _1575156), _1575158), _1575160)), hAPP(c_Relation_Oconverse(_1575156, _1575154), _1575162))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575156, _1575154)), hAPP(hAPP(c_Product__Type_OPair(_1575156, _1575154), _1575160), _1575158)), _1575162)))], (40609 ^ _784416) ^ [_1575321, _1575323, _1575325, _1575327, _1575329] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575323, _1575321)), hAPP(hAPP(c_Product__Type_OPair(_1575323, _1575321), _1575327), _1575325)), _1575329)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575321, _1575323)), hAPP(hAPP(c_Product__Type_OPair(_1575321, _1575323), _1575325), _1575327)), hAPP(c_Relation_Oconverse(_1575323, _1575321), _1575329))))], (40615 ^ _784416) ^ [_1575494, _1575496, _1575498, _1575500, _1575502] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575494, _1575496)), hAPP(hAPP(c_Product__Type_OPair(_1575494, _1575496), _1575498), _1575500)), _1575502)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575496, _1575494)), hAPP(hAPP(c_Product__Type_OPair(_1575496, _1575494), _1575500), _1575498)), hAPP(c_Relation_Oconverse(_1575494, _1575496), _1575502))))], (40621 ^ _784416) ^ [_1575665, _1575667, _1575669, _1575671, _1575673] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575665, _1575667)), hAPP(hAPP(c_Product__Type_OPair(_1575665, _1575667), _1575669), _1575671)), hAPP(c_Relation_Oconverse(_1575667, _1575665), _1575673))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575667, _1575665)), hAPP(hAPP(c_Product__Type_OPair(_1575667, _1575665), _1575671), _1575669)), _1575673)))], (40627 ^ _784416) ^ [_1575854, _1575856, _1575858] : [c_Relation_Orefl__on(_1575854, _1575856, hAPP(c_Relation_Oconverse(_1575854, _1575854), _1575858)), -(c_Relation_Orefl__on(_1575854, _1575856, _1575858))], (40633 ^ _784416) ^ [_1575945, _1575947, _1575949] : [c_Relation_Orefl__on(_1575945, _1575947, _1575949), -(c_Relation_Orefl__on(_1575945, _1575947, hAPP(c_Relation_Oconverse(_1575945, _1575945), _1575949)))], (40639 ^ _784416) ^ [_1576042, _1576044, _1576046, _1576048, _1576050] : [-(hAPP(c_Relation_Oconverse(_1576042, _1576044), hAPP(hAPP(c_Relation_Orel__comp(_1576042, _1576046, _1576044), _1576048), _1576050)) = hAPP(hAPP(c_Relation_Orel__comp(_1576044, _1576046, _1576042), hAPP(c_Relation_Oconverse(_1576046, _1576044), _1576050)), hAPP(c_Relation_Oconverse(_1576042, _1576046), _1576048)))], (40641 ^ _784416) ^ [_1576111, _1576113, _1576115, _1576117] : [-(hAPP(c_Relation_Oconverse(_1576111, _1576113), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1576111, _1576113), tc_HOL_Obool)), _1576115), _1576117)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1576113, _1576111), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1576111, _1576113), _1576115)), hAPP(c_Relation_Oconverse(_1576111, _1576113), _1576117)))], (40643 ^ _784416) ^ [_1576204, _1576206, _1576208] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1576204, _1576206)), hAPP(c_Relation_Oconverse(_1576206, _1576204), _1576208))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1576206, _1576204)), _1576208)))], (40649 ^ _784416) ^ [_1576319, _1576321, _1576323] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1576321, _1576319)), _1576323)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1576319, _1576321)), hAPP(c_Relation_Oconverse(_1576321, _1576319), _1576323))))], (40655 ^ _784416) ^ [_1576458, _1576460, _1576462] : [c_Relation_Ototal__on(_1576458, _1576460, hAPP(c_Relation_Oconverse(_1576458, _1576458), _1576462)), -(c_Relation_Ototal__on(_1576458, _1576460, _1576462))], (40661 ^ _784416) ^ [_1576549, _1576551, _1576553] : [c_Relation_Ototal__on(_1576549, _1576551, _1576553), -(c_Relation_Ototal__on(_1576549, _1576551, hAPP(c_Relation_Oconverse(_1576549, _1576549), _1576553)))], (40667 ^ _784416) ^ [_1576646, _1576648, _1576650] : [-(hAPP(c_Relation_Oconverse(_1576646, _1576648), hAPP(c_Relation_Oconverse(_1576648, _1576646), _1576650)) = _1576650)], (40669 ^ _784416) ^ [_1576685, _1576687] : [-(hAPP(c_Relation_OField(_1576685), hAPP(c_Relation_Oconverse(_1576685, _1576685), _1576687)) = hAPP(c_Relation_OField(_1576685), _1576687))], (40671 ^ _784416) ^ [_1576726, _1576728] : [-(hAPP(c_Relation_Oconverse(_1576726, _1576726), c_Relation_OId__on(_1576726, _1576728)) = c_Relation_OId__on(_1576726, _1576728))], (40673 ^ _784416) ^ [_1576763, _1576765, _1576767, _1576769] : [-(hAPP(c_Relation_Oconverse(_1576763, _1576765), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1576763, _1576765), tc_HOL_Obool)), _1576767), _1576769)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1576765, _1576763), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1576763, _1576765), _1576767)), hAPP(c_Relation_Oconverse(_1576763, _1576765), _1576769)))], (40675 ^ _784416) ^ [_1576838, _1576840, _1576842, _1576844] : [-(hAPP(c_Relation_Oconverse(_1576838, _1576838), hAPP(hAPP(c_Relation_Oinv__image(_1576840, _1576838), _1576842), _1576844)) = hAPP(hAPP(c_Relation_Oinv__image(_1576840, _1576838), hAPP(c_Relation_Oconverse(_1576840, _1576840), _1576842)), _1576844))], (40677 ^ _784416) ^ [_1576897, _1576899, _1576901, _1576903, _1576905] : [-(hAPP(c_Relation_Oconverse(_1576897, _1576899), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1576901, tc_fun(tc_prod(_1576897, _1576899), tc_HOL_Obool)), _1576903), _1576905)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1576901, tc_fun(tc_prod(_1576899, _1576897), tc_HOL_Obool)), _1576903), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1576897, _1576899), tc_HOL_Obool), tc_fun(tc_prod(_1576899, _1576897), tc_HOL_Obool), _1576901), c_Relation_Oconverse(_1576897, _1576899)), _1576905)))], (40679 ^ _784416) ^ [_1577004, _1577006] : [c_Wellfounded_Oacyclic(_1577004, hAPP(c_Relation_Oconverse(_1577004, _1577004), _1577006)), -(c_Wellfounded_Oacyclic(_1577004, _1577006))], (40685 ^ _784416) ^ [_1577089, _1577091] : [c_Wellfounded_Oacyclic(_1577089, _1577091), -(c_Wellfounded_Oacyclic(_1577089, hAPP(c_Relation_Oconverse(_1577089, _1577089), _1577091)))], (40691 ^ _784416) ^ [_1577180, _1577182] : [c_Wellfounded_Owf(_1577180, hAPP(c_Relation_Oconverse(_1577180, _1577180), _1577182)), -(c_Wellfounded_Owf(_1577180, hAPP(c_Relation_Oconverse(_1577180, _1577180), c_Transitive__Closure_Otrancl(_1577180, _1577182))))], (40697 ^ _784416) ^ [_1577287, _1577289, _1577291] : [c_Equiv__Relations_Oequiv(_1577287, _1577289, _1577291), -(hAPP(hAPP(c_Relation_Orel__comp(_1577287, _1577287, _1577287), hAPP(c_Relation_Oconverse(_1577287, _1577287), _1577291)), _1577291) = _1577291)], (40703 ^ _784416) ^ [_1577400, _1577402, _1577404] : [-(hAPP(c_Relation_ORange(_1577400, _1577402), hAPP(c_Relation_Oconverse(_1577402, _1577400), _1577404)) = hAPP(c_Relation_ODomain(_1577402, _1577400), _1577404))], (40705 ^ _784416) ^ [_1577445, _1577447, _1577449] : [-(hAPP(c_Relation_ODomain(_1577445, _1577447), hAPP(c_Relation_Oconverse(_1577447, _1577445), _1577449)) = hAPP(c_Relation_ORange(_1577447, _1577445), _1577449))], (40707 ^ _784416) ^ [_1577490, _1577492, _1577494] : [-(hAPP(c_Relation_ORange(_1577490, _1577492), _1577494) = hAPP(c_Relation_ODomain(_1577492, _1577490), hAPP(c_Relation_Oconverse(_1577490, _1577492), _1577494)))], (40709 ^ _784416) ^ [_1577535, _1577537] : [-(c_Relation_Ototal__on(_1577535, c_Orderings_Obot__class_Obot(tc_fun(_1577535, tc_HOL_Obool)), _1577537))], (40711 ^ _784416) ^ [_1577566, _1577568, _1577570, _1577572] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577566, _1577566)), hAPP(hAPP(c_Product__Type_OPair(_1577566, _1577566), _1577568), _1577570)), c_Transitive__Closure_Ortrancl(_1577566, _1577572))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577566, _1577566)), hAPP(hAPP(c_Product__Type_OPair(_1577566, _1577566), _1577570), _1577568)), c_Transitive__Closure_Ortrancl(_1577566, hAPP(c_Relation_Oconverse(_1577566, _1577566), _1577572)))))], (40717 ^ _784416) ^ [_1577747, _1577749, _1577751, _1577753] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577747, _1577747)), hAPP(hAPP(c_Product__Type_OPair(_1577747, _1577747), _1577749), _1577751)), c_Transitive__Closure_Ortrancl(_1577747, hAPP(c_Relation_Oconverse(_1577747, _1577747), _1577753)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577747, _1577747)), hAPP(hAPP(c_Product__Type_OPair(_1577747, _1577747), _1577751), _1577749)), c_Transitive__Closure_Ortrancl(_1577747, _1577753))))], (40723 ^ _784416) ^ [_1577928, _1577930, _1577932, _1577934] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577928, _1577928)), hAPP(hAPP(c_Product__Type_OPair(_1577928, _1577928), _1577930), _1577932)), c_Transitive__Closure_Otrancl(_1577928, hAPP(c_Relation_Oconverse(_1577928, _1577928), _1577934)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577928, _1577928)), hAPP(hAPP(c_Product__Type_OPair(_1577928, _1577928), _1577930), _1577932)), hAPP(c_Relation_Oconverse(_1577928, _1577928), c_Transitive__Closure_Otrancl(_1577928, _1577934)))))], (40729 ^ _784416) ^ [_1578121, _1578123, _1578125, _1578127] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578121, _1578121)), hAPP(hAPP(c_Product__Type_OPair(_1578121, _1578121), _1578123), _1578125)), hAPP(c_Relation_Oconverse(_1578121, _1578121), c_Transitive__Closure_Otrancl(_1578121, _1578127)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578121, _1578121)), hAPP(hAPP(c_Product__Type_OPair(_1578121, _1578121), _1578123), _1578125)), c_Transitive__Closure_Otrancl(_1578121, hAPP(c_Relation_Oconverse(_1578121, _1578121), _1578127)))))], (40735 ^ _784416) ^ [_1578338, _1578340, _1578342, _1578344, _1578346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1578338, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1578340, _1578338, _1578342), _1578344)), _1578346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1578340, tc_HOL_Obool)), _1578344), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1578340, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1578338, _1578340, hAPP(c_Relation_Oconverse(_1578340, _1578338), _1578342)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1578338, tc_HOL_Obool)), _1578346))))))], (40741 ^ _784416) ^ [_1578529, _1578531, _1578533, _1578535, _1578537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1578531, tc_HOL_Obool)), _1578535), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1578531, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1578529, _1578531, hAPP(c_Relation_Oconverse(_1578531, _1578529), _1578533)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1578529, tc_HOL_Obool)), _1578537))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1578529, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1578531, _1578529, _1578533), _1578535)), _1578537)))], (40747 ^ _784416) ^ [_1578726, _1578728, _1578730] : [c_Relation_Orefl__on(_1578726, _1578728, _1578730), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1578726, _1578726), tc_HOL_Obool)), _1578730), hAPP(hAPP(c_Relation_Orel__comp(_1578726, _1578726, _1578726), hAPP(c_Relation_Oconverse(_1578726, _1578726), _1578730)), _1578730))))], (40753 ^ _784416) ^ [_1578865, _1578867, _1578869] : [hAPP(hAPP(c_Relation_Orel__comp(_1578865, _1578865, _1578865), hAPP(c_Relation_Oconverse(_1578865, _1578865), _1578867)), _1578867) = _1578867, hAPP(c_Relation_ODomain(_1578865, _1578865), _1578867) = _1578869, -(c_Equiv__Relations_Oequiv(_1578865, _1578869, _1578867))], (40763 ^ _784416) ^ [_1579044, _1579046] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1579044, _1579044)), _1579046)), c_Wellfounded_Oacyclic(_1579044, _1579046), -(c_Wellfounded_Owf(_1579044, hAPP(c_Relation_Oconverse(_1579044, _1579044), _1579046)))], (40795 ^ _784416) ^ [_1579706, _1579708, _1579710] : [40797 ^ _784416 : [(40798 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1579706), 40796 ^ [_1579706, _1579708, _1579710]), _1579708)))], (40801 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1579706), 40799 ^ [_1579706, _1579708, _1579710]), _1579708)))], (40803 ^ _784416) ^ [] : [40796 ^ [_1579706, _1579708, _1579710] = 40799 ^ [_1579706, _1579708, _1579710]], (40805 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579706, _1579706)), hAPP(hAPP(c_Product__Type_OPair(_1579706, _1579706), 40796 ^ [_1579706, _1579708, _1579710]), 40799 ^ [_1579706, _1579708, _1579710])), _1579710))], (40807 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579706, _1579706)), hAPP(hAPP(c_Product__Type_OPair(_1579706, _1579706), 40799 ^ [_1579706, _1579708, _1579710]), 40796 ^ [_1579706, _1579708, _1579710])), _1579710))]], -(c_Relation_Ototal__on(_1579706, _1579708, _1579710))], (40773 ^ _784416) ^ [_1579217, _1579219, _1579221] : [c_Relation_Ototal__on(_1579217, _1579219, _1579221), 40776 ^ _784416 : [(40777 ^ _784416) ^ [_1579361] : [hBOOL(hAPP(hAPP(c_member(_1579217), _1579361), _1579219)), 40780 ^ _784416 : [(40781 ^ _784416) ^ [_1579501] : [hBOOL(hAPP(hAPP(c_member(_1579217), _1579501), _1579219)), -(_1579361 = _1579501), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579217, _1579217)), hAPP(hAPP(c_Product__Type_OPair(_1579217, _1579217), _1579361), _1579501)), _1579221))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579217, _1579217)), hAPP(hAPP(c_Product__Type_OPair(_1579217, _1579217), _1579501), _1579361)), _1579221)))]]]]], (40811 ^ _784416) ^ [_1580288, _1580290, _1580292] : [-(hAPP(c_Relation_Oconverse(_1580288, _1580290), _1580292) = hAPP(c_Set_OCollect(tc_prod(_1580290, _1580288)), hAPP(c_Product__Type_Oprod_Oprod__case(_1580290, _1580288, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1580290, tc_fun(tc_prod(_1580288, _1580290), tc_HOL_Obool), tc_fun(_1580288, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1580288, tc_fun(tc_fun(tc_prod(_1580288, _1580290), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1580288, _1580290), tc_HOL_Obool), tc_fun(_1580288, tc_HOL_Obool)), _1580290), c_COMBC(_1580288, tc_fun(tc_prod(_1580288, _1580290), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1580288, tc_prod(_1580288, _1580290)), tc_fun(_1580288, tc_fun(tc_fun(tc_prod(_1580288, _1580290), tc_HOL_Obool), tc_HOL_Obool)), _1580290), hAPP(c_COMBB(tc_prod(_1580288, _1580290), tc_fun(tc_fun(tc_prod(_1580288, _1580290), tc_HOL_Obool), tc_HOL_Obool), _1580288), c_member(tc_prod(_1580288, _1580290)))), hAPP(c_COMBC(_1580288, _1580290, tc_prod(_1580288, _1580290)), c_Product__Type_OPair(_1580288, _1580290))))), _1580292))))], (40813 ^ _784416) ^ [_1580464, _1580466, _1580468] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580464, _1580464)), _1580466), c_Transitive__Closure_Ortrancl(_1580464, _1580468))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580464, _1580464)), _1580466), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1580464, _1580464), 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(_1580464, _1580464), tc_HOL_Obool), tc_fun(tc_prod(_1580464, _1580464), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1580464, _1580464), tc_HOL_Obool)), _1580468)))))], (40819 ^ _784416) ^ [_1580671, _1580673] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580671, _1580671)), hAPP(hAPP(c_Product__Type_OPair(_1580671, _1580671), 40820 ^ [_1580671, _1580673]), 40820 ^ [_1580671, _1580673])), c_Transitive__Closure_Otrancl(_1580671, _1580673)))), -(c_Wellfounded_Oacyclic(_1580671, _1580673))], (40826 ^ _784416) ^ [_1580743, _1580745, _1580747, _1580749, _1580751] : [c_Relation_Osingle__valued(_1580743, _1580745, hAPP(c_Relation_Oconverse(_1580745, _1580743), _1580747)), -(hAPP(c_Relation_OImage(_1580745, _1580743, _1580747), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1580745, tc_HOL_Obool)), _1580749), _1580751)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1580743, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1580745, _1580743, _1580747), _1580749)), hAPP(c_Relation_OImage(_1580745, _1580743, _1580747), _1580751)))], (40832 ^ _784416) ^ [_1580926, _1580928, _1580930, _1580932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580926, _1580928), tc_HOL_Obool)), _1580930), _1580932)), c_Relation_Osingle__valued(_1580926, _1580928, _1580932), -(c_Relation_Osingle__valued(_1580926, _1580928, _1580930))], (40842 ^ _784416) ^ [_1581093, _1581095, _1581097, _1581099, _1581101] : [c_Relation_Osingle__valued(_1581093, _1581095, _1581097), c_Relation_Osingle__valued(_1581095, _1581099, _1581101), -(c_Relation_Osingle__valued(_1581093, _1581099, hAPP(hAPP(c_Relation_Orel__comp(_1581093, _1581095, _1581099), _1581097), _1581101)))], (40852 ^ _784416) ^ [_1581260, _1581262, _1581264] : [c_Wellfounded_Owf(_1581260, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581260, _1581260), tc_HOL_Obool), _1581262), _1581264)), -(c_Wellfounded_Owf(_1581260, _1581264))], (40858 ^ _784416) ^ [_1581363, _1581365, _1581367, _1581369] : [-(hAPP(_1581363, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1581365, _1581365), _1581367), _1581363), _1581369)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1581365, _1581365), _1581367), _1581363), hAPP(_1581363, _1581369)))], (40860 ^ _784416) ^ [_1581422, _1581424, _1581426, _1581428] : [-(hAPP(hAPP(c_Nat_Ocompow(_1581422, _1581422), _1581424), hAPP(hAPP(c_Nat_Ocompow(_1581422, _1581422), _1581426), _1581428)) = hAPP(hAPP(c_Nat_Ocompow(_1581422, _1581422), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1581426), _1581424)), _1581428))], (40862 ^ _784416) ^ [_1581484, _1581486, _1581488, _1581490] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1581484, _1581486), tc_fun(_1581484, _1581486)), _1581488), c_Fun_Ocomp(_1581486, _1581486, _1581484, _1581490)) = c_Fun_Ocomp(_1581486, _1581486, _1581484, hAPP(hAPP(c_Nat_Ocompow(_1581486, _1581486), _1581488), _1581490)))], (40864 ^ _784416) ^ [_1581547, _1581549, _1581551] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1581547, _1581547, _1581547), _1581549), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581547, _1581547), tc_HOL_Obool), _1581551), _1581549)) = hAPP(hAPP(c_Relation_Orel__comp(_1581547, _1581547, _1581547), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581547, _1581547), tc_HOL_Obool), _1581551), _1581549)), _1581549))], (40866 ^ _784416) ^ [_1581618, _1581620] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581618, _1581618), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1581620) = _1581620)], (40868 ^ _784416) ^ [_1581655, _1581657, _1581659] : [c_Relation_Osingle__valued(_1581655, _1581655, _1581657), -(c_Relation_Osingle__valued(_1581655, _1581655, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581655, _1581655), tc_HOL_Obool), _1581659), _1581657)))], (40874 ^ _784416) ^ [_1581762] : [-(c_Relation_Osingle__valued(_1581762, _1581762, c_Relation_OId(_1581762)))], (40876 ^ _784416) ^ [_1581788, _1581790, _1581792, _1581794] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581788, _1581788)), _1581790), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581788, _1581788), tc_HOL_Obool), _1581792), _1581794))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581788, _1581788)), _1581790), c_Transitive__Closure_Ortrancl(_1581788, _1581794))))], (40882 ^ _784416) ^ [_1581957, _1581959, _1581961] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581957, _1581957)), _1581959), c_Transitive__Closure_Ortrancl(_1581957, _1581961))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581957, _1581957)), _1581959), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1581957, _1581957), tc_HOL_Obool), 40885 ^ [_1581957, _1581959, _1581961]), _1581961))))], (40889 ^ _784416) ^ [_1582116, _1582118, _1582120] : [40890 ^ _784416 : [(40891 ^ _784416) ^ [_1582192] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582116, _1582116)), _1582118), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582116, _1582116), tc_HOL_Obool), _1582192), _1582120)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582116, _1582116)), _1582118), c_Transitive__Closure_Ortrancl(_1582116, _1582120))))], (40895 ^ _784416) ^ [_1582280, _1582282] : [-(c_Relation_Osingle__valued(_1582280, _1582280, c_Relation_OId__on(_1582280, _1582282)))], (40897 ^ _784416) ^ [_1582309, _1582311, _1582313] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582309, _1582309), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1582311)), _1582313) = hAPP(hAPP(c_Relation_Orel__comp(_1582309, _1582309, _1582309), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582309, _1582309), tc_HOL_Obool), _1582311), _1582313)), _1582313))], (40899 ^ _784416) ^ [_1582373, _1582375, _1582377, _1582379] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582373, _1582373), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1582375), _1582377)), _1582379) = hAPP(hAPP(c_Relation_Orel__comp(_1582373, _1582373, _1582373), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582373, _1582373), tc_HOL_Obool), _1582375), _1582379)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582373, _1582373), tc_HOL_Obool), _1582377), _1582379)))], (40901 ^ _784416) ^ [_1582454, _1582456] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582454, _1582454), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1582456) = c_Relation_OId(_1582454))], (40903 ^ _784416) ^ [_1582493, _1582495, _1582497] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582493, _1582493)), hAPP(hAPP(c_Product__Type_OPair(_1582493, _1582493), _1582495), _1582495)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582493, _1582493), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1582497))))], (40905 ^ _784416) ^ [_1582551, _1582553, _1582555, _1582557] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582551, _1582551)), hAPP(hAPP(c_Product__Type_OPair(_1582551, _1582551), _1582553), _1582555)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582551, _1582551), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1582557))), -(_1582553 = _1582555)], (40911 ^ _784416) ^ [_1582694, _1582696, _1582698, _1582700, _1582702, _1582704] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582694, _1582694)), hAPP(hAPP(c_Product__Type_OPair(_1582694, _1582694), _1582696), _1582698)), _1582700)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1582694, _1582694)), hAPP(hAPP(c_Product__Type_OPair(_1582694, _1582694), _1582698), _1582702)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582694, _1582694), tc_HOL_Obool), _1582704), _1582700))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582694, _1582694)), hAPP(hAPP(c_Product__Type_OPair(_1582694, _1582694), _1582696), _1582702)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582694, _1582694), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1582704)), _1582700))))], (40921 ^ _784416) ^ [_1583007, _1583009, _1583011, _1583013, _1583015, _1583017] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583007, _1583007)), hAPP(hAPP(c_Product__Type_OPair(_1583007, _1583007), _1583009), _1583011)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583007, _1583007), tc_HOL_Obool), _1583013), _1583015))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583007, _1583007)), hAPP(hAPP(c_Product__Type_OPair(_1583007, _1583007), _1583011), _1583017)), _1583015)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583007, _1583007)), hAPP(hAPP(c_Product__Type_OPair(_1583007, _1583007), _1583009), _1583017)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583007, _1583007), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1583013)), _1583015))))], (40931 ^ _784416) ^ [_1583320, _1583322, _1583324] : [-(hAPP(hAPP(c_Nat_Ocompow(_1583320, _1583320), hAPP(c_Nat_OSuc, _1583322)), _1583324) = hAPP(c_Fun_Ocomp(_1583320, _1583320, _1583320, _1583324), hAPP(hAPP(c_Nat_Ocompow(_1583320, _1583320), _1583322), _1583324)))], (40933 ^ _784416) ^ [_1583376, _1583378, _1583380, _1583382] : [-(hAPP(hAPP(c_Nat_Ocompow(_1583376, _1583376), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1583378), _1583380)), _1583382) = hAPP(c_Fun_Ocomp(_1583376, _1583376, _1583376, hAPP(hAPP(c_Nat_Ocompow(_1583376, _1583376), _1583378), _1583382)), hAPP(hAPP(c_Nat_Ocompow(_1583376, _1583376), _1583380), _1583382)))], (40949 ^ _784416) ^ [_1583838, _1583840, _1583842] : [40952 ^ _784416 : [(40953 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583838, _1583840)), hAPP(hAPP(c_Product__Type_OPair(_1583838, _1583840), 40950 ^ [_1583838, _1583840, _1583842]), 40951 ^ [_1583838, _1583840, _1583842])), _1583842)))], (40956 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583838, _1583840)), hAPP(hAPP(c_Product__Type_OPair(_1583838, _1583840), 40950 ^ [_1583838, _1583840, _1583842]), 40954 ^ [_1583838, _1583840, _1583842])), _1583842)))], (40958 ^ _784416) ^ [] : [40951 ^ [_1583838, _1583840, _1583842] = 40954 ^ [_1583838, _1583840, _1583842]]], -(c_Relation_Osingle__valued(_1583838, _1583840, _1583842))], (40935 ^ _784416) ^ [_1583464, _1583466, _1583468] : [c_Relation_Osingle__valued(_1583464, _1583466, _1583468), 40938 ^ _784416 : [(40939 ^ _784416) ^ [_1583585, _1583587] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583464, _1583466)), hAPP(hAPP(c_Product__Type_OPair(_1583464, _1583466), _1583587), _1583585)), _1583468)), 40942 ^ _784416 : [(40943 ^ _784416) ^ [_1583711] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583464, _1583466)), hAPP(hAPP(c_Product__Type_OPair(_1583464, _1583466), _1583587), _1583711)), _1583468)), -(_1583585 = _1583711)]]]]], (40962 ^ _784416) ^ [_1584208, _1584210, _1584212, _1584214, _1584216, _1584218] : [c_Relation_Osingle__valued(_1584208, _1584210, _1584212), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584208, _1584210)), hAPP(hAPP(c_Product__Type_OPair(_1584208, _1584210), _1584214), _1584216)), _1584212)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584208, _1584210)), hAPP(hAPP(c_Product__Type_OPair(_1584208, _1584210), _1584214), _1584218)), _1584212)), -(_1584216 = _1584218)], (40976 ^ _784416) ^ [_1584491, _1584493] : [-(hAPP(hAPP(c_Nat_Ocompow(_1584491, _1584491), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1584493) = c_Fun_Oid(_1584491))], (40978 ^ _784416) ^ [_1584545, _1584547, _1584549] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584545, _1584545)), _1584547), c_Transitive__Closure_Otrancl(_1584545, _1584549))), 40982 ^ _784416 : [(40983 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 40981 ^ [_1584545, _1584547, _1584549])))], (40985 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584545, _1584545)), _1584547), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584545, _1584545), tc_HOL_Obool), 40981 ^ [_1584545, _1584547, _1584549]), _1584549))))]]], (40987 ^ _784416) ^ [_1584743, _1584745, _1584747] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584743, _1584743)), _1584745), c_Transitive__Closure_Otrancl(_1584743, _1584747)))), 40988 ^ _784416 : [(40989 ^ _784416) ^ [_1584822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1584822)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584743, _1584743)), _1584745), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584743, _1584743), tc_HOL_Obool), _1584822), _1584747)))]]], (40997 ^ _784416) ^ [_1584993, _1584995] : [-(c_Transitive__Closure_Ortrancl(_1584993, _1584995) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1584993, _1584993), 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(_1584993, _1584993), tc_HOL_Obool), tc_fun(tc_prod(_1584993, _1584993), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1584993, _1584993), tc_HOL_Obool)), _1584995)))], (40999 ^ _784416) ^ [_1585064, _1585066, _1585068, _1585070, _1585072] : [c_Relation_Osingle__valued(_1585064, _1585064, _1585066), hBOOL(hAPP(hAPP(c_member(tc_prod(_1585064, _1585064)), hAPP(hAPP(c_Product__Type_OPair(_1585064, _1585064), _1585068), _1585070)), c_Transitive__Closure_Ortrancl(_1585064, _1585066))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1585064, _1585064)), hAPP(hAPP(c_Product__Type_OPair(_1585064, _1585064), _1585068), _1585072)), c_Transitive__Closure_Ortrancl(_1585064, _1585066))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585064, _1585064)), hAPP(hAPP(c_Product__Type_OPair(_1585064, _1585064), _1585070), _1585072)), c_Transitive__Closure_Ortrancl(_1585064, _1585066)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585064, _1585064)), hAPP(hAPP(c_Product__Type_OPair(_1585064, _1585064), _1585072), _1585070)), c_Transitive__Closure_Ortrancl(_1585064, _1585066))))], (41017 ^ _784416) ^ [_1585454] : [-(c_Nat_Ofunpow(_1585454) = c_Nat_Ocompow(_1585454, _1585454))], (41019 ^ _784416) ^ [_1585482, _1585484, _1585486, _1585488, _1585490] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585482, _1585482)), hAPP(hAPP(c_Product__Type_OPair(_1585482, _1585482), _1585484), _1585486)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585482, _1585482), tc_HOL_Obool), _1585488), _1585490))), 41024 ^ _784416 : [(41025 ^ _784416) ^ [] : [-(_1585488 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41027 ^ _784416) ^ [] : [-(_1585484 = _1585486)]], 41030 ^ _784416 : [(41031 ^ _784416) ^ [] : [-(_1585488 = hAPP(c_Nat_OSuc, 41029 ^ [_1585482, _1585484, _1585486, _1585488, _1585490]))], (41033 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585482, _1585482)), hAPP(hAPP(c_Product__Type_OPair(_1585482, _1585482), _1585484), 41028 ^ [_1585482, _1585484, _1585486, _1585488, _1585490])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585482, _1585482), tc_HOL_Obool), 41029 ^ [_1585482, _1585484, _1585486, _1585488, _1585490]), _1585490))))], (41035 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585482, _1585482)), hAPP(hAPP(c_Product__Type_OPair(_1585482, _1585482), 41028 ^ [_1585482, _1585484, _1585486, _1585488, _1585490]), _1585486)), _1585490)))]]], (41037 ^ _784416) ^ [_1585924, _1585926, _1585928, _1585930, _1585932] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585924, _1585924)), hAPP(hAPP(c_Product__Type_OPair(_1585924, _1585924), _1585926), _1585928)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585924, _1585924), tc_HOL_Obool), _1585930), _1585932))), 41042 ^ _784416 : [(41043 ^ _784416) ^ [] : [-(_1585930 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41045 ^ _784416) ^ [] : [-(_1585926 = _1585928)]], 41048 ^ _784416 : [(41049 ^ _784416) ^ [] : [-(_1585930 = hAPP(c_Nat_OSuc, 41047 ^ [_1585924, _1585926, _1585928, _1585930, _1585932]))], (41051 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585924, _1585924)), hAPP(hAPP(c_Product__Type_OPair(_1585924, _1585924), _1585926), 41046 ^ [_1585924, _1585926, _1585928, _1585930, _1585932])), _1585932)))], (41053 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585924, _1585924)), hAPP(hAPP(c_Product__Type_OPair(_1585924, _1585924), 41046 ^ [_1585924, _1585926, _1585928, _1585930, _1585932]), _1585928)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585924, _1585924), tc_HOL_Obool), 41047 ^ [_1585924, _1585926, _1585928, _1585930, _1585932]), _1585932))))]]], (41055 ^ _784416) ^ [_1586366, _1586368, _1586370, _1586372, _1586374] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586366, _1586366)), hAPP(hAPP(c_Product__Type_OPair(_1586366, _1586366), _1586368), _1586370)), c_Transitive__Closure_Ortrancl(_1586366, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1586366, _1586366), tc_HOL_Obool)), _1586372), _1586374)))), 41061 ^ _784416 : [(41062 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586366, _1586366)), hAPP(hAPP(c_Product__Type_OPair(_1586366, _1586366), 41060 ^ [_1586366, _1586368, _1586370, _1586372, _1586374]), _1586370)), c_Transitive__Closure_Ortrancl(_1586366, _1586372))))], (41065 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586366, _1586366)), hAPP(hAPP(c_Product__Type_OPair(_1586366, _1586366), 41063 ^ [_1586366, _1586368, _1586370, _1586372, _1586374]), 41060 ^ [_1586366, _1586368, _1586370, _1586372, _1586374])), _1586374)))], (41067 ^ _784416) ^ [] : [41063 ^ [_1586366, _1586368, _1586370, _1586372, _1586374] = 41060 ^ [_1586366, _1586368, _1586370, _1586372, _1586374]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586366, _1586366)), hAPP(hAPP(c_Product__Type_OPair(_1586366, _1586366), _1586368), _1586370)), c_Transitive__Closure_Ortrancl(_1586366, _1586372))))], (41071 ^ _784416) ^ [_1586925, _1586927, _1586929, _1586931, _1586933] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586925, _1586925)), hAPP(hAPP(c_Product__Type_OPair(_1586925, _1586925), _1586927), _1586929)), c_Transitive__Closure_Ortrancl(_1586925, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1586925, _1586925), tc_HOL_Obool)), _1586931), _1586933)))), 41077 ^ _784416 : [(41078 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586925, _1586925)), hAPP(hAPP(c_Product__Type_OPair(_1586925, _1586925), _1586927), 41076 ^ [_1586925, _1586927, _1586929, _1586931, _1586933])), c_Transitive__Closure_Ortrancl(_1586925, _1586931))))], (41081 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586925, _1586925)), hAPP(hAPP(c_Product__Type_OPair(_1586925, _1586925), 41076 ^ [_1586925, _1586927, _1586929, _1586931, _1586933]), 41079 ^ [_1586925, _1586927, _1586929, _1586931, _1586933])), _1586933)))], (41083 ^ _784416) ^ [] : [41076 ^ [_1586925, _1586927, _1586929, _1586931, _1586933] = 41079 ^ [_1586925, _1586927, _1586929, _1586931, _1586933]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586925, _1586925)), hAPP(hAPP(c_Product__Type_OPair(_1586925, _1586925), _1586927), _1586929)), c_Transitive__Closure_Ortrancl(_1586925, _1586931))))], (41087 ^ _784416) ^ [_1587484, _1587486, _1587488, _1587490, _1587492] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587484, _1587484)), hAPP(hAPP(c_Product__Type_OPair(_1587484, _1587484), _1587486), _1587488)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1587484, _1587484), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1587490)), _1587492))), 41091 ^ _784416 : [(41092 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587484, _1587484)), hAPP(hAPP(c_Product__Type_OPair(_1587484, _1587484), _1587486), 41090 ^ [_1587484, _1587486, _1587488, _1587490, _1587492])), _1587492)))], (41094 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587484, _1587484)), hAPP(hAPP(c_Product__Type_OPair(_1587484, _1587484), 41090 ^ [_1587484, _1587486, _1587488, _1587490, _1587492]), _1587488)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1587484, _1587484), tc_HOL_Obool), _1587490), _1587492))))]]], (41096 ^ _784416) ^ [_1587792, _1587794, _1587796, _1587798, _1587800] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587792, _1587792)), hAPP(hAPP(c_Product__Type_OPair(_1587792, _1587792), _1587794), _1587796)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1587792, _1587792), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1587798)), _1587800))), 41100 ^ _784416 : [(41101 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587792, _1587792)), hAPP(hAPP(c_Product__Type_OPair(_1587792, _1587792), _1587794), 41099 ^ [_1587792, _1587794, _1587796, _1587798, _1587800])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1587792, _1587792), tc_HOL_Obool), _1587798), _1587800))))], (41103 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587792, _1587792)), hAPP(hAPP(c_Product__Type_OPair(_1587792, _1587792), 41099 ^ [_1587792, _1587794, _1587796, _1587798, _1587800]), _1587796)), _1587800)))]]], (41105 ^ _784416) ^ [_1588104, _1588106, _1588108, _1588110, _1588112] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588104, _1588104)), hAPP(hAPP(c_Product__Type_OPair(_1588104, _1588104), _1588106), _1588108)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1588104, _1588104), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1588110)), _1588112))), 41109 ^ _784416 : [(41110 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588104, _1588104)), hAPP(hAPP(c_Product__Type_OPair(_1588104, _1588104), _1588106), 41108 ^ [_1588104, _1588106, _1588108, _1588110, _1588112])), _1588112)))], (41112 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588104, _1588104)), hAPP(hAPP(c_Product__Type_OPair(_1588104, _1588104), 41108 ^ [_1588104, _1588106, _1588108, _1588110, _1588112]), _1588108)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1588104, _1588104), tc_HOL_Obool), _1588110), _1588112))))]]], (41114 ^ _784416) ^ [_1588416, _1588418, _1588420, _1588422] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588416, _1588416)), hAPP(hAPP(c_Product__Type_OPair(_1588416, _1588416), _1588418), _1588420)), c_Transitive__Closure_Otrancl(_1588416, _1588422))), 41118 ^ _784416 : [(41119 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588416, _1588416)), hAPP(hAPP(c_Product__Type_OPair(_1588416, _1588416), _1588418), 41117 ^ [_1588416, _1588418, _1588420, _1588422])), _1588422)))], (41121 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588416, _1588416)), hAPP(hAPP(c_Product__Type_OPair(_1588416, _1588416), 41117 ^ [_1588416, _1588418, _1588420, _1588422]), _1588420)), c_Transitive__Closure_Ortrancl(_1588416, _1588422))))]]], (41123 ^ _784416) ^ [_1588676, _1588678, _1588680, _1588682] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588676, _1588676)), hAPP(hAPP(c_Product__Type_OPair(_1588676, _1588676), _1588678), _1588680)), c_Transitive__Closure_Otrancl(_1588676, _1588682))), 41127 ^ _784416 : [(41128 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588676, _1588676)), hAPP(hAPP(c_Product__Type_OPair(_1588676, _1588676), _1588678), 41126 ^ [_1588676, _1588678, _1588680, _1588682])), c_Transitive__Closure_Ortrancl(_1588676, _1588682))))], (41130 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588676, _1588676)), hAPP(hAPP(c_Product__Type_OPair(_1588676, _1588676), 41126 ^ [_1588676, _1588678, _1588680, _1588682]), _1588680)), _1588682)))]]], (41132 ^ _784416) ^ [_1588936, _1588938] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588936, _1588936)), _1588938), c_Relation_OId(_1588936))), -(_1588938 = hAPP(hAPP(c_Product__Type_OPair(_1588936, _1588936), 41135 ^ [_1588936, _1588938]), 41135 ^ [_1588936, _1588938]))], (41139 ^ _784416) ^ [_1589078, _1589080, _1589082, _1589084] : [41141 ^ _784416 : [(41142 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1589078), 41140 ^ [_1589078, _1589080, _1589082, _1589084])))], (41144 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41140 ^ [_1589078, _1589080, _1589082, _1589084]), _1589080)))], (41146 ^ _784416) ^ [] : [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(_1589082, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 41140 ^ [_1589078, _1589080, _1589082, _1589084]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1589082, 41140 ^ [_1589078, _1589080, _1589082, _1589084])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1589078), _1589080)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1589082, _1589078)), _1589084)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1589084), hAPP(_1589082, _1589080))), 41160 ^ _784416 : [(41161 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1589078), 41159 ^ [_1589078, _1589080, _1589082, _1589084])))], (41163 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41159 ^ [_1589078, _1589080, _1589082, _1589084]), _1589080)))], (41165 ^ _784416) ^ [] : [-(hAPP(_1589082, 41159 ^ [_1589078, _1589080, _1589082, _1589084]) = _1589084)]]], (41167 ^ _784416) ^ [_1589704, _1589706, _1589708] : [class_Orderings_Olinorder(_1589704), hBOOL(hAPP(c_Finite__Set_Ofinite(_1589704), _1589706)), -(hBOOL(hAPP(hAPP(c_member(_1589704), _1589708), _1589706))), -(c_Big__Operators_Olattice_OSup__fin(_1589704, c_Orderings_Oord__class_Omax(_1589704), hAPP(hAPP(c_Set_Oinsert(_1589704), _1589708), _1589706)) = hAPP(hAPP(c_Finite__Set_Ofold(_1589704, _1589704, c_Orderings_Oord__class_Omax(_1589704)), _1589708), _1589706))], (41181 ^ _784416) ^ [_1589924, _1589926, _1589928] : [class_Orderings_Olinorder(_1589924), hBOOL(hAPP(c_Finite__Set_Ofinite(_1589924), _1589926)), -(hBOOL(hAPP(hAPP(c_member(_1589924), _1589928), _1589926))), -(c_Big__Operators_Olattice_OInf__fin(_1589924, c_Orderings_Oord__class_Omin(_1589924), hAPP(hAPP(c_Set_Oinsert(_1589924), _1589928), _1589926)) = hAPP(hAPP(c_Finite__Set_Ofold(_1589924, _1589924, c_Orderings_Oord__class_Omin(_1589924)), _1589928), _1589926))], (41195 ^ _784416) ^ [_1590144, _1590146, _1590148, _1590150] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1590144, _1590146, _1590148), _1590150), c_Orderings_Obot__class_Obot(tc_fun(_1590144, tc_HOL_Obool))) = _1590150)], (41197 ^ _784416) ^ [_1590188, _1590190, _1590192, _1590194] : [-(hAPP(c_Finite__Set_Ofold__image(_1590188, _1590190, _1590192), _1590194) = c_Finite__Set_Ofold(_1590190, _1590188, hAPP(hAPP(c_COMBB(_1590188, tc_fun(_1590188, _1590188), _1590190), _1590192), _1590194)))], (41199 ^ _784416) ^ [_1590241, _1590243, _1590245, _1590247, _1590249, _1590251] : [c_Finite__Set_Ofolding(_1590241, _1590243, _1590245, _1590247), hBOOL(hAPP(c_Finite__Set_Ofinite(_1590241), _1590249)), -(hAPP(hAPP(_1590247, _1590249), _1590251) = hAPP(hAPP(c_Finite__Set_Ofold(_1590241, _1590243, _1590245), _1590251), _1590249))], (41209 ^ _784416) ^ [_1590430, _1590432, _1590434, _1590436, _1590438] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1590430, _1590432, _1590434), _1590436), _1590438) = c_HOL_OThe(_1590432, c_Finite__Set_Ofold__graph(_1590430, _1590432, _1590434, _1590436, _1590438)))], (41211 ^ _784416) ^ [_1590480, _1590482, _1590484] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1590480), _1590482)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1590480, tc_HOL_Obool)), _1590482), _1590484) = hAPP(hAPP(c_Finite__Set_Ofold(_1590480, tc_fun(_1590480, tc_HOL_Obool), c_Set_Oinsert(_1590480)), _1590484), _1590482))], (41217 ^ _784416) ^ [_1590619, _1590621, _1590623, _1590625] : [class_Lattices_Osemilattice__sup(_1590619), hBOOL(hAPP(c_Finite__Set_Ofinite(_1590619), _1590621)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1590619, _1590619, c_Lattices_Osemilattice__sup__class_Osup(_1590619)), _1590623), hAPP(hAPP(c_Set_Oinsert(_1590619), _1590625), _1590621)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1590619), _1590625), hAPP(hAPP(c_Finite__Set_Ofold(_1590619, _1590619, c_Lattices_Osemilattice__sup__class_Osup(_1590619)), _1590623), _1590621)))], (41227 ^ _784416) ^ [_1590842, _1590844, _1590846, _1590848] : [class_Lattices_Osemilattice__inf(_1590842), hBOOL(hAPP(c_Finite__Set_Ofinite(_1590842), _1590844)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1590842, _1590842, c_Lattices_Osemilattice__inf__class_Oinf(_1590842)), _1590846), hAPP(hAPP(c_Set_Oinsert(_1590842), _1590848), _1590844)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1590842), _1590848), hAPP(hAPP(c_Finite__Set_Ofold(_1590842, _1590842, c_Lattices_Osemilattice__inf__class_Oinf(_1590842)), _1590846), _1590844)))], (41237 ^ _784416) ^ [_1591065, _1591067, _1591069, _1591071] : [class_Orderings_Olinorder(_1591065), hBOOL(hAPP(c_Finite__Set_Ofinite(_1591065), _1591067)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1591065, _1591065, c_Orderings_Oord__class_Omin(_1591065)), _1591069), hAPP(hAPP(c_Set_Oinsert(_1591065), _1591071), _1591067)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1591065), _1591071), hAPP(hAPP(c_Finite__Set_Ofold(_1591065, _1591065, c_Orderings_Oord__class_Omin(_1591065)), _1591069), _1591067)))], (41247 ^ _784416) ^ [_1591288, _1591290, _1591292, _1591294] : [class_Orderings_Olinorder(_1591288), hBOOL(hAPP(c_Finite__Set_Ofinite(_1591288), _1591290)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1591288, _1591288, c_Orderings_Oord__class_Omax(_1591288)), _1591292), hAPP(hAPP(c_Set_Oinsert(_1591288), _1591294), _1591290)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1591288), _1591294), hAPP(hAPP(c_Finite__Set_Ofold(_1591288, _1591288, c_Orderings_Oord__class_Omax(_1591288)), _1591292), _1591290)))], (41257 ^ _784416) ^ [_1591511, _1591513, _1591515, _1591517, _1591519, _1591521] : [c_Finite__Set_Ofun__left__comm__idem(_1591511, _1591513, _1591515), hBOOL(hAPP(c_Finite__Set_Ofinite(_1591511), _1591517)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1591511, _1591513, _1591515), _1591519), hAPP(hAPP(c_Set_Oinsert(_1591511), _1591521), _1591517)) = hAPP(hAPP(_1591515, _1591521), hAPP(hAPP(c_Finite__Set_Ofold(_1591511, _1591513, _1591515), _1591519), _1591517)))], (41267 ^ _784416) ^ [_1591734, _1591736, _1591738, _1591740, _1591742, _1591744] : [c_Finite__Set_Ofun__left__comm__idem(_1591734, _1591736, _1591738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1591734), _1591740)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1591734, _1591736, _1591738), _1591742), hAPP(hAPP(c_Set_Oinsert(_1591734), _1591744), _1591740)) = hAPP(hAPP(c_Finite__Set_Ofold(_1591734, _1591736, _1591738), hAPP(hAPP(_1591738, _1591744), _1591742)), _1591740))], (41277 ^ _784416) ^ [_1591957, _1591959, _1591961, _1591963, _1591965] : [class_Complete__Lattice_Ocomplete__lattice(_1591957), hBOOL(hAPP(c_Finite__Set_Ofinite(_1591959), _1591961)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1591957), _1591963), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1591959, _1591957), _1591961), _1591965)) = hAPP(hAPP(c_Finite__Set_Ofold(_1591959, _1591957, hAPP(hAPP(c_COMBB(_1591957, tc_fun(_1591957, _1591957), _1591959), c_Lattices_Osemilattice__sup__class_Osup(_1591957)), _1591965)), _1591963), _1591961))], (41287 ^ _784416) ^ [_1592188, _1592190, _1592192, _1592194, _1592196] : [c_Finite__Set_Ofolding__one__idem(_1592188, _1592190, _1592192), hBOOL(hAPP(c_Finite__Set_Ofinite(_1592188), _1592194)), -(hAPP(_1592192, hAPP(hAPP(c_Set_Oinsert(_1592188), _1592196), _1592194)) = hAPP(hAPP(c_Finite__Set_Ofold(_1592188, _1592188, _1592190), _1592196), _1592194))], (41297 ^ _784416) ^ [_1592381, _1592383, _1592385, _1592387] : [class_Lattices_Osemilattice__sup(_1592381), hBOOL(hAPP(c_Finite__Set_Ofinite(_1592381), _1592383)), hBOOL(hAPP(hAPP(c_member(_1592381), _1592385), _1592383)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1592381), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1592381), _1592385), _1592387)), hAPP(hAPP(c_Finite__Set_Ofold(_1592381, _1592381, c_Lattices_Osemilattice__sup__class_Osup(_1592381)), _1592387), _1592383))))], (41311 ^ _784416) ^ [_1592648, _1592650, _1592652, _1592654] : [class_Lattices_Osemilattice__inf(_1592648), hBOOL(hAPP(c_Finite__Set_Ofinite(_1592648), _1592650)), hBOOL(hAPP(hAPP(c_member(_1592648), _1592652), _1592650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1592648), hAPP(hAPP(c_Finite__Set_Ofold(_1592648, _1592648, c_Lattices_Osemilattice__inf__class_Oinf(_1592648)), _1592654), _1592650)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1592648), _1592652), _1592654))))], (41325 ^ _784416) ^ [_1592915, _1592917, _1592919, _1592921] : [class_Orderings_Olinorder(_1592915), hBOOL(hAPP(c_Finite__Set_Ofinite(_1592915), _1592917)), hBOOL(hAPP(hAPP(c_member(_1592915), _1592919), _1592917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1592915), hAPP(hAPP(c_Finite__Set_Ofold(_1592915, _1592915, c_Orderings_Oord__class_Omin(_1592915)), _1592921), _1592917)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1592915), _1592919), _1592921))))], (41339 ^ _784416) ^ [_1593182, _1593184, _1593186, _1593188] : [class_Orderings_Olinorder(_1593182), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593182), _1593184)), hBOOL(hAPP(hAPP(c_member(_1593182), _1593186), _1593184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1593182), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1593182), _1593186), _1593188)), hAPP(hAPP(c_Finite__Set_Ofold(_1593182, _1593182, c_Orderings_Oord__class_Omax(_1593182)), _1593188), _1593184))))], (41353 ^ _784416) ^ [_1593449, _1593451, _1593453] : [class_Lattices_Oab__semigroup__idem__mult(_1593449), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593449), _1593451)), -(hAPP(c_Finite__Set_Ofold1(_1593449, c_Groups_Otimes__class_Otimes(_1593449)), hAPP(hAPP(c_Set_Oinsert(_1593449), _1593453), _1593451)) = hAPP(hAPP(c_Finite__Set_Ofold(_1593449, _1593449, c_Groups_Otimes__class_Otimes(_1593449)), _1593453), _1593451))], (41363 ^ _784416) ^ [_1593644, _1593646, _1593648] : [class_Lattices_Olattice(_1593644), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593644), _1593646)), -(c_Big__Operators_Olattice__class_OSup__fin(_1593644, hAPP(hAPP(c_Set_Oinsert(_1593644), _1593648), _1593646)) = hAPP(hAPP(c_Finite__Set_Ofold(_1593644, _1593644, c_Lattices_Osemilattice__sup__class_Osup(_1593644)), _1593648), _1593646))], (41373 ^ _784416) ^ [_1593829, _1593831, _1593833] : [class_Lattices_Olattice(_1593829), hBOOL(hAPP(c_Finite__Set_Ofinite(_1593829), _1593831)), -(c_Big__Operators_Olattice__class_OInf__fin(_1593829, hAPP(hAPP(c_Set_Oinsert(_1593829), _1593833), _1593831)) = hAPP(hAPP(c_Finite__Set_Ofold(_1593829, _1593829, c_Lattices_Osemilattice__inf__class_Oinf(_1593829)), _1593833), _1593831))], (41383 ^ _784416) ^ [_1594014, _1594016, _1594018] : [class_Orderings_Olinorder(_1594014), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594014), _1594016)), -(c_Big__Operators_Olinorder__class_OMin(_1594014, hAPP(hAPP(c_Set_Oinsert(_1594014), _1594018), _1594016)) = hAPP(hAPP(c_Finite__Set_Ofold(_1594014, _1594014, c_Orderings_Oord__class_Omin(_1594014)), _1594018), _1594016))], (41393 ^ _784416) ^ [_1594199, _1594201, _1594203] : [class_Orderings_Olinorder(_1594199), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594199), _1594201)), -(c_Big__Operators_Olinorder__class_OMax(_1594199, hAPP(hAPP(c_Set_Oinsert(_1594199), _1594203), _1594201)) = hAPP(hAPP(c_Finite__Set_Ofold(_1594199, _1594199, c_Orderings_Oord__class_Omax(_1594199)), _1594203), _1594201))], (41403 ^ _784416) ^ [_1594384, _1594386, _1594388] : [class_Orderings_Olinorder(_1594384), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594384), _1594386)), -(c_Big__Operators_Olattice_OInf__fin(_1594384, c_Orderings_Oord__class_Omin(_1594384), hAPP(hAPP(c_Set_Oinsert(_1594384), _1594388), _1594386)) = hAPP(hAPP(c_Finite__Set_Ofold(_1594384, _1594384, c_Orderings_Oord__class_Omin(_1594384)), _1594388), _1594386))], (41413 ^ _784416) ^ [_1594575, _1594577, _1594579] : [class_Orderings_Olinorder(_1594575), hBOOL(hAPP(c_Finite__Set_Ofinite(_1594575), _1594577)), -(c_Big__Operators_Olattice_OSup__fin(_1594575, c_Orderings_Oord__class_Omax(_1594575), hAPP(hAPP(c_Set_Oinsert(_1594575), _1594579), _1594577)) = hAPP(hAPP(c_Finite__Set_Ofold(_1594575, _1594575, c_Orderings_Oord__class_Omax(_1594575)), _1594579), _1594577))], (41423 ^ _784416) ^ [_1594766, _1594768, _1594770] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1594766), _1594768)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1594766, tc_HOL_Obool)), _1594770), _1594768) = hAPP(hAPP(c_Finite__Set_Ofold(_1594766, tc_fun(_1594766, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1594766, tc_HOL_Obool), tc_fun(tc_fun(_1594766, tc_HOL_Obool), tc_fun(_1594766, tc_HOL_Obool)), _1594766), hAPP(c_COMBC(tc_fun(_1594766, tc_HOL_Obool), tc_fun(_1594766, tc_HOL_Obool), tc_fun(_1594766, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1594766, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1594766, tc_fun(_1594766, tc_HOL_Obool), tc_fun(_1594766, tc_HOL_Obool)), c_Set_Oinsert(_1594766)), c_Orderings_Obot__class_Obot(tc_fun(_1594766, tc_HOL_Obool))))), _1594770), _1594768))], (41429 ^ _784416) ^ [_1595033, _1595035, _1595037, _1595039, _1595041] : [c_Finite__Set_Ofolding__one(_1595033, _1595035, _1595037), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595033), _1595039)), -(hBOOL(hAPP(hAPP(c_member(_1595033), _1595041), _1595039))), -(hAPP(_1595037, hAPP(hAPP(c_Set_Oinsert(_1595033), _1595041), _1595039)) = hAPP(hAPP(c_Finite__Set_Ofold(_1595033, _1595033, _1595035), _1595041), _1595039))], (41443 ^ _784416) ^ [_1595255, _1595257, _1595259, _1595261] : [class_Complete__Lattice_Ocomplete__lattice(_1595255), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595257), _1595259)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1595257, _1595255), _1595259), _1595261) = hAPP(hAPP(c_Finite__Set_Ofold(_1595257, _1595255, hAPP(hAPP(c_COMBB(_1595255, tc_fun(_1595255, _1595255), _1595257), c_Lattices_Osemilattice__sup__class_Osup(_1595255)), _1595261)), c_Orderings_Obot__class_Obot(_1595255)), _1595259))], (41453 ^ _784416) ^ [_1595470, _1595472, _1595474] : [class_Groups_Oab__semigroup__mult(_1595470), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595470), _1595472)), -(hBOOL(hAPP(hAPP(c_member(_1595470), _1595474), _1595472))), -(hAPP(c_Finite__Set_Ofold1(_1595470, c_Groups_Otimes__class_Otimes(_1595470)), hAPP(hAPP(c_Set_Oinsert(_1595470), _1595474), _1595472)) = hAPP(hAPP(c_Finite__Set_Ofold(_1595470, _1595470, c_Groups_Otimes__class_Otimes(_1595470)), _1595474), _1595472))], (41467 ^ _784416) ^ [_1595694, _1595696, _1595698] : [class_Lattices_Olattice(_1595694), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595694), _1595696)), -(hBOOL(hAPP(hAPP(c_member(_1595694), _1595698), _1595696))), -(c_Big__Operators_Olattice__class_OSup__fin(_1595694, hAPP(hAPP(c_Set_Oinsert(_1595694), _1595698), _1595696)) = hAPP(hAPP(c_Finite__Set_Ofold(_1595694, _1595694, c_Lattices_Osemilattice__sup__class_Osup(_1595694)), _1595698), _1595696))], (41481 ^ _784416) ^ [_1595908, _1595910, _1595912] : [class_Lattices_Olattice(_1595908), hBOOL(hAPP(c_Finite__Set_Ofinite(_1595908), _1595910)), -(hBOOL(hAPP(hAPP(c_member(_1595908), _1595912), _1595910))), -(c_Big__Operators_Olattice__class_OInf__fin(_1595908, hAPP(hAPP(c_Set_Oinsert(_1595908), _1595912), _1595910)) = hAPP(hAPP(c_Finite__Set_Ofold(_1595908, _1595908, c_Lattices_Osemilattice__inf__class_Oinf(_1595908)), _1595912), _1595910))], (41495 ^ _784416) ^ [_1596122, _1596124, _1596126] : [class_Orderings_Olinorder(_1596122), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596122), _1596124)), -(hBOOL(hAPP(hAPP(c_member(_1596122), _1596126), _1596124))), -(c_Big__Operators_Olinorder__class_OMin(_1596122, hAPP(hAPP(c_Set_Oinsert(_1596122), _1596126), _1596124)) = hAPP(hAPP(c_Finite__Set_Ofold(_1596122, _1596122, c_Orderings_Oord__class_Omin(_1596122)), _1596126), _1596124))], (41509 ^ _784416) ^ [_1596336, _1596338, _1596340] : [class_Orderings_Olinorder(_1596336), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596336), _1596338)), -(hBOOL(hAPP(hAPP(c_member(_1596336), _1596340), _1596338))), -(c_Big__Operators_Olinorder__class_OMax(_1596336, hAPP(hAPP(c_Set_Oinsert(_1596336), _1596340), _1596338)) = hAPP(hAPP(c_Finite__Set_Ofold(_1596336, _1596336, c_Orderings_Oord__class_Omax(_1596336)), _1596340), _1596338))], (41523 ^ _784416) ^ [_1596550, _1596552, _1596554, _1596556, _1596558, _1596560] : [c_Finite__Set_Ofun__left__comm(_1596550, _1596552, _1596554), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596550), _1596556)), hBOOL(hAPP(hAPP(c_member(_1596550), _1596558), _1596556)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1596550, _1596552, _1596554), _1596560), _1596556) = hAPP(hAPP(_1596554, _1596558), hAPP(hAPP(c_Finite__Set_Ofold(_1596550, _1596552, _1596554), _1596560), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1596550, tc_HOL_Obool)), _1596556), hAPP(hAPP(c_Set_Oinsert(_1596550), _1596558), c_Orderings_Obot__class_Obot(tc_fun(_1596550, tc_HOL_Obool)))))))], (41537 ^ _784416) ^ [_1596879, _1596881, _1596883, _1596885, _1596887, _1596889] : [c_Finite__Set_Ofun__left__comm(_1596879, _1596881, _1596883), hBOOL(hAPP(c_Finite__Set_Ofinite(_1596879), _1596885)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1596879, _1596881, _1596883), _1596887), hAPP(hAPP(c_Set_Oinsert(_1596879), _1596889), _1596885)) = hAPP(hAPP(_1596883, _1596889), hAPP(hAPP(c_Finite__Set_Ofold(_1596879, _1596881, _1596883), _1596887), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1596879, tc_HOL_Obool)), _1596885), hAPP(hAPP(c_Set_Oinsert(_1596879), _1596889), c_Orderings_Obot__class_Obot(tc_fun(_1596879, tc_HOL_Obool)))))))], (41547 ^ _784416) ^ [_1597150, _1597152, _1597154, _1597156, _1597158, _1597160] : [c_Finite__Set_Ofun__left__comm(_1597150, _1597152, _1597154), -(hAPP(hAPP(_1597154, _1597156), hAPP(hAPP(_1597154, _1597158), _1597160)) = hAPP(hAPP(_1597154, _1597158), hAPP(hAPP(_1597154, _1597156), _1597160)))], (41553 ^ _784416) ^ [_1597285, _1597287, _1597289, _1597291, _1597293] : [c_Finite__Set_Ofun__left__comm(_1597285, _1597287, _1597289), -(c_Finite__Set_Ofun__left__comm(_1597291, _1597287, hAPP(hAPP(c_COMBB(_1597285, tc_fun(_1597287, _1597287), _1597291), _1597289), _1597293)))], (41559 ^ _784416) ^ [_1597398] : [class_Groups_Oab__semigroup__mult(_1597398), -(c_Finite__Set_Ofun__left__comm(_1597398, _1597398, c_Groups_Otimes__class_Otimes(_1597398)))], (41565 ^ _784416) ^ [_1597477, _1597479, _1597481, _1597483, _1597485, _1597487, _1597489] : [c_Finite__Set_Ofun__left__comm(_1597477, _1597479, _1597481), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1597477, _1597479, _1597481, _1597483, _1597485), _1597487)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1597477, _1597479, _1597481, _1597483, _1597485), _1597489)), -(_1597489 = _1597487)], (41579 ^ _784416) ^ [_1597722, _1597724, _1597726, _1597728, _1597730] : [c_Finite__Set_Ofun__left__comm(_1597722, _1597724, _1597726), -(hAPP(c_Fun_Ocomp(_1597724, _1597724, _1597724, hAPP(_1597726, _1597728)), hAPP(_1597726, _1597730)) = hAPP(c_Fun_Ocomp(_1597724, _1597724, _1597724, hAPP(_1597726, _1597730)), hAPP(_1597726, _1597728)))], (41585 ^ _784416) ^ [_1597863, _1597865, _1597867, _1597869, _1597871, _1597873] : [c_Finite__Set_Ofun__left__comm(_1597863, _1597865, _1597867), hBOOL(hAPP(c_Finite__Set_Ofinite(_1597863), _1597869)), -(hAPP(hAPP(_1597867, _1597871), hAPP(hAPP(c_Finite__Set_Ofold(_1597863, _1597865, _1597867), _1597873), _1597869)) = hAPP(hAPP(c_Finite__Set_Ofold(_1597863, _1597865, _1597867), hAPP(hAPP(_1597867, _1597871), _1597873)), _1597869))], (41595 ^ _784416) ^ [_1598082, _1598084, _1598086, _1598088, _1598090, _1598092] : [c_Finite__Set_Ofun__left__comm(_1598082, _1598084, _1598086), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1598082, _1598084, _1598086, _1598088, _1598090), _1598092)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1598082, _1598084, _1598086), _1598088), _1598090) = _1598092)], (41605 ^ _784416) ^ [_1598265, _1598267, _1598269, _1598271, _1598273] : [c_Finite__Set_Ofun__left__comm(_1598265, _1598267, _1598269), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598265), _1598271)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1598265, _1598267, _1598269, _1598273, _1598271), hAPP(hAPP(c_Finite__Set_Ofold(_1598265, _1598267, _1598269), _1598273), _1598271))))], (41615 ^ _784416) ^ [_1598452, _1598454, _1598456, _1598458, _1598460, _1598462] : [c_Finite__Set_Ofun__left__comm(_1598452, _1598454, _1598456), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598452), _1598458)), -(hBOOL(hAPP(hAPP(c_member(_1598452), _1598460), _1598458))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1598452, _1598454, _1598456), _1598462), hAPP(hAPP(c_Set_Oinsert(_1598452), _1598460), _1598458)) = hAPP(hAPP(_1598456, _1598460), hAPP(hAPP(c_Finite__Set_Ofold(_1598452, _1598454, _1598456), _1598462), _1598458)))], (41629 ^ _784416) ^ [_1598704, _1598706, _1598708, _1598710, _1598712, _1598714] : [c_Finite__Set_Ofun__left__comm(_1598704, _1598706, _1598708), hBOOL(hAPP(c_Finite__Set_Ofinite(_1598704), _1598710)), -(hBOOL(hAPP(hAPP(c_member(_1598704), _1598712), _1598710))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1598704, _1598706, _1598708), _1598714), hAPP(hAPP(c_Set_Oinsert(_1598704), _1598712), _1598710)) = hAPP(hAPP(c_Finite__Set_Ofold(_1598704, _1598706, _1598708), hAPP(hAPP(_1598708, _1598712), _1598714)), _1598710))], (41643 ^ _784416) ^ [_1598956, _1598958, _1598960, _1598962, _1598964, _1598966, _1598968] : [c_Finite__Set_Ofun__left__comm(_1598956, _1598958, _1598960), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1598956, _1598958, _1598960, _1598962, _1598964), _1598966)), hBOOL(hAPP(hAPP(c_member(_1598956), _1598968), _1598964)), 41655 ^ _784416 : [(41656 ^ _784416) ^ [] : [-(_1598966 = hAPP(hAPP(_1598960, _1598968), 41654 ^ [_1598956, _1598958, _1598960, _1598962, _1598964, _1598966, _1598968]))], (41658 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1598956, _1598958, _1598960, _1598962, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1598956, tc_HOL_Obool)), _1598964), hAPP(hAPP(c_Set_Oinsert(_1598956), _1598968), c_Orderings_Obot__class_Obot(tc_fun(_1598956, tc_HOL_Obool))))), 41654 ^ [_1598956, _1598958, _1598960, _1598962, _1598964, _1598966, _1598968])))]]], (41660 ^ _784416) ^ [_1599340, _1599342, _1599344, _1599346] : [class_Complete__Lattice_Ocomplete__lattice(_1599340), hBOOL(hAPP(c_Finite__Set_Ofinite(_1599342), _1599344)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599342, _1599340), _1599344), _1599346) = hAPP(hAPP(c_Finite__Set_Ofold(_1599342, _1599340, hAPP(hAPP(c_COMBB(_1599340, tc_fun(_1599340, _1599340), _1599342), c_Lattices_Osemilattice__inf__class_Oinf(_1599340)), _1599346)), c_Orderings_Otop__class_Otop(_1599340)), _1599344))], (41670 ^ _784416) ^ [_1599555, _1599557, _1599559, _1599561, _1599563, _1599565] : [hBOOL(hAPP(hAPP(c_member(_1599555), _1599557), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599559, tc_fun(_1599555, tc_HOL_Obool)), _1599561), _1599563))), hBOOL(hAPP(hAPP(c_member(_1599559), _1599565), _1599561)), -(hBOOL(hAPP(hAPP(c_member(_1599555), _1599557), hAPP(_1599563, _1599565))))], (41680 ^ _784416) ^ [_1599772, _1599774, _1599776, _1599778, _1599780, _1599782] : [hBOOL(hAPP(hAPP(c_member(_1599772), _1599774), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599776, tc_fun(_1599772, tc_HOL_Obool)), _1599778), _1599780))), -(hBOOL(hAPP(hAPP(c_member(_1599772), _1599774), hAPP(_1599780, _1599782)))), hBOOL(hAPP(hAPP(c_member(_1599776), _1599782), _1599778))], (41690 ^ _784416) ^ [_1599993, _1599995, _1599997, _1599999, _1600001, _1600003] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1599993, tc_fun(_1599995, tc_HOL_Obool)), _1599997), _1599999), _1600001)), -(hBOOL(hAPP(hAPP(_1599999, _1600003), _1600001))), hBOOL(hAPP(hAPP(c_member(_1599993), _1600003), _1599997))], (41700 ^ _784416) ^ [_1600194, _1600196, _1600198, _1600200, _1600202, _1600204] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600194, tc_fun(_1600196, tc_HOL_Obool)), _1600198), _1600200), _1600202)), hBOOL(hAPP(hAPP(c_member(_1600194), _1600204), _1600198)), -(hBOOL(hAPP(hAPP(_1600200, _1600204), _1600202)))], (41710 ^ _784416) ^ [_1600391, _1600393, _1600395, _1600397, _1600399, _1600401, _1600403, _1600405] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600391, tc_fun(_1600393, tc_fun(_1600395, tc_HOL_Obool))), _1600397), _1600399), _1600401), _1600403)), -(hBOOL(hAPP(hAPP(hAPP(_1600399, _1600405), _1600401), _1600403))), hBOOL(hAPP(hAPP(c_member(_1600391), _1600405), _1600397))], (41720 ^ _784416) ^ [_1600618, _1600620, _1600622, _1600624, _1600626, _1600628, _1600630, _1600632] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600618, tc_fun(_1600620, tc_fun(_1600622, tc_HOL_Obool))), _1600624), _1600626), _1600628), _1600630)), hBOOL(hAPP(hAPP(c_member(_1600618), _1600632), _1600624)), -(hBOOL(hAPP(hAPP(hAPP(_1600626, _1600632), _1600628), _1600630)))], (41730 ^ _784416) ^ [_1600841, _1600843, _1600845, _1600847] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1600845), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1600841, tc_fun(_1600845, tc_HOL_Obool)), _1600843), _1600847)))), 41731 ^ _784416 : [(41732 ^ _784416) ^ [_1600915] : [hBOOL(hAPP(hAPP(c_member(_1600841), _1600915), _1600843)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1600845), hAPP(_1600847, _1600915)))]]], (41740 ^ _784416) ^ [_1601069, _1601071, _1601073, _1601075] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1601069, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1601071, tc_fun(_1601069, tc_HOL_Obool)), _1601073), _1601075)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601071, tc_fun(_1601069, tc_HOL_Obool)), _1601073), hAPP(hAPP(c_COMBB(tc_fun(_1601069, tc_HOL_Obool), tc_fun(_1601069, tc_HOL_Obool), _1601071), c_Groups_Ouminus__class_Ouminus(tc_fun(_1601069, tc_HOL_Obool))), _1601075)))], (41742 ^ _784416) ^ [_1601151, _1601153, _1601155, _1601157] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1601151, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601153, tc_fun(_1601151, tc_HOL_Obool)), _1601155), _1601157)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1601153, tc_fun(_1601151, tc_HOL_Obool)), _1601155), hAPP(hAPP(c_COMBB(tc_fun(_1601151, tc_HOL_Obool), tc_fun(_1601151, tc_HOL_Obool), _1601153), c_Groups_Ouminus__class_Ouminus(tc_fun(_1601151, tc_HOL_Obool))), _1601157)))], (41744 ^ _784416) ^ [_1601233, _1601235, _1601237, _1601239, _1601241, _1601243] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601233, tc_fun(_1601235, tc_HOL_Obool)), _1601237), hAPP(hAPP(c_COMBC(_1601233, tc_fun(_1601239, tc_fun(_1601235, tc_HOL_Obool)), tc_fun(_1601235, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1601239, tc_HOL_Obool), tc_fun(tc_fun(_1601239, tc_fun(_1601235, tc_HOL_Obool)), tc_fun(_1601235, tc_HOL_Obool)), _1601233), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601239, tc_fun(_1601235, tc_HOL_Obool))), _1601241)), _1601243)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601239, tc_fun(_1601235, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1601233, tc_fun(_1601239, tc_HOL_Obool)), _1601237), _1601241)), _1601243))], (41746 ^ _784416) ^ [_1601352, _1601354, _1601356, _1601358, _1601360, _1601362] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601352, tc_fun(_1601354, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1601356, tc_fun(_1601352, tc_HOL_Obool)), _1601358), _1601360)), _1601362) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601356, tc_fun(_1601354, tc_HOL_Obool)), _1601358), hAPP(hAPP(c_COMBC(_1601356, tc_fun(_1601352, tc_fun(_1601354, tc_HOL_Obool)), tc_fun(_1601354, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1601352, tc_HOL_Obool), tc_fun(tc_fun(_1601352, tc_fun(_1601354, tc_HOL_Obool)), tc_fun(_1601354, tc_HOL_Obool)), _1601356), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601352, tc_fun(_1601354, tc_HOL_Obool))), _1601360)), _1601362)))], (41748 ^ _784416) ^ [_1601471, _1601473, _1601475, _1601477, _1601479] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1601471, tc_fun(_1601473, tc_HOL_Obool)), _1601475), hAPP(hAPP(c_COMBB(tc_fun(_1601473, tc_HOL_Obool), tc_fun(_1601473, tc_HOL_Obool), _1601471), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1601473, tc_HOL_Obool)), _1601477)), _1601479)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1601473, tc_HOL_Obool)), _1601477), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601471, tc_fun(_1601473, tc_HOL_Obool)), _1601475), _1601479)))], (41750 ^ _784416) ^ [_1601561, _1601563, _1601565, _1601567, _1601569] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1601561, tc_HOL_Obool)), _1601563), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601565, tc_fun(_1601561, tc_HOL_Obool)), _1601567), _1601569)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1601565, tc_fun(_1601561, tc_HOL_Obool)), _1601567), hAPP(hAPP(c_COMBB(tc_fun(_1601561, tc_HOL_Obool), tc_fun(_1601561, tc_HOL_Obool), _1601565), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1601561, tc_HOL_Obool)), _1601563)), _1601569)))], (41752 ^ _784416) ^ [_1601672, _1601674, _1601676, _1601678] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601672, tc_fun(_1601674, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1601672, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1601674, tc_HOL_Obool), tc_fun(_1601674, tc_HOL_Obool), _1601672), hAPP(c_COMBC(_1601674, tc_fun(_1601674, tc_HOL_Obool), tc_HOL_Obool), c_member(_1601674))), _1601676)), _1601678)), -(hBOOL(hAPP(hAPP(c_member(_1601674), _1601678), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601672, tc_fun(_1601674, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1601672, tc_HOL_Obool))), _1601676))))], (41758 ^ _784416) ^ [_1601891, _1601893, _1601895, _1601897] : [hBOOL(hAPP(hAPP(c_member(_1601893), _1601897), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601891, tc_fun(_1601893, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1601891, tc_HOL_Obool))), _1601895))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1601891, tc_fun(_1601893, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1601891, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1601893, tc_HOL_Obool), tc_fun(_1601893, tc_HOL_Obool), _1601891), hAPP(c_COMBC(_1601893, tc_fun(_1601893, tc_HOL_Obool), tc_HOL_Obool), c_member(_1601893))), _1601895)), _1601897)))], (41764 ^ _784416) ^ [_1602116, _1602118, _1602120, _1602122, _1602124] : [-(hAPP(hAPP(c_Set_Oinsert(_1602116), _1602118), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602120, tc_fun(_1602116, tc_HOL_Obool)), _1602122), _1602124)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602120, tc_fun(_1602116, tc_HOL_Obool)), _1602122), hAPP(hAPP(c_COMBB(tc_fun(_1602116, tc_HOL_Obool), tc_fun(_1602116, tc_HOL_Obool), _1602120), hAPP(c_Set_Oinsert(_1602116), _1602118)), _1602124)))], (41766 ^ _784416) ^ [_1602200, _1602202, _1602204, _1602206, _1602208] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602200, tc_fun(_1602202, tc_HOL_Obool)), _1602204), hAPP(hAPP(c_COMBB(tc_fun(_1602202, tc_HOL_Obool), tc_fun(_1602202, tc_HOL_Obool), _1602200), hAPP(c_Set_Oinsert(_1602202), _1602206)), _1602208)) = hAPP(hAPP(c_Set_Oinsert(_1602202), _1602206), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602200, tc_fun(_1602202, tc_HOL_Obool)), _1602204), _1602208)))], (41778 ^ _784416) ^ [_1602551, _1602553, _1602555, _1602557, _1602559] : [41780 ^ _784416 : [(41781 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1602555), 41779 ^ [_1602551, _1602553, _1602555, _1602557, _1602559]), _1602557)))], (41783 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1602551), _1602553), hAPP(_1602559, 41779 ^ [_1602551, _1602553, _1602555, _1602557, _1602559])))]], -(hBOOL(hAPP(hAPP(c_member(_1602551), _1602553), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602555, tc_fun(_1602551, tc_HOL_Obool)), _1602557), _1602559))))], (41768 ^ _784416) ^ [_1602308, _1602310, _1602312, _1602314, _1602316] : [hBOOL(hAPP(hAPP(c_member(_1602308), _1602310), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602312, tc_fun(_1602308, tc_HOL_Obool)), _1602314), _1602316))), 41771 ^ _784416 : [(41772 ^ _784416) ^ [_1602432] : [hBOOL(hAPP(hAPP(c_member(_1602312), _1602432), _1602314)), -(hBOOL(hAPP(hAPP(c_member(_1602308), _1602310), hAPP(_1602316, _1602432))))]]], (41797 ^ _784416) ^ [_1603049, _1603051, _1603053, _1603055] : [41799 ^ _784416 : [(41800 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1603051), 41798 ^ [_1603049, _1603051, _1603053, _1603055]), _1603053)))], (41802 ^ _784416) ^ [] : [hAPP(_1603055, 41798 ^ [_1603049, _1603051, _1603053, _1603055]) = c_Orderings_Otop__class_Otop(tc_fun(_1603049, tc_HOL_Obool))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1603049, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603051, tc_fun(_1603049, tc_HOL_Obool)), _1603053), _1603055))], (41787 ^ _784416) ^ [_1602820, _1602822, _1602824, _1602826] : [c_Orderings_Otop__class_Otop(tc_fun(_1602820, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1602822, tc_fun(_1602820, tc_HOL_Obool)), _1602824), _1602826), 41790 ^ _784416 : [(41791 ^ _784416) ^ [_1602936] : [hBOOL(hAPP(hAPP(c_member(_1602822), _1602936), _1602824)), -(hAPP(_1602826, _1602936) = c_Orderings_Otop__class_Otop(tc_fun(_1602820, tc_HOL_Obool)))]]], (41816 ^ _784416) ^ [_1603529, _1603531, _1603533, _1603535] : [41818 ^ _784416 : [(41819 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1603529), 41817 ^ [_1603529, _1603531, _1603533, _1603535]), _1603533)))], (41821 ^ _784416) ^ [] : [hAPP(_1603535, 41817 ^ [_1603529, _1603531, _1603533, _1603535]) = c_Orderings_Otop__class_Otop(tc_fun(_1603531, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603529, tc_fun(_1603531, tc_HOL_Obool)), _1603533), _1603535) = c_Orderings_Otop__class_Otop(tc_fun(_1603531, tc_HOL_Obool)))], (41806 ^ _784416) ^ [_1603300, _1603302, _1603304, _1603306] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603300, tc_fun(_1603302, tc_HOL_Obool)), _1603304), _1603306) = c_Orderings_Otop__class_Otop(tc_fun(_1603302, tc_HOL_Obool)), 41809 ^ _784416 : [(41810 ^ _784416) ^ [_1603416] : [hBOOL(hAPP(hAPP(c_member(_1603300), _1603416), _1603304)), -(hAPP(_1603306, _1603416) = c_Orderings_Otop__class_Otop(tc_fun(_1603302, tc_HOL_Obool)))]]], (41825 ^ _784416) ^ [_1603759, _1603761, _1603763, _1603765, _1603767, _1603769] : [class_Complete__Lattice_Ocomplete__lattice(_1603759), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603761, _1603759), _1603763), hAPP(hAPP(c_COMBB(tc_fun(_1603765, _1603759), _1603759, _1603761), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603765, _1603759), _1603767)), _1603769)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603765, _1603759), _1603767), hAPP(hAPP(c_COMBB(tc_fun(_1603761, _1603759), _1603759, _1603765), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603761, _1603759), _1603763)), hAPP(c_COMBC(_1603761, _1603765, _1603759), _1603769))))], (41831 ^ _784416) ^ [_1603968, _1603970, _1603972, _1603974] : [-(hAPP(c_Set_OPow(_1603968), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603970, tc_fun(_1603968, tc_HOL_Obool)), _1603972), _1603974)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1603970, tc_fun(tc_fun(_1603968, tc_HOL_Obool), tc_HOL_Obool)), _1603972), hAPP(hAPP(c_COMBB(tc_fun(_1603968, tc_HOL_Obool), tc_fun(tc_fun(_1603968, tc_HOL_Obool), tc_HOL_Obool), _1603970), c_Set_OPow(_1603968)), _1603974)))], (41833 ^ _784416) ^ [_1604050, _1604052, _1604054, _1604056, _1604058, _1604060] : [class_Complete__Lattice_Ocomplete__lattice(_1604050), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604052, tc_fun(_1604054, _1604050)), _1604056), _1604058), _1604060) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604052, _1604050), _1604056), hAPP(hAPP(c_COMBC(_1604052, _1604054, _1604050), _1604058), _1604060)))], (41839 ^ _784416) ^ [_1604201, _1604203, _1604205, _1604207, _1604209] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604201, tc_fun(_1604203, tc_HOL_Obool)), _1604205), hAPP(hAPP(c_COMBS(_1604201, tc_fun(_1604203, tc_HOL_Obool), tc_fun(_1604203, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1604203, tc_HOL_Obool), tc_fun(tc_fun(_1604203, tc_HOL_Obool), tc_fun(_1604203, tc_HOL_Obool)), _1604201), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1604203, tc_HOL_Obool))), _1604207)), _1604209)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1604203, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604201, tc_fun(_1604203, tc_HOL_Obool)), _1604205), _1604207)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604201, tc_fun(_1604203, tc_HOL_Obool)), _1604205), _1604209)))], (41841 ^ _784416) ^ [_1604349, _1604351, _1604353, _1604355, _1604357, _1604359] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604349, tc_fun(_1604351, tc_fun(_1604353, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1604349, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1604351, _1604353), tc_HOL_Obool), tc_fun(_1604351, tc_fun(_1604353, tc_HOL_Obool)), _1604349), hAPP(c_COMBC(_1604351, tc_fun(tc_prod(_1604351, _1604353), tc_HOL_Obool), tc_fun(_1604353, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1604353, tc_fun(tc_fun(tc_prod(_1604351, _1604353), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1604351, _1604353), tc_HOL_Obool), tc_fun(_1604353, tc_HOL_Obool)), _1604351), c_COMBC(_1604353, tc_fun(tc_prod(_1604351, _1604353), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1604353, tc_prod(_1604351, _1604353)), tc_fun(_1604353, tc_fun(tc_fun(tc_prod(_1604351, _1604353), tc_HOL_Obool), tc_HOL_Obool)), _1604351), hAPP(c_COMBB(tc_prod(_1604351, _1604353), tc_fun(tc_fun(tc_prod(_1604351, _1604353), tc_HOL_Obool), tc_HOL_Obool), _1604353), c_member(tc_prod(_1604351, _1604353)))), c_Product__Type_OPair(_1604351, _1604353))))), _1604355)), _1604357), _1604359)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604351, _1604353)), hAPP(hAPP(c_Product__Type_OPair(_1604351, _1604353), _1604357), _1604359)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604349, tc_fun(tc_prod(_1604351, _1604353), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1604349, tc_HOL_Obool))), _1604355))))], (41847 ^ _784416) ^ [_1604832, _1604834, _1604836, _1604838, _1604840, _1604842] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604834, _1604836)), hAPP(hAPP(c_Product__Type_OPair(_1604834, _1604836), _1604840), _1604842)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604832, tc_fun(tc_prod(_1604834, _1604836), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1604832, tc_HOL_Obool))), _1604838))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1604832, tc_fun(_1604834, tc_fun(_1604836, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1604832, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1604834, _1604836), tc_HOL_Obool), tc_fun(_1604834, tc_fun(_1604836, tc_HOL_Obool)), _1604832), hAPP(c_COMBC(_1604834, tc_fun(tc_prod(_1604834, _1604836), tc_HOL_Obool), tc_fun(_1604836, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1604836, tc_fun(tc_fun(tc_prod(_1604834, _1604836), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1604834, _1604836), tc_HOL_Obool), tc_fun(_1604836, tc_HOL_Obool)), _1604834), c_COMBC(_1604836, tc_fun(tc_prod(_1604834, _1604836), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1604836, tc_prod(_1604834, _1604836)), tc_fun(_1604836, tc_fun(tc_fun(tc_prod(_1604834, _1604836), tc_HOL_Obool), tc_HOL_Obool)), _1604834), hAPP(c_COMBB(tc_prod(_1604834, _1604836), tc_fun(tc_fun(tc_prod(_1604834, _1604836), tc_HOL_Obool), tc_HOL_Obool), _1604836), c_member(tc_prod(_1604834, _1604836)))), c_Product__Type_OPair(_1604834, _1604836))))), _1604838)), _1604840), _1604842)))], (41853 ^ _784416) ^ [_1605321, _1605323, _1605325, _1605327, _1605329, _1605331] : [-(hAPP(c_Set_Ovimage(_1605321, _1605323, _1605325), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605327, tc_fun(_1605323, tc_HOL_Obool)), _1605329), _1605331)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605327, tc_fun(_1605321, tc_HOL_Obool)), _1605329), hAPP(hAPP(c_COMBB(tc_fun(_1605323, tc_HOL_Obool), tc_fun(_1605321, tc_HOL_Obool), _1605327), c_Set_Ovimage(_1605321, _1605323, _1605325)), _1605331)))], (41855 ^ _784416) ^ [_1605405, _1605407, _1605409, _1605411, _1605413, _1605415] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605405, tc_fun(_1605407, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1605409, _1605405, _1605411), _1605413)), _1605415) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605409, tc_fun(_1605407, tc_HOL_Obool)), _1605413), hAPP(hAPP(c_COMBB(_1605405, tc_fun(_1605407, tc_HOL_Obool), _1605409), _1605415), _1605411)))], (41857 ^ _784416) ^ [_1605482, _1605484, _1605486, _1605488, _1605490, _1605492] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605482, tc_fun(_1605484, tc_HOL_Obool)), _1605486), hAPP(hAPP(c_COMBB(_1605488, tc_fun(_1605484, tc_HOL_Obool), _1605482), _1605490), _1605492)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605488, tc_fun(_1605484, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1605482, _1605488, _1605492), _1605486)), _1605490))], (41859 ^ _784416) ^ [_1605559] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605559, tc_HOL_Obool) = c_Set_OBall(_1605559))], (41861 ^ _784416) ^ [_1605587, _1605589, _1605591, _1605593, _1605595, _1605597] : [hBOOL(hAPP(hAPP(c_member(_1605587), _1605589), _1605591)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605587, tc_fun(_1605593, tc_HOL_Obool)), _1605591), hAPP(hAPP(c_COMBB(tc_fun(_1605593, tc_HOL_Obool), tc_fun(_1605593, tc_HOL_Obool), _1605587), hAPP(c_Set_Oinsert(_1605593), _1605595)), _1605597)) = hAPP(hAPP(c_Set_Oinsert(_1605593), _1605595), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605587, tc_fun(_1605593, tc_HOL_Obool)), _1605591), _1605597)))], (41867 ^ _784416) ^ [_1605792, _1605794, _1605796, _1605798, _1605800] : [hBOOL(hAPP(hAPP(c_member(_1605792), _1605794), _1605796)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1605798, tc_HOL_Obool)), hAPP(_1605800, _1605794)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605792, tc_fun(_1605798, tc_HOL_Obool)), _1605796), _1605800)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605792, tc_fun(_1605798, tc_HOL_Obool)), _1605796), _1605800))], (41873 ^ _784416) ^ [_1605965, _1605967, _1605969, _1605971] : [class_Complete__Lattice_Ocomplete__lattice(_1605965), -(_1605967 = c_Orderings_Obot__class_Obot(tc_fun(_1605969, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1605969, _1605965), _1605967), hAPP(c_COMBK(_1605965, _1605969), _1605971)) = _1605971)], (41883 ^ _784416) ^ [_1606117, _1606119, _1606121, _1606123, _1606125] : [_1606117 = c_Orderings_Obot__class_Obot(tc_fun(_1606119, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1606121, tc_HOL_Obool)), _1606123), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606119, tc_fun(_1606121, tc_HOL_Obool)), _1606117), _1606125)) = _1606123)], (41889 ^ _784416) ^ [_1606250, _1606252, _1606254, _1606256, _1606258] : [-(_1606250 = c_Orderings_Obot__class_Obot(tc_fun(_1606252, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1606254, tc_HOL_Obool)), _1606256), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606252, tc_fun(_1606254, tc_HOL_Obool)), _1606250), _1606258)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606252, tc_fun(_1606254, tc_HOL_Obool)), _1606250), hAPP(hAPP(c_COMBB(tc_fun(_1606254, tc_HOL_Obool), tc_fun(_1606254, tc_HOL_Obool), _1606252), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1606254, tc_HOL_Obool)), _1606256)), _1606258)))], (41895 ^ _784416) ^ [_1606376, _1606378, _1606380, _1606382, _1606384] : [_1606376 = c_Orderings_Obot__class_Obot(tc_fun(_1606378, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1606380, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606378, tc_fun(_1606380, tc_HOL_Obool)), _1606376), _1606382)), _1606384) = _1606384)], (41901 ^ _784416) ^ [_1606509, _1606511, _1606513, _1606515, _1606517] : [-(_1606509 = c_Orderings_Obot__class_Obot(tc_fun(_1606511, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1606513, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606511, tc_fun(_1606513, tc_HOL_Obool)), _1606509), _1606515)), _1606517) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606511, tc_fun(_1606513, tc_HOL_Obool)), _1606509), hAPP(hAPP(c_COMBC(_1606511, tc_fun(_1606513, tc_HOL_Obool), tc_fun(_1606513, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1606513, tc_HOL_Obool), tc_fun(tc_fun(_1606513, tc_HOL_Obool), tc_fun(_1606513, tc_HOL_Obool)), _1606511), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1606513, tc_HOL_Obool))), _1606515)), _1606517)))], (41907 ^ _784416) ^ [_1606636, _1606638, _1606640] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606636, tc_fun(_1606638, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1606636, tc_HOL_Obool))), _1606640) = c_Orderings_Otop__class_Otop(tc_fun(_1606638, tc_HOL_Obool)))], (41909 ^ _784416) ^ [_1606700, _1606702, _1606704, _1606706] : [_1606700 = c_Orderings_Obot__class_Obot(tc_fun(_1606702, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606702, tc_fun(_1606704, tc_HOL_Obool)), _1606700), hAPP(c_COMBK(tc_fun(_1606704, tc_HOL_Obool), _1606702), _1606706)) = c_Orderings_Otop__class_Otop(tc_fun(_1606704, tc_HOL_Obool)))], (41915 ^ _784416) ^ [_1606837, _1606839, _1606841, _1606843] : [-(_1606837 = c_Orderings_Obot__class_Obot(tc_fun(_1606839, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606839, tc_fun(_1606841, tc_HOL_Obool)), _1606837), hAPP(c_COMBK(tc_fun(_1606841, tc_HOL_Obool), _1606839), _1606843)) = _1606843)], (41921 ^ _784416) ^ [_1606905, _1606907, _1606909, _1606911, _1606913] : [class_Complete__Lattice_Ocomplete__lattice(_1606905), class_Orderings_Olinorder(_1606905), 41928 ^ _784416 : [(41929 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1606905), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606907, _1606905), _1606909), _1606911)), _1606913)), 41933 ^ _784416 : [(41934 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1606907), 41932 ^ [_1606905, _1606907, _1606909, _1606911, _1606913]), _1606909)))], (41936 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1606905), hAPP(_1606911, 41932 ^ [_1606905, _1606907, _1606909, _1606911, _1606913])), _1606913)))]]], (41938 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1606905), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1606907, _1606905), _1606909), _1606911)), _1606913))), 41939 ^ _784416 : [(41940 ^ _784416) ^ [_1607253] : [hBOOL(hAPP(hAPP(c_member(_1606907), _1607253), _1606909)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1606905), hAPP(_1606911, _1607253)), _1606913))]]]]], (41948 ^ _784416) ^ [_1607423, _1607425, _1607427, _1607429, _1607431] : [class_Complete__Lattice_Ocomplete__lattice(_1607423), 41951 ^ _784416 : [(41962 ^ _784416) ^ [] : [41964 ^ _784416 : [(41965 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1607427), 41963 ^ [_1607423, _1607425, _1607427, _1607429, _1607431]), _1607429)))], (41967 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1607423), _1607425), hAPP(_1607431, 41963 ^ [_1607423, _1607425, _1607427, _1607429, _1607431])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1607423), _1607425), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607427, _1607423), _1607429), _1607431))))], (41952 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1607423), _1607425), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607427, _1607423), _1607429), _1607431))), 41955 ^ _784416 : [(41956 ^ _784416) ^ [_1607604] : [hBOOL(hAPP(hAPP(c_member(_1607427), _1607604), _1607429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1607423), _1607425), hAPP(_1607431, _1607604))))]]]]], (41981 ^ _784416) ^ [_1608199, _1608201, _1608203, _1608205, _1608207] : [41983 ^ _784416 : [(41984 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1608203), 41982 ^ [_1608199, _1608201, _1608203, _1608205, _1608207]), _1608205)))], (41986 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1608199, tc_HOL_Obool)), _1608201), hAPP(_1608207, 41982 ^ [_1608199, _1608201, _1608203, _1608205, _1608207])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1608199, tc_HOL_Obool)), _1608201), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608203, tc_fun(_1608199, tc_HOL_Obool)), _1608205), _1608207))))], (41971 ^ _784416) ^ [_1607941, _1607943, _1607945, _1607947, _1607949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1607941, tc_HOL_Obool)), _1607943), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1607945, tc_fun(_1607941, tc_HOL_Obool)), _1607947), _1607949))), 41974 ^ _784416 : [(41975 ^ _784416) ^ [_1608074] : [hBOOL(hAPP(hAPP(c_member(_1607945), _1608074), _1607947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1607941, tc_HOL_Obool)), _1607943), hAPP(_1607949, _1608074))))]]], (41990 ^ _784416) ^ [_1608462, _1608464, _1608466, _1608468, _1608470] : [hBOOL(hAPP(hAPP(c_member(_1608462), _1608464), _1608466)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1608468, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608462, tc_fun(_1608468, tc_HOL_Obool)), _1608466), _1608470)), hAPP(_1608470, _1608464))))], (41996 ^ _784416) ^ [_1608609, _1608611, _1608613, _1608615, _1608617] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608609, tc_fun(_1608611, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1608609, tc_HOL_Obool)), _1608613), _1608615)), _1608617) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1608611, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608609, tc_fun(_1608611, tc_HOL_Obool)), _1608613), _1608617)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608609, tc_fun(_1608611, tc_HOL_Obool)), _1608615), _1608617)))], (41998 ^ _784416) ^ [_1608698, _1608700, _1608702, _1608704] : [-(hAPP(c_Set_OCollect(_1608698), hAPP(hAPP(c_COMBB(tc_fun(_1608700, tc_HOL_Obool), tc_HOL_Obool, _1608698), c_HOL_OAll(_1608700)), hAPP(hAPP(c_COMBB(tc_fun(_1608700, tc_HOL_Obool), tc_fun(_1608700, tc_HOL_Obool), _1608698), hAPP(c_COMBS(_1608700, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1608700), c_fimplies), hAPP(hAPP(c_COMBC(_1608700, tc_fun(_1608700, tc_HOL_Obool), tc_HOL_Obool), c_member(_1608700)), _1608702)))), _1608704))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608700, tc_fun(_1608698, tc_HOL_Obool)), _1608702), hAPP(hAPP(c_COMBB(tc_fun(_1608698, tc_HOL_Obool), tc_fun(_1608698, tc_HOL_Obool), _1608700), c_Set_OCollect(_1608698)), hAPP(c_COMBC(_1608698, _1608700, tc_HOL_Obool), _1608704))))], (42000 ^ _784416) ^ [_1608832, _1608834, _1608836, _1608838, _1608840] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608832, tc_fun(_1608834, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1608832), _1608836), _1608838)), _1608840) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1608834, tc_HOL_Obool)), hAPP(_1608840, _1608836)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608832, tc_fun(_1608834, tc_HOL_Obool)), _1608838), _1608840)))], (42002 ^ _784416) ^ [_1608909, _1608911, _1608913, _1608915, _1608917] : [-(hAPP(c_Relation_Oconverse(_1608909, _1608911), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608913, tc_fun(tc_prod(_1608909, _1608911), tc_HOL_Obool)), _1608915), _1608917)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1608913, tc_fun(tc_prod(_1608911, _1608909), tc_HOL_Obool)), _1608915), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1608909, _1608911), tc_HOL_Obool), tc_fun(tc_prod(_1608911, _1608909), tc_HOL_Obool), _1608913), c_Relation_Oconverse(_1608909, _1608911)), _1608917)))], (42004 ^ _784416) ^ [_1609001, _1609003, _1609005, _1609007, _1609009, _1609011, _1609013] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609001, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609003, tc_fun(_1609001, tc_HOL_Obool)), _1609005), _1609007)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609009, tc_fun(_1609001, tc_HOL_Obool)), _1609011), _1609013)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609003, tc_fun(_1609001, tc_HOL_Obool)), _1609005), hAPP(hAPP(c_COMBB(tc_fun(_1609009, tc_fun(_1609001, tc_HOL_Obool)), tc_fun(_1609001, tc_HOL_Obool), _1609003), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609009, tc_fun(_1609001, tc_HOL_Obool)), _1609011)), hAPP(hAPP(c_COMBC(_1609003, tc_fun(_1609009, tc_fun(_1609001, tc_HOL_Obool)), tc_fun(_1609009, tc_fun(_1609001, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1609001, tc_HOL_Obool), tc_fun(_1609001, tc_HOL_Obool)), tc_fun(tc_fun(_1609009, tc_fun(_1609001, tc_HOL_Obool)), tc_fun(_1609009, tc_fun(_1609001, tc_HOL_Obool))), _1609003), c_COMBB(tc_fun(_1609001, tc_HOL_Obool), tc_fun(_1609001, tc_HOL_Obool), _1609009)), hAPP(hAPP(c_COMBB(tc_fun(_1609001, tc_HOL_Obool), tc_fun(tc_fun(_1609001, tc_HOL_Obool), tc_fun(_1609001, tc_HOL_Obool)), _1609003), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609001, tc_HOL_Obool))), _1609007))), _1609013))))], (42006 ^ _784416) ^ [_1609204, _1609206, _1609208, _1609210, _1609212] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609204, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609206, tc_fun(_1609204, tc_HOL_Obool)), _1609208), _1609210)), _1609212) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609206, tc_fun(_1609204, tc_HOL_Obool)), _1609208), hAPP(hAPP(c_COMBC(_1609206, tc_fun(_1609204, tc_HOL_Obool), tc_fun(_1609204, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1609204, tc_HOL_Obool), tc_fun(tc_fun(_1609204, tc_HOL_Obool), tc_fun(_1609204, tc_HOL_Obool)), _1609206), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609204, tc_HOL_Obool))), _1609210)), _1609212)))], (42008 ^ _784416) ^ [_1609313, _1609315, _1609317, _1609319, _1609321] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609313, tc_HOL_Obool)), _1609315), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609317, tc_fun(_1609313, tc_HOL_Obool)), _1609319), _1609321)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609317, tc_fun(_1609313, tc_HOL_Obool)), _1609319), hAPP(hAPP(c_COMBB(tc_fun(_1609313, tc_HOL_Obool), tc_fun(_1609313, tc_HOL_Obool), _1609317), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609313, tc_HOL_Obool)), _1609315)), _1609321)))], (42010 ^ _784416) ^ [_1609403, _1609405, _1609407, _1609409, _1609411] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609403, tc_HOL_Obool)), _1609405), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609407, tc_fun(_1609403, tc_HOL_Obool)), _1609409), _1609411)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609407, tc_fun(_1609403, tc_HOL_Obool)), _1609409), hAPP(hAPP(c_COMBB(tc_fun(_1609403, tc_HOL_Obool), tc_fun(_1609403, tc_HOL_Obool), _1609407), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609403, tc_HOL_Obool)), _1609405)), _1609411)))], (42012 ^ _784416) ^ [_1609493, _1609495, _1609497, _1609499, _1609501] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609493, tc_fun(_1609495, tc_HOL_Obool)), _1609497), hAPP(hAPP(c_COMBC(_1609493, tc_fun(_1609495, tc_HOL_Obool), tc_fun(_1609495, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1609495, tc_HOL_Obool), tc_fun(tc_fun(_1609495, tc_HOL_Obool), tc_fun(_1609495, tc_HOL_Obool)), _1609493), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609495, tc_HOL_Obool))), _1609499)), _1609501)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609495, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609493, tc_fun(_1609495, tc_HOL_Obool)), _1609497), _1609499)), _1609501))], (42014 ^ _784416) ^ [_1609602, _1609604, _1609606, _1609608, _1609610] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609602, tc_fun(_1609604, tc_HOL_Obool)), _1609606), hAPP(hAPP(c_COMBB(tc_fun(_1609604, tc_HOL_Obool), tc_fun(_1609604, tc_HOL_Obool), _1609602), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609604, tc_HOL_Obool)), _1609608)), _1609610)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609604, tc_HOL_Obool)), _1609608), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609602, tc_fun(_1609604, tc_HOL_Obool)), _1609606), _1609610)))], (42016 ^ _784416) ^ [_1609692, _1609694, _1609696, _1609698, _1609700, _1609702] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1609692, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1609694, _1609692, _1609696), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609698, tc_fun(_1609694, tc_HOL_Obool)), _1609700), _1609702))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609698, tc_fun(_1609692, tc_HOL_Obool)), _1609700), hAPP(hAPP(c_COMBB(tc_fun(_1609694, tc_HOL_Obool), tc_fun(_1609692, tc_HOL_Obool), _1609698), c_Relation_OImage(_1609694, _1609692, _1609696)), _1609702)))))], (42018 ^ _784416) ^ [_1609786, _1609788, _1609790, _1609792, _1609794] : [class_Complete__Lattice_Ocomplete__lattice(_1609786), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1609788, tc_HOL_Obool)), _1609790), _1609792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1609786), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609788, _1609786), _1609792), _1609794)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609788, _1609786), _1609790), _1609794))))], (42028 ^ _784416) ^ [_1609995, _1609997, _1609999, _1610001] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1609995, tc_fun(_1609997, tc_HOL_Obool)), _1609999), _1610001) = hAPP(c_Set_OCollect(_1609997), hAPP(hAPP(c_COMBB(tc_fun(_1609995, tc_HOL_Obool), tc_HOL_Obool, _1609997), c_HOL_OAll(_1609995)), hAPP(hAPP(c_COMBB(tc_fun(_1609995, tc_HOL_Obool), tc_fun(_1609995, tc_HOL_Obool), _1609997), hAPP(c_COMBS(_1609995, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1609995), c_fimplies), hAPP(hAPP(c_COMBC(_1609995, tc_fun(_1609995, tc_HOL_Obool), tc_HOL_Obool), c_member(_1609995)), _1609999)))), hAPP(hAPP(c_COMBC(_1609997, tc_fun(_1609995, tc_fun(_1609997, tc_HOL_Obool)), tc_fun(_1609995, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1609997, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1609995, tc_fun(_1609997, tc_HOL_Obool)), tc_fun(_1609995, tc_HOL_Obool)), _1609997), c_COMBB(tc_fun(_1609997, tc_HOL_Obool), tc_HOL_Obool, _1609995)), c_member(_1609997))), _1610001)))))], (42030 ^ _784416) ^ [_1610178, _1610180, _1610182, _1610184, _1610186] : [_1610178 = c_Orderings_Obot__class_Obot(tc_fun(_1610180, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610180, tc_fun(_1610182, tc_HOL_Obool)), _1610178), hAPP(hAPP(c_COMBC(_1610180, tc_fun(_1610182, tc_HOL_Obool), tc_fun(_1610182, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1610182, tc_HOL_Obool), tc_fun(tc_fun(_1610182, tc_HOL_Obool), tc_fun(_1610182, tc_HOL_Obool)), _1610180), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1610182, tc_HOL_Obool))), _1610184)), _1610186)) = c_Orderings_Otop__class_Otop(tc_fun(_1610182, tc_HOL_Obool)))], (42036 ^ _784416) ^ [_1610385, _1610387, _1610389, _1610391, _1610393] : [-(_1610385 = c_Orderings_Obot__class_Obot(tc_fun(_1610387, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610387, tc_fun(_1610389, tc_HOL_Obool)), _1610385), hAPP(hAPP(c_COMBC(_1610387, tc_fun(_1610389, tc_HOL_Obool), tc_fun(_1610389, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1610389, tc_HOL_Obool), tc_fun(tc_fun(_1610389, tc_HOL_Obool), tc_fun(_1610389, tc_HOL_Obool)), _1610387), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1610389, tc_HOL_Obool))), _1610391)), _1610393)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1610389, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610387, tc_fun(_1610389, tc_HOL_Obool)), _1610385), _1610391)), _1610393))], (42042 ^ _784416) ^ [_1610530, _1610532, _1610534, _1610536, _1610538] : [_1610530 = c_Orderings_Obot__class_Obot(tc_fun(_1610532, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610532, tc_fun(_1610534, tc_HOL_Obool)), _1610530), hAPP(hAPP(c_COMBB(tc_fun(_1610534, tc_HOL_Obool), tc_fun(_1610534, tc_HOL_Obool), _1610532), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1610534, tc_HOL_Obool)), _1610536)), _1610538)) = c_Orderings_Otop__class_Otop(tc_fun(_1610534, tc_HOL_Obool)))], (42048 ^ _784416) ^ [_1610699, _1610701, _1610703, _1610705, _1610707] : [-(_1610699 = c_Orderings_Obot__class_Obot(tc_fun(_1610701, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610701, tc_fun(_1610703, tc_HOL_Obool)), _1610699), hAPP(hAPP(c_COMBB(tc_fun(_1610703, tc_HOL_Obool), tc_fun(_1610703, tc_HOL_Obool), _1610701), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1610703, tc_HOL_Obool)), _1610705)), _1610707)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1610703, tc_HOL_Obool)), _1610705), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610701, tc_fun(_1610703, tc_HOL_Obool)), _1610699), _1610707)))], (42054 ^ _784416) ^ [_1610825, _1610827, _1610829, _1610831, _1610833] : [_1610825 = c_Orderings_Obot__class_Obot(tc_fun(_1610827, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1610829, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610827, tc_fun(_1610829, tc_HOL_Obool)), _1610825), _1610831)), _1610833) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1610829, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1610829, tc_HOL_Obool))), _1610833))], (42060 ^ _784416) ^ [_1610990, _1610992, _1610994, _1610996, _1610998] : [-(_1610990 = c_Orderings_Obot__class_Obot(tc_fun(_1610992, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1610994, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610992, tc_fun(_1610994, tc_HOL_Obool)), _1610990), _1610996)), _1610998) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1610992, tc_fun(_1610994, tc_HOL_Obool)), _1610990), hAPP(hAPP(c_COMBC(_1610992, tc_fun(_1610994, tc_HOL_Obool), tc_fun(_1610994, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1610994, tc_HOL_Obool), tc_fun(tc_fun(_1610994, tc_HOL_Obool), tc_fun(_1610994, tc_HOL_Obool)), _1610992), c_Groups_Ominus__class_Ominus(tc_fun(_1610994, tc_HOL_Obool))), _1610996)), _1610998)))], (42066 ^ _784416) ^ [_1611135, _1611137, _1611139, _1611141, _1611143] : [_1611135 = c_Orderings_Obot__class_Obot(tc_fun(_1611137, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611137, tc_fun(_1611139, tc_HOL_Obool)), _1611135), hAPP(hAPP(c_COMBC(_1611137, tc_fun(_1611139, tc_HOL_Obool), tc_fun(_1611139, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1611139, tc_HOL_Obool), tc_fun(tc_fun(_1611139, tc_HOL_Obool), tc_fun(_1611139, tc_HOL_Obool)), _1611137), c_Groups_Ominus__class_Ominus(tc_fun(_1611139, tc_HOL_Obool))), _1611141)), _1611143)) = c_Orderings_Otop__class_Otop(tc_fun(_1611139, tc_HOL_Obool)))], (42072 ^ _784416) ^ [_1611342, _1611344, _1611346, _1611348, _1611350] : [-(_1611342 = c_Orderings_Obot__class_Obot(tc_fun(_1611344, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611344, tc_fun(_1611346, tc_HOL_Obool)), _1611342), hAPP(hAPP(c_COMBC(_1611344, tc_fun(_1611346, tc_HOL_Obool), tc_fun(_1611346, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1611346, tc_HOL_Obool), tc_fun(tc_fun(_1611346, tc_HOL_Obool), tc_fun(_1611346, tc_HOL_Obool)), _1611344), c_Groups_Ominus__class_Ominus(tc_fun(_1611346, tc_HOL_Obool))), _1611348)), _1611350)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1611346, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611344, tc_fun(_1611346, tc_HOL_Obool)), _1611342), _1611348)), _1611350))], (42078 ^ _784416) ^ [_1611487, _1611489, _1611491, _1611493, _1611495] : [_1611487 = c_Orderings_Obot__class_Obot(tc_fun(_1611489, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1611491, tc_HOL_Obool)), _1611493), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1611489, tc_fun(_1611491, tc_HOL_Obool)), _1611487), _1611495)) = _1611493)], (42084 ^ _784416) ^ [_1611620, _1611622, _1611624, _1611626, _1611628] : [-(_1611620 = c_Orderings_Obot__class_Obot(tc_fun(_1611622, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1611624, tc_HOL_Obool)), _1611626), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1611622, tc_fun(_1611624, tc_HOL_Obool)), _1611620), _1611628)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611622, tc_fun(_1611624, tc_HOL_Obool)), _1611620), hAPP(hAPP(c_COMBB(tc_fun(_1611624, tc_HOL_Obool), tc_fun(_1611624, tc_HOL_Obool), _1611622), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1611624, tc_HOL_Obool)), _1611626)), _1611628)))], (42090 ^ _784416) ^ [_1611728, _1611730, _1611732, _1611734, _1611736] : [class_Complete__Lattice_Ocomplete__lattice(_1611728), hBOOL(hAPP(hAPP(c_member(_1611730), _1611732), _1611734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1611728), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611730, _1611728), _1611734), _1611736)), hAPP(_1611736, _1611732))))], (42100 ^ _784416) ^ [] : [-(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)))], (42102 ^ _784416) ^ [_1611955, _1611957, _1611959, _1611961, _1611963] : [_1611955 = c_Orderings_Obot__class_Obot(tc_fun(_1611957, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611957, tc_fun(_1611959, tc_HOL_Obool)), _1611955), hAPP(hAPP(c_COMBB(tc_fun(_1611959, tc_HOL_Obool), tc_fun(_1611959, tc_HOL_Obool), _1611957), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1611959, tc_HOL_Obool)), _1611961)), _1611963)) = c_Orderings_Otop__class_Otop(tc_fun(_1611959, tc_HOL_Obool)))], (42108 ^ _784416) ^ [_1612124, _1612126, _1612128, _1612130, _1612132] : [-(_1612124 = c_Orderings_Obot__class_Obot(tc_fun(_1612126, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612126, tc_fun(_1612128, tc_HOL_Obool)), _1612124), hAPP(hAPP(c_COMBB(tc_fun(_1612128, tc_HOL_Obool), tc_fun(_1612128, tc_HOL_Obool), _1612126), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1612128, tc_HOL_Obool)), _1612130)), _1612132)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1612128, tc_HOL_Obool)), _1612130), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1612126, tc_fun(_1612128, tc_HOL_Obool)), _1612124), _1612132)))], (42114 ^ _784416) ^ [_1612232, _1612234, _1612236, _1612238, _1612240, _1612242] : [c_Relation_Osingle__valued(_1612232, _1612234, hAPP(c_Relation_Oconverse(_1612234, _1612232), _1612236)), -(_1612238 = c_Orderings_Obot__class_Obot(tc_fun(_1612240, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1612234, _1612232, _1612236), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612240, tc_fun(_1612234, tc_HOL_Obool)), _1612238), _1612242)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612240, tc_fun(_1612232, tc_HOL_Obool)), _1612238), hAPP(hAPP(c_COMBB(tc_fun(_1612234, tc_HOL_Obool), tc_fun(_1612232, tc_HOL_Obool), _1612240), c_Relation_OImage(_1612234, _1612232, _1612236)), _1612242)))], (42124 ^ _784416) ^ [_1612458, _1612460, _1612462, _1612464, _1612466] : [class_Complete__Lattice_Ocomplete__lattice(_1612458), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612460), _1612462)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1612458), _1612464), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1612460, _1612458), _1612462), _1612466)) = hAPP(hAPP(c_Finite__Set_Ofold(_1612460, _1612458, hAPP(hAPP(c_COMBB(_1612458, tc_fun(_1612458, _1612458), _1612460), c_Lattices_Osemilattice__inf__class_Oinf(_1612458)), _1612466)), _1612464), _1612462))], (42134 ^ _784416) ^ [_1612689, _1612691] : [class_Complete__Lattice_Ocomplete__lattice(_1612689), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612689), _1612691)), -(c_Complete__Lattice_OInf__class_OInf(_1612689, _1612691) = hAPP(hAPP(c_Finite__Set_Ofold(_1612689, _1612689, c_Lattices_Osemilattice__inf__class_Oinf(_1612689)), c_Orderings_Otop__class_Otop(_1612689)), _1612691))], (42144 ^ _784416) ^ [_1612858, _1612860] : [class_Complete__Lattice_Ocomplete__lattice(_1612858), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612858), _1612860)), -(c_Complete__Lattice_OSup__class_OSup(_1612858, _1612860) = hAPP(hAPP(c_Finite__Set_Ofold(_1612858, _1612858, c_Lattices_Osemilattice__sup__class_Osup(_1612858)), c_Orderings_Obot__class_Obot(_1612858)), _1612860))], (42154 ^ _784416) ^ [_1613027, _1613029] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1613027), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1613027, tc_HOL_Obool), _1613029)))), 42155 ^ _784416 : [(42156 ^ _784416) ^ [_1613091] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1613027, tc_HOL_Obool)), _1613091), _1613029)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613027), _1613091))]]], (42164 ^ _784416) ^ [_1613235, _1613237, _1613239, _1613241] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1613235, tc_HOL_Obool)), _1613237), _1613239)), hBOOL(hAPP(hAPP(c_member(_1613235), _1613241), _1613237)), -(hBOOL(hAPP(hAPP(c_member(_1613235), _1613241), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1613235, tc_HOL_Obool), _1613239))))], (42174 ^ _784416) ^ [_1613432, _1613434, _1613436, _1613438] : [hBOOL(hAPP(hAPP(c_member(_1613432), _1613434), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1613432, tc_HOL_Obool), _1613436))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1613432, tc_HOL_Obool)), _1613438), _1613436)), -(hBOOL(hAPP(hAPP(c_member(_1613432), _1613434), _1613438)))], (42184 ^ _784416) ^ [_1613629, _1613631, _1613633, _1613635] : [hBOOL(hAPP(hAPP(c_member(_1613629), _1613631), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1613629, tc_HOL_Obool), _1613633))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1613629, tc_HOL_Obool)), _1613635), _1613633)), -(hBOOL(hAPP(hAPP(c_member(_1613629), _1613631), _1613635)))], (42204 ^ _784416) ^ [_1614103, _1614105, _1614107, _1614109, _1614111, _1614113, _1614115] : [42206 ^ _784416 : [(42207 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1614103), 42205 ^ [_1614103, _1614105, _1614107, _1614109, _1614111, _1614113, _1614115]), _1614109)))], (42209 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1614111, 42205 ^ [_1614103, _1614105, _1614107, _1614109, _1614111, _1614113, _1614115]), _1614113), _1614115))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614103, tc_fun(_1614105, tc_fun(_1614107, tc_HOL_Obool))), _1614109), _1614111), _1614113), _1614115)))], (42194 ^ _784416) ^ [_1613856, _1613858, _1613860, _1613862, _1613864, _1613866, _1613868] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1613856, tc_fun(_1613858, tc_fun(_1613860, tc_HOL_Obool))), _1613862), _1613864), _1613866), _1613868)), 42197 ^ _784416 : [(42198 ^ _784416) ^ [_1613984] : [hBOOL(hAPP(hAPP(c_member(_1613856), _1613984), _1613862)), -(hBOOL(hAPP(hAPP(hAPP(_1613864, _1613984), _1613866), _1613868)))]]], (42213 ^ _784416) ^ [_1614363, _1614365, _1614367, _1614369] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1614363, tc_HOL_Obool), tc_fun(_1614365, tc_HOL_Obool)), _1614367), hAPP(hAPP(c_COMBC(tc_fun(_1614363, tc_HOL_Obool), tc_fun(_1614363, tc_fun(_1614365, tc_HOL_Obool)), tc_fun(_1614365, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614363, tc_fun(_1614365, tc_HOL_Obool))), _1614369)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614363, tc_fun(_1614365, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1614363, tc_HOL_Obool), _1614367)), _1614369))], (42215 ^ _784416) ^ [_1614453, _1614455, _1614457, _1614459] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614453, tc_fun(_1614455, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1614453, tc_HOL_Obool), _1614457)), _1614459) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1614453, tc_HOL_Obool), tc_fun(_1614455, tc_HOL_Obool)), _1614457), hAPP(hAPP(c_COMBC(tc_fun(_1614453, tc_HOL_Obool), tc_fun(_1614453, tc_fun(_1614455, tc_HOL_Obool)), tc_fun(_1614455, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614453, tc_fun(_1614455, tc_HOL_Obool))), _1614459)))], (42227 ^ _784416) ^ [_1614785, _1614787, _1614789, _1614791, _1614793] : [42229 ^ _784416 : [(42230 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1614785), 42228 ^ [_1614785, _1614787, _1614789, _1614791, _1614793]), _1614789)))], (42232 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1614791, 42228 ^ [_1614785, _1614787, _1614789, _1614791, _1614793]), _1614793))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614785, tc_fun(_1614787, tc_HOL_Obool)), _1614789), _1614791), _1614793)))], (42217 ^ _784416) ^ [_1614567, _1614569, _1614571, _1614573, _1614575] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1614567, tc_fun(_1614569, tc_HOL_Obool)), _1614571), _1614573), _1614575)), 42220 ^ _784416 : [(42221 ^ _784416) ^ [_1614676] : [hBOOL(hAPP(hAPP(c_member(_1614567), _1614676), _1614571)), -(hBOOL(hAPP(hAPP(_1614573, _1614676), _1614575)))]]], (42236 ^ _784416) ^ [_1615008, _1615010, _1615012, _1615014] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615008, tc_fun(_1615010, tc_HOL_Obool)), _1615012), _1615014) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1615010, tc_HOL_Obool), hAPP(c_Set_Oimage(_1615008, tc_fun(_1615010, tc_HOL_Obool), _1615014), _1615012)))], (42238 ^ _784416) ^ [_1615065, _1615067, _1615069, _1615071] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1615065, tc_HOL_Obool), hAPP(c_Set_Oimage(_1615067, tc_fun(_1615065, tc_HOL_Obool), _1615069), _1615071)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615067, tc_fun(_1615065, tc_HOL_Obool)), _1615071), _1615069))], (42240 ^ _784416) ^ [_1615122, _1615124, _1615126] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1615122, tc_HOL_Obool)), _1615124), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1615122, tc_HOL_Obool), _1615126)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1615122, tc_HOL_Obool), tc_fun(_1615122, tc_HOL_Obool)), _1615126), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1615122, tc_HOL_Obool)), _1615124)))], (42242 ^ _784416) ^ [_1615189, _1615191, _1615193] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1615189, tc_HOL_Obool)), _1615191), _1615193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1615189, tc_HOL_Obool)), _1615191), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1615189, tc_HOL_Obool), _1615193))))], (42248 ^ _784416) ^ [_1615320, _1615322, _1615324] : [class_Complete__Lattice_Ocomplete__lattice(_1615320), 42251 ^ _784416 : [(42262 ^ _784416) ^ [] : [42264 ^ _784416 : [(42265 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1615320), 42263 ^ [_1615320, _1615322, _1615324]), _1615322)))], (42267 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1615320), 42263 ^ [_1615320, _1615322, _1615324]), _1615324))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1615320), c_Complete__Lattice_OSup__class_OSup(_1615320, _1615322)), _1615324)))], (42252 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1615320), c_Complete__Lattice_OSup__class_OSup(_1615320, _1615322)), _1615324)), 42255 ^ _784416 : [(42256 ^ _784416) ^ [_1615478] : [hBOOL(hAPP(hAPP(c_member(_1615320), _1615478), _1615322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1615320), _1615478), _1615324)))]]]]], (42271 ^ _784416) ^ [_1615754, _1615756, _1615758] : [class_Complete__Lattice_Ocomplete__lattice(_1615754), 42274 ^ _784416 : [(42285 ^ _784416) ^ [] : [42287 ^ _784416 : [(42288 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1615754), 42286 ^ [_1615754, _1615756, _1615758]), _1615758)))], (42290 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1615754), _1615756), 42286 ^ [_1615754, _1615756, _1615758]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1615754), _1615756), c_Complete__Lattice_OInf__class_OInf(_1615754, _1615758))))], (42275 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1615754), _1615756), c_Complete__Lattice_OInf__class_OInf(_1615754, _1615758))), 42278 ^ _784416 : [(42279 ^ _784416) ^ [_1615912] : [hBOOL(hAPP(hAPP(c_member(_1615754), _1615912), _1615758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1615754), _1615756), _1615912)))]]]]], (42294 ^ _784416) ^ [_1616188, _1616190, _1616192] : [class_Complete__Lattice_Ocomplete__lattice(_1616188), class_Orderings_Olinorder(_1616188), 42301 ^ _784416 : [(42302 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1616188), _1616190), c_Complete__Lattice_OSup__class_OSup(_1616188, _1616192))), 42306 ^ _784416 : [(42307 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1616188), 42305 ^ [_1616188, _1616190, _1616192]), _1616192)))], (42309 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1616188), _1616190), 42305 ^ [_1616188, _1616190, _1616192])))]]], (42311 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1616188), _1616190), c_Complete__Lattice_OSup__class_OSup(_1616188, _1616192)))), 42312 ^ _784416 : [(42313 ^ _784416) ^ [_1616494] : [hBOOL(hAPP(hAPP(c_member(_1616188), _1616494), _1616192)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1616188), _1616190), _1616494))]]]]], (42321 ^ _784416) ^ [_1616648, _1616650, _1616652] : [class_Complete__Lattice_Ocomplete__lattice(_1616648), class_Orderings_Olinorder(_1616648), 42328 ^ _784416 : [(42329 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1616648), c_Complete__Lattice_OInf__class_OInf(_1616648, _1616650)), _1616652)), 42333 ^ _784416 : [(42334 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1616648), 42332 ^ [_1616648, _1616650, _1616652]), _1616650)))], (42336 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1616648), 42332 ^ [_1616648, _1616650, _1616652]), _1616652)))]]], (42338 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1616648), c_Complete__Lattice_OInf__class_OInf(_1616648, _1616650)), _1616652))), 42339 ^ _784416 : [(42340 ^ _784416) ^ [_1616954] : [hBOOL(hAPP(hAPP(c_member(_1616648), _1616954), _1616650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1616648), _1616954), _1616652))]]]]], (42348 ^ _784416) ^ [_1617108, _1617110] : [-(hAPP(c_Relation_OField(_1617108), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1617108, _1617108), tc_HOL_Obool), _1617110)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617108, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1617108, _1617108), tc_HOL_Obool), tc_fun(_1617108, tc_HOL_Obool), c_Relation_OField(_1617108)), _1617110)))], (42350 ^ _784416) ^ [_1617171, _1617173] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617171, tc_HOL_Obool), hAPP(c_Set_OPow(_1617171), _1617173)) = _1617173)], (42362 ^ _784416) ^ [_1617493, _1617495, _1617497] : [42364 ^ _784416 : [(42365 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1617493, tc_HOL_Obool)), 42363 ^ [_1617493, _1617495, _1617497]), _1617495)))], (42367 ^ _784416) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1617493, tc_HOL_Obool)), 42363 ^ [_1617493, _1617495, _1617497]), _1617497) = c_Orderings_Obot__class_Obot(tc_fun(_1617493, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1617493, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617493, tc_HOL_Obool), _1617495)), _1617497) = c_Orderings_Obot__class_Obot(tc_fun(_1617493, tc_HOL_Obool)))], (42352 ^ _784416) ^ [_1617225, _1617227, _1617229] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1617225, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617225, tc_HOL_Obool), _1617227)), _1617229) = c_Orderings_Obot__class_Obot(tc_fun(_1617225, tc_HOL_Obool)), 42355 ^ _784416 : [(42356 ^ _784416) ^ [_1617360] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1617225, tc_HOL_Obool)), _1617360), _1617227)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1617225, tc_HOL_Obool)), _1617360), _1617229) = c_Orderings_Obot__class_Obot(tc_fun(_1617225, tc_HOL_Obool)))]]], (42371 ^ _784416) ^ [_1617756, _1617758, _1617760] : [-(hAPP(c_Relation_ODomain(_1617756, _1617758), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1617756, _1617758), tc_HOL_Obool), _1617760)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1617756, _1617758), tc_HOL_Obool), tc_fun(_1617756, tc_HOL_Obool)), _1617760), c_Relation_ODomain(_1617756, _1617758)))], (42373 ^ _784416) ^ [_1617819, _1617821, _1617823, _1617825] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1617819, tc_fun(_1617821, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617819, tc_HOL_Obool), _1617823)), _1617825) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1617819, tc_HOL_Obool), tc_fun(_1617821, tc_HOL_Obool)), _1617823), hAPP(hAPP(c_COMBC(tc_fun(_1617819, tc_HOL_Obool), tc_fun(_1617819, tc_fun(_1617821, tc_HOL_Obool)), tc_fun(_1617821, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1617819, tc_fun(_1617821, tc_HOL_Obool))), _1617825)))], (42375 ^ _784416) ^ [_1617909, _1617911, _1617913, _1617915] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1617909, tc_HOL_Obool), tc_fun(_1617911, tc_HOL_Obool)), _1617913), hAPP(hAPP(c_COMBC(tc_fun(_1617909, tc_HOL_Obool), tc_fun(_1617909, tc_fun(_1617911, tc_HOL_Obool)), tc_fun(_1617911, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1617909, tc_fun(_1617911, tc_HOL_Obool))), _1617915)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1617909, tc_fun(_1617911, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1617909, tc_HOL_Obool), _1617913)), _1617915))], (42377 ^ _784416) ^ [_1617999, _1618001, _1618003] : [-(hAPP(c_Relation_ORange(_1617999, _1618001), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1617999, _1618001), tc_HOL_Obool), _1618003)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1617999, _1618001), tc_HOL_Obool), tc_fun(_1618001, tc_HOL_Obool)), _1618003), c_Relation_ORange(_1617999, _1618001)))], (42379 ^ _784416) ^ [_1618062, _1618064, _1618066] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1618062, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1618062, tc_HOL_Obool), _1618064)), _1618066) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1618062, tc_HOL_Obool), tc_fun(_1618062, tc_HOL_Obool)), _1618064), hAPP(hAPP(c_COMBC(tc_fun(_1618062, tc_HOL_Obool), tc_fun(_1618062, tc_HOL_Obool), tc_fun(_1618062, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1618062, tc_HOL_Obool))), _1618066)))], (42381 ^ _784416) ^ [_1618145, _1618147, _1618149] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1618145, tc_HOL_Obool)), _1618147), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1618145, tc_HOL_Obool), _1618149)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1618145, tc_HOL_Obool), tc_fun(_1618145, tc_HOL_Obool)), _1618149), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1618145, tc_HOL_Obool)), _1618147)))], (42383 ^ _784416) ^ [_1618212, _1618214, _1618216, _1618218] : [-(hAPP(c_Set_Ovimage(_1618212, _1618214, _1618216), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1618214, tc_HOL_Obool), _1618218)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1618214, tc_HOL_Obool), tc_fun(_1618212, tc_HOL_Obool)), _1618218), c_Set_Ovimage(_1618212, _1618214, _1618216)))], (42385 ^ _784416) ^ [_1618273, _1618275, _1618277, _1618279] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1618273, _1618275), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1618273, tc_HOL_Obool), _1618277)), _1618279) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1618273, tc_HOL_Obool), tc_fun(tc_prod(_1618273, _1618275), tc_HOL_Obool)), _1618277), hAPP(hAPP(c_COMBC(tc_fun(_1618273, tc_HOL_Obool), tc_fun(_1618273, tc_fun(_1618275, tc_HOL_Obool)), tc_fun(tc_prod(_1618273, _1618275), tc_HOL_Obool)), c_Product__Type_OSigma(_1618273, _1618275)), _1618279)))], (42387 ^ _784416) ^ [_1618363, _1618365, _1618367, _1618369] : [-(hAPP(c_Set_Oimage(_1618363, _1618365, _1618367), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1618363, tc_HOL_Obool), _1618369)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1618363, tc_HOL_Obool), tc_fun(_1618365, tc_HOL_Obool)), _1618369), c_Set_Oimage(_1618363, _1618365, _1618367)))], (42389 ^ _784416) ^ [_1618424, _1618426, _1618428] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1618424, tc_HOL_Obool)), _1618426), _1618428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1618424, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1618424, tc_HOL_Obool), _1618428)), _1618426)))], (42395 ^ _784416) ^ [_1618555, _1618557] : [class_Complete__Lattice_Ocomplete__lattice(_1618555), -(c_Complete__Lattice_OSup__class_OSup(_1618555, _1618557) = c_Complete__Lattice_OInf__class_OInf(_1618555, hAPP(c_Set_OCollect(_1618555), hAPP(hAPP(c_COMBB(tc_fun(_1618555, tc_HOL_Obool), tc_HOL_Obool, _1618555), c_HOL_OAll(_1618555)), hAPP(hAPP(c_COMBB(tc_fun(_1618555, tc_HOL_Obool), tc_fun(_1618555, tc_HOL_Obool), _1618555), hAPP(c_COMBS(_1618555, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1618555), c_fimplies), hAPP(hAPP(c_COMBC(_1618555, tc_fun(_1618555, tc_HOL_Obool), tc_HOL_Obool), c_member(_1618555)), _1618557)))), hAPP(c_COMBC(_1618555, _1618555, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1618555)))))))], (42401 ^ _784416) ^ [_1618796, _1618798] : [class_Complete__Lattice_Ocomplete__lattice(_1618796), -(c_Complete__Lattice_OInf__class_OInf(_1618796, _1618798) = c_Complete__Lattice_OSup__class_OSup(_1618796, hAPP(c_Set_OCollect(_1618796), hAPP(hAPP(c_COMBB(tc_fun(_1618796, tc_HOL_Obool), tc_HOL_Obool, _1618796), c_HOL_OAll(_1618796)), hAPP(hAPP(c_COMBB(tc_fun(_1618796, tc_HOL_Obool), tc_fun(_1618796, tc_HOL_Obool), _1618796), hAPP(c_COMBS(_1618796, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1618796), c_fimplies), hAPP(hAPP(c_COMBC(_1618796, tc_fun(_1618796, tc_HOL_Obool), tc_HOL_Obool), c_member(_1618796)), _1618798)))), c_Orderings_Oord__class_Oless__eq(_1618796))))))], (42407 ^ _784416) ^ [_1619023] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619023, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1619023, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1619023, tc_HOL_Obool)))], (42409 ^ _784416) ^ [_1619065, _1619067, _1619069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1619065, tc_HOL_Obool), tc_HOL_Obool)), _1619067), _1619069)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1619065, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619065, tc_HOL_Obool), _1619067)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619065, tc_HOL_Obool), _1619069))))], (42415 ^ _784416) ^ [_1619214, _1619216, _1619218] : [c_Equiv__Relations_Oequiv(_1619214, _1619216, _1619218), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619214, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1619214), _1619216), _1619218)) = _1619216)], (42421 ^ _784416) ^ [_1619323, _1619325, _1619327] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619323, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1619323, tc_HOL_Obool)), _1619325), _1619327)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1619323, tc_HOL_Obool)), _1619325), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619323, tc_HOL_Obool), _1619327)))], (42423 ^ _784416) ^ [_1619384, _1619386] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1619384), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619384, tc_HOL_Obool), _1619386))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1619384, tc_HOL_Obool)), _1619386)))], (42429 ^ _784416) ^ [_1619495, _1619497] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1619495, tc_HOL_Obool), tc_HOL_Obool)), _1619497), hAPP(c_Set_OPow(_1619495), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619495, tc_HOL_Obool), _1619497)))))], (42431 ^ _784416) ^ [_1619544, _1619546, _1619548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1619544, tc_HOL_Obool), tc_HOL_Obool)), _1619546), _1619548)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1619544, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619544, tc_HOL_Obool), _1619548)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619544, tc_HOL_Obool), _1619546))))], (42437 ^ _784416) ^ [_1619693] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619693, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1619693, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1619693, tc_HOL_Obool)))], (42439 ^ _784416) ^ [_1619735, _1619737] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619735, tc_HOL_Obool), _1619737) = hAPP(c_Set_OCollect(_1619735), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1619735, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1619735), c_HOL_OAll(tc_fun(_1619735, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1619735, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1619735, tc_HOL_Obool), tc_HOL_Obool), _1619735), hAPP(c_COMBS(tc_fun(_1619735, 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(_1619735, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1619735, tc_HOL_Obool), tc_fun(tc_fun(_1619735, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1619735, tc_HOL_Obool))), _1619737)))), c_member(_1619735)))))], (42441 ^ _784416) ^ [_1619863] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619863, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1619863, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1619863, tc_HOL_Obool)))], (42443 ^ _784416) ^ [_1619905, _1619907, _1619909] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619905, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1619905, tc_HOL_Obool), tc_HOL_Obool)), _1619907), _1619909)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1619905, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619905, tc_HOL_Obool), _1619907)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1619905, tc_HOL_Obool), _1619909)))], (42445 ^ _784416) ^ [_1619975, _1619977, _1619979] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619975, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1619975, tc_HOL_Obool)), _1619977), _1619979)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1619975, tc_HOL_Obool)), _1619977), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1619975, tc_HOL_Obool), _1619979)))], (42447 ^ _784416) ^ [_1620036, _1620038, _1620040, _1620042] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1620036, tc_fun(_1620038, tc_HOL_Obool)), _1620040), _1620042) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620038, tc_HOL_Obool), hAPP(c_Set_Oimage(_1620036, tc_fun(_1620038, tc_HOL_Obool), _1620042), _1620040)))], (42449 ^ _784416) ^ [_1620093, _1620095, _1620097, _1620099] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1620093, tc_HOL_Obool), hAPP(c_Set_Oimage(_1620095, tc_fun(_1620093, tc_HOL_Obool), _1620097), _1620099)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1620095, tc_fun(_1620093, tc_HOL_Obool)), _1620099), _1620097))], (42451 ^ _784416) ^ [_1620150, _1620152, _1620154] : [class_Complete__Lattice_Ocomplete__lattice(_1620150), hBOOL(hAPP(hAPP(c_member(_1620150), _1620152), _1620154)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620150), _1620152), c_Complete__Lattice_OSup__class_OSup(_1620150, _1620154))))], (42461 ^ _784416) ^ [_1620315] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620315, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1620315, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1620315, tc_HOL_Obool)))], (42463 ^ _784416) ^ [_1620357, _1620359, _1620361] : [class_Complete__Lattice_Ocomplete__lattice(_1620357), hBOOL(hAPP(hAPP(c_member(_1620357), _1620359), _1620361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620357), c_Complete__Lattice_OInf__class_OInf(_1620357, _1620361)), _1620359)))], (42473 ^ _784416) ^ [_1620522, _1620524, _1620526] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620522, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1620522, tc_HOL_Obool), tc_HOL_Obool)), _1620524), _1620526)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1620522, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620522, tc_HOL_Obool), _1620524)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620522, tc_HOL_Obool), _1620526)))], (42475 ^ _784416) ^ [_1620592] : [class_Complete__Lattice_Ocomplete__lattice(_1620592), -(c_Complete__Lattice_OSup__class_OSup(_1620592, c_Orderings_Obot__class_Obot(tc_fun(_1620592, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1620592))], (42481 ^ _784416) ^ [_1620685, _1620687] : [class_Complete__Lattice_Ocomplete__lattice(_1620685), -(c_Complete__Lattice_OSup__class_OSup(_1620685, hAPP(hAPP(c_Set_Oinsert(_1620685), _1620687), c_Orderings_Obot__class_Obot(tc_fun(_1620685, tc_HOL_Obool)))) = _1620687)], (42487 ^ _784416) ^ [_1620792, _1620794, _1620796] : [class_Complete__Lattice_Ocomplete__lattice(_1620792), -(c_Complete__Lattice_OSup__class_OSup(_1620792, hAPP(hAPP(c_Set_Oinsert(_1620792), _1620794), _1620796)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1620792), _1620794), c_Complete__Lattice_OSup__class_OSup(_1620792, _1620796)))], (42493 ^ _784416) ^ [_1620913, _1620915, _1620917, _1620919, _1620921] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1620913, tc_fun(_1620915, tc_HOL_Obool)), _1620917), hAPP(hAPP(c_COMBS(_1620913, tc_fun(_1620915, tc_HOL_Obool), tc_fun(_1620915, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1620915, tc_HOL_Obool), tc_fun(tc_fun(_1620915, tc_HOL_Obool), tc_fun(_1620915, tc_HOL_Obool)), _1620913), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1620915, tc_HOL_Obool))), _1620919)), _1620921)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1620915, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620915, tc_HOL_Obool), hAPP(c_Set_Oimage(_1620913, tc_fun(_1620915, tc_HOL_Obool), _1620919), _1620917))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1620915, tc_HOL_Obool), hAPP(c_Set_Oimage(_1620913, tc_fun(_1620915, tc_HOL_Obool), _1620921), _1620917))))], (42495 ^ _784416) ^ [_1621042] : [class_Complete__Lattice_Ocomplete__lattice(_1621042), -(c_Complete__Lattice_OSup__class_OSup(_1621042, c_Orderings_Otop__class_Otop(tc_fun(_1621042, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1621042))], (42501 ^ _784416) ^ [_1621135, _1621137] : [class_Complete__Lattice_Ocomplete__lattice(_1621135), -(c_Complete__Lattice_OInf__class_OInf(_1621135, hAPP(hAPP(c_Set_Oinsert(_1621135), _1621137), c_Orderings_Obot__class_Obot(tc_fun(_1621135, tc_HOL_Obool)))) = _1621137)], (42507 ^ _784416) ^ [_1621242] : [class_Complete__Lattice_Ocomplete__lattice(_1621242), -(c_Complete__Lattice_OInf__class_OInf(_1621242, c_Orderings_Obot__class_Obot(tc_fun(_1621242, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1621242))], (42513 ^ _784416) ^ [_1621335] : [class_Complete__Lattice_Ocomplete__lattice(_1621335), -(c_Complete__Lattice_OInf__class_OInf(_1621335, c_Orderings_Otop__class_Otop(tc_fun(_1621335, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1621335))], (42519 ^ _784416) ^ [_1621428, _1621430, _1621432] : [class_Complete__Lattice_Ocomplete__lattice(_1621428), -(c_Complete__Lattice_OInf__class_OInf(_1621428, hAPP(hAPP(c_Set_Oinsert(_1621428), _1621430), _1621432)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1621428), _1621430), c_Complete__Lattice_OInf__class_OInf(_1621428, _1621432)))], (42525 ^ _784416) ^ [_1621549, _1621551, _1621553] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1621549, tc_HOL_Obool)), _1621551), _1621553) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1621549, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1621549, tc_HOL_Obool)), _1621551), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1621549, tc_HOL_Obool)), _1621553), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1621549, tc_HOL_Obool), tc_HOL_Obool))))))], (42527 ^ _784416) ^ [_1621623, _1621625, _1621627, _1621629, _1621631] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1621623, tc_fun(_1621625, tc_HOL_Obool)), _1621627), hAPP(hAPP(c_COMBS(_1621623, tc_fun(_1621625, tc_HOL_Obool), tc_fun(_1621625, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1621625, tc_HOL_Obool), tc_fun(tc_fun(_1621625, tc_HOL_Obool), tc_fun(_1621625, tc_HOL_Obool)), _1621623), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1621625, tc_HOL_Obool))), _1621629)), _1621631)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1621625, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1621625, tc_HOL_Obool), hAPP(c_Set_Oimage(_1621623, tc_fun(_1621625, tc_HOL_Obool), _1621629), _1621627))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1621625, tc_HOL_Obool), hAPP(c_Set_Oimage(_1621623, tc_fun(_1621625, tc_HOL_Obool), _1621631), _1621627))))], (42529 ^ _784416) ^ [_1621752, _1621754, _1621756] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621752, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1621752, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1621752, tc_HOL_Obool), tc_HOL_Obool)), _1621754), _1621756))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1621752, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1621752, tc_HOL_Obool), _1621754)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1621752, tc_HOL_Obool), _1621756)))))], (42531 ^ _784416) ^ [_1621832, _1621834, _1621836] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1621832, tc_HOL_Obool)), _1621834), _1621836) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1621832, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1621832, tc_HOL_Obool)), _1621834), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1621832, tc_HOL_Obool)), _1621836), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1621832, tc_HOL_Obool), tc_HOL_Obool))))))], (42533 ^ _784416) ^ [_1621906, _1621908, _1621910] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621906, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1621906, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1621906, tc_HOL_Obool), _1621908)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1621906, tc_HOL_Obool), _1621910))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1621906, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1621906, tc_HOL_Obool), tc_HOL_Obool)), _1621908), _1621910)))))], (42535 ^ _784416) ^ [_1621986, _1621988, _1621990] : [class_Complete__Lattice_Ocomplete__lattice(_1621986), -(c_Complete__Lattice_OSup__class_OSup(_1621986, hAPP(hAPP(c_Set_Oinsert(_1621986), _1621988), hAPP(hAPP(c_Set_Oinsert(_1621986), _1621990), c_Orderings_Obot__class_Obot(tc_fun(_1621986, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1621986), _1621988), _1621990))], (42541 ^ _784416) ^ [_1622127, _1622129, _1622131] : [class_Complete__Lattice_Ocomplete__lattice(_1622127), -(c_Complete__Lattice_OInf__class_OInf(_1622127, hAPP(hAPP(c_Set_Oinsert(_1622127), _1622129), hAPP(hAPP(c_Set_Oinsert(_1622127), _1622131), c_Orderings_Obot__class_Obot(tc_fun(_1622127, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1622127), _1622129), _1622131))], (42547 ^ _784416) ^ [_1622268, _1622270, _1622272] : [class_Complete__Lattice_Ocomplete__lattice(_1622268), hBOOL(hAPP(c_Finite__Set_Ofinite(_1622268), _1622270)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1622268), _1622272), c_Complete__Lattice_OSup__class_OSup(_1622268, _1622270)) = hAPP(hAPP(c_Finite__Set_Ofold(_1622268, _1622268, c_Lattices_Osemilattice__sup__class_Osup(_1622268)), _1622272), _1622270))], (42557 ^ _784416) ^ [_1622453, _1622455] : [class_Complete__Lattice_Ocomplete__lattice(_1622453), hBOOL(hAPP(c_Finite__Set_Ofinite(_1622453), _1622455)), -(_1622455 = c_Orderings_Obot__class_Obot(tc_fun(_1622453, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1622453, _1622455) = c_Complete__Lattice_OSup__class_OSup(_1622453, _1622455))], (42571 ^ _784416) ^ [_1622625, _1622627, _1622629] : [class_Complete__Lattice_Ocomplete__lattice(_1622625), hBOOL(hAPP(c_Finite__Set_Ofinite(_1622625), _1622627)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1622625), _1622629), c_Complete__Lattice_OInf__class_OInf(_1622625, _1622627)) = hAPP(hAPP(c_Finite__Set_Ofold(_1622625, _1622625, c_Lattices_Osemilattice__inf__class_Oinf(_1622625)), _1622629), _1622627))], (42581 ^ _784416) ^ [_1622810, _1622812] : [class_Complete__Lattice_Ocomplete__lattice(_1622810), hBOOL(hAPP(c_Finite__Set_Ofinite(_1622810), _1622812)), -(_1622812 = c_Orderings_Obot__class_Obot(tc_fun(_1622810, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1622810, _1622812) = c_Complete__Lattice_OInf__class_OInf(_1622810, _1622812))], (42595 ^ _784416) ^ [_1622982, _1622984, _1622986, _1622988, _1622990, _1622992, _1622994, _1622996] : [c_Fun_Oinj__on(_1622982, _1622984, _1622986, _1622988), 42601 ^ _784416 : [(42602 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622990), 42600 ^ [_1622982, _1622984, _1622986, _1622988, _1622990, _1622992, _1622994, _1622996]), _1622992)))], (42604 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1622982, tc_HOL_Obool)), hAPP(_1622994, 42600 ^ [_1622982, _1622984, _1622986, _1622988, _1622990, _1622992, _1622994, _1622996])), _1622988))]], hBOOL(hAPP(hAPP(c_member(_1622990), _1622996), _1622992)), -(hAPP(c_Set_Oimage(_1622982, _1622984, _1622986), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1622990, tc_fun(_1622982, tc_HOL_Obool)), _1622992), _1622994)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1622990, tc_fun(_1622984, tc_HOL_Obool)), _1622992), hAPP(hAPP(c_COMBB(tc_fun(_1622982, tc_HOL_Obool), tc_fun(_1622984, tc_HOL_Obool), _1622990), c_Set_Oimage(_1622982, _1622984, _1622986)), _1622994)))], (42612 ^ _784416) ^ [_1623471, _1623473, _1623475] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1623471, tc_HOL_Obool)), _1623473)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623471), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623471, tc_HOL_Obool), _1623473))), 42622 ^ _784416 : [(42623 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1623471, tc_HOL_Obool)), 42621 ^ [_1623471, _1623473, _1623475]), _1623473)))], (42625 ^ _784416) ^ [] : [hAPP(c_Finite__Set_Ocard(_1623471), 42621 ^ [_1623471, _1623473, _1623475]) = _1623475]], 42629 ^ _784416 : [(42630 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1623471, tc_HOL_Obool)), 42628 ^ [_1623471, _1623473, _1623475]), _1623473)))], (42633 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1623471, tc_HOL_Obool)), 42631 ^ [_1623471, _1623473, _1623475]), _1623473)))], (42635 ^ _784416) ^ [] : [42628 ^ [_1623471, _1623473, _1623475] = 42631 ^ [_1623471, _1623473, _1623475]], (42637 ^ _784416) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1623471, tc_HOL_Obool)), 42628 ^ [_1623471, _1623473, _1623475]), 42631 ^ [_1623471, _1623473, _1623475]) = c_Orderings_Obot__class_Obot(tc_fun(_1623471, tc_HOL_Obool))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1623475), hAPP(c_Finite__Set_Ocard(tc_fun(_1623471, tc_HOL_Obool)), _1623473)) = hAPP(c_Finite__Set_Ocard(_1623471), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1623471, tc_HOL_Obool), _1623473)))], (42641 ^ _784416) ^ [_1624253, _1624255] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1624253, tc_HOL_Obool), _1624255) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1624253, tc_HOL_Obool), tc_fun(_1624253, tc_HOL_Obool)), _1624255), c_COMBI(tc_fun(_1624253, tc_HOL_Obool))))], (42643 ^ _784416) ^ [_1624304, _1624306] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1624304, tc_HOL_Obool), _1624306) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1624304, tc_HOL_Obool), tc_fun(_1624304, tc_HOL_Obool)), _1624306), c_COMBI(tc_fun(_1624304, tc_HOL_Obool))))], (42645 ^ _784416) ^ [_1624355, _1624357] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1624355, tc_HOL_Obool)), _1624357)), 42651 ^ _784416 : [(42652 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1624355, tc_HOL_Obool)), 42650 ^ [_1624355, _1624357]), _1624357)))], (42654 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1624355), 42650 ^ [_1624355, _1624357]))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1624355), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1624355, tc_HOL_Obool), _1624357))))], (42658 ^ _784416) ^ [_1624613, _1624615, _1624617] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1624613, tc_HOL_Obool)), _1624615), _1624617))), 42664 ^ _784416 : [(42665 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1624613, tc_HOL_Obool)), 42663 ^ [_1624613, _1624615, _1624617]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1624613, tc_HOL_Obool)), _1624615), _1624617))))], (42668 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1624613, tc_HOL_Obool)), 42666 ^ [_1624613, _1624615, _1624617]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1624613, tc_HOL_Obool)), _1624615), _1624617))))], (42670 ^ _784416) ^ [] : [42663 ^ [_1624613, _1624615, _1624617] = 42666 ^ [_1624613, _1624615, _1624617]], (42672 ^ _784416) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624613, tc_HOL_Obool)), 42663 ^ [_1624613, _1624615, _1624617]), 42666 ^ [_1624613, _1624615, _1624617]) = c_Orderings_Obot__class_Obot(tc_fun(_1624613, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624613, tc_HOL_Obool)), _1624615), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1624613, tc_HOL_Obool), _1624617)) = c_Orderings_Obot__class_Obot(tc_fun(_1624613, tc_HOL_Obool)))], (42676 ^ _784416) ^ [_1625206, _1625208, _1625210, _1625212] : [-(_1625206 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1625208, tc_HOL_Obool), tc_HOL_Obool))), 42682 ^ _784416 : [(42683 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1625208, tc_HOL_Obool)), 42681 ^ [_1625206, _1625208, _1625210, _1625212]), _1625206)))], (42685 ^ _784416) ^ [] : [c_Fun_Oinj__on(_1625208, _1625210, _1625212, 42681 ^ [_1625206, _1625208, _1625210, _1625212])]], -(c_Fun_Oinj__on(_1625208, _1625210, _1625212, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1625208, tc_HOL_Obool), _1625206)))], (42689 ^ _784416) ^ [_1625467, _1625469, _1625471] : [42691 ^ _784416 : [(42692 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1625467, tc_HOL_Obool)), 42690 ^ [_1625467, _1625469, _1625471]), _1625469)))], (42694 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1625467, tc_HOL_Obool)), 42690 ^ [_1625467, _1625469, _1625471]), _1625471))]], -(_1625469 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1625467, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1625467, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1625467, tc_HOL_Obool), _1625469)), _1625471)))], (42702 ^ _784416) ^ [_1625728, _1625730, _1625732, _1625734, _1625736, _1625738] : [-(_1625728 = c_Orderings_Obot__class_Obot(tc_fun(_1625730, tc_HOL_Obool))), 42708 ^ _784416 : [(42709 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1625730), 42707 ^ [_1625728, _1625730, _1625732, _1625734, _1625736, _1625738]), _1625728)))], (42711 ^ _784416) ^ [] : [c_Fun_Oinj__on(_1625732, _1625734, _1625736, hAPP(_1625738, 42707 ^ [_1625728, _1625730, _1625732, _1625734, _1625736, _1625738]))]], -(c_Fun_Oinj__on(_1625732, _1625734, _1625736, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1625730, tc_fun(_1625732, tc_HOL_Obool)), _1625728), _1625738)))], (42715 ^ _784416) ^ [_1626020, _1626022, _1626024, _1626026, _1626028, _1626030, _1626032] : [c_Finite__Set_Ofun__left__comm(_1626020, _1626022, _1626024), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1626020, _1626022, _1626024, _1626026, hAPP(hAPP(c_Set_Oinsert(_1626020), _1626028), _1626030)), _1626032)), -(hBOOL(hAPP(hAPP(c_member(_1626020), _1626028), _1626030))), 42727 ^ _784416 : [(42728 ^ _784416) ^ [] : [-(_1626032 = hAPP(hAPP(_1626024, _1626028), 42726 ^ [_1626020, _1626022, _1626024, _1626026, _1626028, _1626030, _1626032]))], (42730 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1626020, _1626022, _1626024, _1626026, _1626030), 42726 ^ [_1626020, _1626022, _1626024, _1626026, _1626028, _1626030, _1626032])))]]], (42732 ^ _784416) ^ [_1626346, _1626348, _1626350, _1626352] : [class_Orderings_Olinorder(_1626346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626346), _1626348)), 42742 ^ _784416 : [(42743 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1626346), 42741 ^ [_1626346, _1626348, _1626350, _1626352]), _1626348)))], (42745 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1626346), 42741 ^ [_1626346, _1626348, _1626350, _1626352]), _1626350))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1626346), hAPP(hAPP(c_Finite__Set_Ofold(_1626346, _1626346, c_Orderings_Oord__class_Omax(_1626346)), _1626352), _1626348)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1626346), _1626350), _1626352))))], (42749 ^ _784416) ^ [_1626710, _1626712, _1626714, _1626716] : [class_Orderings_Olinorder(_1626710), hBOOL(hAPP(c_Finite__Set_Ofinite(_1626710), _1626712)), 42759 ^ _784416 : [(42760 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1626710), 42758 ^ [_1626710, _1626712, _1626714, _1626716]), _1626712)))], (42762 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1626710), _1626714), 42758 ^ [_1626710, _1626712, _1626714, _1626716]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1626710), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1626710), _1626714), _1626716)), hAPP(hAPP(c_Finite__Set_Ofold(_1626710, _1626710, c_Orderings_Oord__class_Omin(_1626710)), _1626716), _1626712))))], (42766 ^ _784416) ^ [_1627074, _1627076, _1627078] : [42768 ^ _784416 : [(42769 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1627074, tc_HOL_Obool)), 42767 ^ [_1627074, _1627076, _1627078]), _1627076)))], (42771 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1627074), _1627078), 42767 ^ [_1627074, _1627076, _1627078]))]], -(hBOOL(hAPP(hAPP(c_member(_1627074), _1627078), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1627074, tc_HOL_Obool), _1627076))))], (42775 ^ _784416) ^ [_1627290, _1627292, _1627294, _1627296] : [class_Lattices_Osemilattice__inf(_1627290), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627290), _1627292)), 42785 ^ _784416 : [(42786 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1627290), 42784 ^ [_1627290, _1627292, _1627294, _1627296]), _1627292)))], (42788 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1627290), _1627294), 42784 ^ [_1627290, _1627292, _1627294, _1627296]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1627290), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1627290), _1627294), _1627296)), hAPP(hAPP(c_Finite__Set_Ofold(_1627290, _1627290, c_Lattices_Osemilattice__inf__class_Oinf(_1627290)), _1627296), _1627292))))], (42792 ^ _784416) ^ [_1627654, _1627656, _1627658, _1627660] : [class_Lattices_Osemilattice__sup(_1627654), hBOOL(hAPP(c_Finite__Set_Ofinite(_1627654), _1627656)), 42802 ^ _784416 : [(42803 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1627654), 42801 ^ [_1627654, _1627656, _1627658, _1627660]), _1627656)))], (42805 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1627654), 42801 ^ [_1627654, _1627656, _1627658, _1627660]), _1627658))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1627654), hAPP(hAPP(c_Finite__Set_Ofold(_1627654, _1627654, c_Lattices_Osemilattice__sup__class_Osup(_1627654)), _1627660), _1627656)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1627654), _1627658), _1627660))))], (42809 ^ _784416) ^ [_1628018, _1628020, _1628022] : [class_Divides_Osemiring__div(_1628018), -(_1628020 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1628018), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1628018), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1628018), _1628020), _1628022)), _1628022)), c_Divides_Odiv__class_Omod(_1628018, _1628020, _1628022)))], (42832 ^ _784416) ^ [_1628685, _1628687] : [-(c_Wellfounded_Owf(_1628685, _1628687)), 42835 ^ _784416 : [(42836 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1628685), 42834 ^ [_1628685, _1628687]), 42833 ^ [_1628685, _1628687])))], (42838 ^ _784416) ^ [_1628905] : [hBOOL(hAPP(hAPP(c_member(_1628685), _1628905), 42833 ^ [_1628685, _1628687])), 42842 ^ _784416 : [(42843 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1628685, _1628685)), hAPP(hAPP(c_Product__Type_OPair(_1628685, _1628685), 42841 ^ [_1628685, _1628687, _1628905]), _1628905)), _1628687)))], (42845 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1628685), 42841 ^ [_1628685, _1628687, _1628905]), 42833 ^ [_1628685, _1628687])))]]]]], (42815 ^ _784416) ^ [_1628166, _1628168] : [c_Wellfounded_Owf(_1628166, _1628168), 42818 ^ _784416 : [(42819 ^ _784416) ^ [_1628298] : [42820 ^ _784416 : [(42821 ^ _784416) ^ [_1628403] : [hBOOL(hAPP(hAPP(c_member(_1628166), _1628403), _1628298))]], 42823 ^ _784416 : [(42824 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1628166), 42822 ^ [_1628166, _1628168, _1628298]), _1628298)))], (42826 ^ _784416) ^ [_1628525] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1628166, _1628166)), hAPP(hAPP(c_Product__Type_OPair(_1628166, _1628166), _1628525), 42822 ^ [_1628166, _1628168, _1628298])), _1628168)), hBOOL(hAPP(hAPP(c_member(_1628166), _1628525), _1628298))]]]]], (42849 ^ _784416) ^ [_1629161, _1629163, _1629165, _1629167, _1629169, _1629171, _1629173, _1629175] : [c_Finite__Set_Ofolding__image__simple__idem(_1629161, _1629163, _1629165, _1629167, _1629169, _1629171), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629163), _1629173)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629163), _1629175)), -(hAPP(_1629171, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1629163, tc_HOL_Obool)), _1629173), _1629175)) = hAPP(hAPP(_1629165, hAPP(_1629171, _1629173)), hAPP(_1629171, _1629175)))], (42863 ^ _784416) ^ [_1629454, _1629456, _1629458, _1629460, _1629462, _1629464, _1629466] : [c_Finite__Set_Ofolding__image__simple__idem(_1629454, _1629456, _1629458, _1629460, _1629462, _1629464), -(hAPP(hAPP(_1629458, _1629466), _1629466) = _1629466)], (42869 ^ _784416) ^ [_1629561, _1629563, _1629565, _1629567, _1629569, _1629571, _1629573, _1629575] : [c_Finite__Set_Ofolding__image__simple__idem(_1629561, _1629563, _1629565, _1629567, _1629569, _1629571), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629563), _1629573)), hBOOL(hAPP(hAPP(c_member(_1629563), _1629575), _1629573)), -(hAPP(hAPP(_1629565, hAPP(_1629569, _1629575)), hAPP(_1629571, _1629573)) = hAPP(_1629571, _1629573))], (42883 ^ _784416) ^ [_1629838, _1629840, _1629842, _1629844, _1629846, _1629848, _1629850, _1629852] : [c_Finite__Set_Ofolding__image__simple__idem(_1629838, _1629840, _1629842, _1629844, _1629846, _1629848), hBOOL(hAPP(c_Finite__Set_Ofinite(_1629840), _1629850)), -(hAPP(_1629848, hAPP(hAPP(c_Set_Oinsert(_1629840), _1629852), _1629850)) = hAPP(hAPP(_1629842, hAPP(_1629846, _1629852)), hAPP(_1629848, _1629850)))], (42893 ^ _784416) ^ [_1630053, _1630055, _1630057, _1630059, _1630061, _1630063, _1630065, _1630067] : [c_Finite__Set_Ofolding__image__simple__idem(_1630053, _1630055, _1630057, _1630059, _1630061, _1630063), hBOOL(hAPP(c_Finite__Set_Ofinite(_1630055), _1630065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1630055, tc_HOL_Obool)), _1630067), _1630065)), -(hAPP(hAPP(_1630057, hAPP(_1630063, _1630067)), hAPP(_1630063, _1630065)) = hAPP(_1630063, _1630065))], (42907 ^ _784416) ^ [_1630336, _1630338] : [-(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)))), _1630336)) = 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)))), _1630338))), 42909 ^ _784416 : [(42910 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 42908 ^ [_1630336, _1630338])))], (42912 ^ _784416) ^ [] : [42913 ^ _784416 : [(42914 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1630336, 42908 ^ [_1630336, _1630338])))], (42916 ^ _784416) ^ [] : [hBOOL(hAPP(_1630338, 42908 ^ [_1630336, _1630338]))]], 42917 ^ _784416 : [(42918 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1630338, 42908 ^ [_1630336, _1630338])))], (42920 ^ _784416) ^ [] : [hBOOL(hAPP(_1630336, 42908 ^ [_1630336, _1630338]))]]]]], (42924 ^ _784416) ^ [_1630657, _1630659, _1630661] : [hBOOL(hAPP(hAPP(c_member(_1630657), _1630659), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1630657, tc_HOL_Obool), _1630661))), 42928 ^ _784416 : [(42929 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1630657), _1630659), 42927 ^ [_1630657, _1630659, _1630661])))], (42931 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1630657, tc_HOL_Obool)), 42927 ^ [_1630657, _1630659, _1630661]), _1630661)))]]], (42933 ^ _784416) ^ [_1630845, _1630847, _1630849, _1630851, _1630853, _1630855] : [-(hBOOL(hAPP(hAPP(c_member(_1630845), _1630847), c_Map_Odom(_1630845, _1630849, _1630851)))), -(c_Map_Omap__add(_1630845, _1630849, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1630845, tc_Option_Ooption(_1630849)), _1630853), _1630847), hAPP(c_Option_Ooption_OSome(_1630849), _1630855)), _1630851) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1630845, tc_Option_Ooption(_1630849)), c_Map_Omap__add(_1630845, _1630849, _1630853, _1630851)), _1630847), hAPP(c_Option_Ooption_OSome(_1630849), _1630855)))], (42939 ^ _784416) ^ [_1630948, _1630950, _1630952, _1630954] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1630948, _1630950)), _1630952), hAPP(c_Relation_Oconverse(_1630950, _1630948), _1630954))), 42944 ^ _784416 : [(42945 ^ _784416) ^ [] : [-(_1630952 = hAPP(hAPP(c_Product__Type_OPair(_1630948, _1630950), 42943 ^ [_1630948, _1630950, _1630952, _1630954]), 42942 ^ [_1630948, _1630950, _1630952, _1630954]))], (42947 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630950, _1630948)), hAPP(hAPP(c_Product__Type_OPair(_1630950, _1630948), 42942 ^ [_1630948, _1630950, _1630952, _1630954]), 42943 ^ [_1630948, _1630950, _1630952, _1630954])), _1630954)))]]], (42949 ^ _784416) ^ [_1631201, _1631203, _1631205] : [-(c_Map_Omap__add(_1631201, _1631203, hAPP(c_COMBK(tc_Option_Ooption(_1631203), _1631201), c_Option_Ooption_ONone(_1631203)), _1631205) = _1631205)], (42951 ^ _784416) ^ [_1631243, _1631245, _1631247] : [-(c_Map_Omap__add(_1631243, _1631245, _1631247, hAPP(c_COMBK(tc_Option_Ooption(_1631245), _1631243), c_Option_Ooption_ONone(_1631245))) = _1631247)], (42953 ^ _784416) ^ [_1631285, _1631287, _1631289, _1631291, _1631293] : [-(hAPP(c_Map_Omap__add(_1631285, _1631287, _1631289, _1631291), _1631293) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1631287), _1631287, hAPP(_1631289, _1631293), c_Option_Ooption_OSome(_1631287)), hAPP(_1631291, _1631293)))], (42955 ^ _784416) ^ [_1631366, _1631368, _1631370, _1631372, _1631374] : [hAPP(c_Map_Omap__add(_1631366, _1631368, _1631370, _1631372), _1631374) = c_Option_Ooption_ONone(_1631368), 42958 ^ _784416 : [(42959 ^ _784416) ^ [] : [-(hAPP(_1631372, _1631374) = c_Option_Ooption_ONone(_1631368))], (42961 ^ _784416) ^ [] : [-(hAPP(_1631370, _1631374) = c_Option_Ooption_ONone(_1631368))]]], (42963 ^ _784416) ^ [_1631511, _1631513, _1631515, _1631517, _1631519] : [-(hAPP(c_Map_Omap__add(_1631511, _1631513, _1631515, _1631517), _1631519) = c_Option_Ooption_ONone(_1631513)), hAPP(_1631517, _1631519) = c_Option_Ooption_ONone(_1631513), hAPP(_1631515, _1631519) = c_Option_Ooption_ONone(_1631513)], (42973 ^ _784416) ^ [_1631694, _1631696, _1631698, _1631700, _1631702, _1631704] : [hAPP(_1631694, _1631696) = hAPP(c_Option_Ooption_OSome(_1631698), _1631700), -(hAPP(c_Map_Omap__add(_1631702, _1631698, _1631704, _1631694), _1631696) = hAPP(c_Option_Ooption_OSome(_1631698), _1631700))], (42979 ^ _784416) ^ [_1631821, _1631823, _1631825, _1631827, _1631829] : [-(c_Map_Omap__add(_1631821, _1631823, _1631825, c_Map_Omap__add(_1631821, _1631823, _1631827, _1631829)) = c_Map_Omap__add(_1631821, _1631823, c_Map_Omap__add(_1631821, _1631823, _1631825, _1631827), _1631829))], (42981 ^ _784416) ^ [_1631872, _1631874, _1631876, _1631878, _1631880] : [hBOOL(hAPP(hAPP(c_member(_1631872), _1631874), c_Map_Odom(_1631872, _1631876, _1631878))), -(hAPP(c_Map_Omap__add(_1631872, _1631876, _1631880, _1631878), _1631874) = hAPP(_1631878, _1631874))], (42987 ^ _784416) ^ [_1631995, _1631997, _1631999, _1632001, _1632003] : [-(hBOOL(hAPP(hAPP(c_member(_1631995), _1631997), c_Map_Odom(_1631995, _1631999, _1632001)))), -(hAPP(c_Map_Omap__add(_1631995, _1631999, _1632003, _1632001), _1631997) = hAPP(_1632003, _1631997))], (42993 ^ _784416) ^ [_1632055, _1632057, _1632059, _1632061, _1632063] : [-(hBOOL(hAPP(hAPP(c_member(_1632055), _1632057), c_Map_Odom(_1632055, _1632059, _1632061)))), -(hAPP(c_Map_Omap__add(_1632055, _1632059, _1632061, _1632063), _1632057) = hAPP(_1632063, _1632057))], (42999 ^ _784416) ^ [_1632119, _1632121, _1632123, _1632125, _1632127, _1632129] : [hAPP(c_Map_Omap__add(_1632119, _1632121, _1632123, _1632125), _1632127) = hAPP(c_Option_Ooption_OSome(_1632121), _1632129), -(hAPP(_1632125, _1632127) = hAPP(c_Option_Ooption_OSome(_1632121), _1632129)), 43006 ^ _784416 : [(43007 ^ _784416) ^ [] : [-(hAPP(_1632125, _1632127) = c_Option_Ooption_ONone(_1632121))], (43009 ^ _784416) ^ [] : [-(hAPP(_1632123, _1632127) = hAPP(c_Option_Ooption_OSome(_1632121), _1632129))]]], (43011 ^ _784416) ^ [_1632355, _1632357, _1632359, _1632361, _1632363, _1632365] : [hAPP(c_Map_Omap__add(_1632355, _1632357, _1632359, _1632361), _1632363) = hAPP(c_Option_Ooption_OSome(_1632357), _1632365), -(hAPP(_1632361, _1632363) = hAPP(c_Option_Ooption_OSome(_1632357), _1632365)), 43018 ^ _784416 : [(43019 ^ _784416) ^ [] : [-(hAPP(_1632361, _1632363) = c_Option_Ooption_ONone(_1632357))], (43021 ^ _784416) ^ [] : [-(hAPP(_1632359, _1632363) = hAPP(c_Option_Ooption_OSome(_1632357), _1632365))]]], (43023 ^ _784416) ^ [_1632560, _1632562, _1632564, _1632566, _1632568, _1632570] : [-(hAPP(c_Map_Omap__add(_1632560, _1632562, _1632564, _1632566), _1632568) = hAPP(c_Option_Ooption_OSome(_1632562), _1632570)), 43024 ^ _784416 : [(43025 ^ _784416) ^ [] : [hAPP(_1632566, _1632568) = hAPP(c_Option_Ooption_OSome(_1632562), _1632570)], (43027 ^ _784416) ^ [] : [hAPP(_1632566, _1632568) = c_Option_Ooption_ONone(_1632562), hAPP(_1632564, _1632568) = hAPP(c_Option_Ooption_OSome(_1632562), _1632570)]]], (43035 ^ _784416) ^ [_1632811, _1632813, _1632815, _1632817] : [-(c_Map_Odom(_1632811, _1632813, c_Map_Omap__add(_1632811, _1632813, _1632815, _1632817)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1632811, tc_HOL_Obool)), c_Map_Odom(_1632811, _1632813, _1632817)), c_Map_Odom(_1632811, _1632813, _1632815)))], (43037 ^ _784416) ^ [_1632868, _1632870, _1632872, _1632874, _1632876, _1632878] : [-(c_Map_Omap__add(_1632868, _1632870, _1632872, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1632868, tc_Option_Ooption(_1632870)), _1632874), _1632876), hAPP(c_Option_Ooption_OSome(_1632870), _1632878))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1632868, tc_Option_Ooption(_1632870)), c_Map_Omap__add(_1632868, _1632870, _1632872, _1632874)), _1632876), hAPP(c_Option_Ooption_OSome(_1632870), _1632878)))], (43039 ^ _784416) ^ [_1632970, _1632972, _1632974, _1632976] : [c_Fun_Oinj__on(_1632970, tc_Option_Ooption(_1632972), c_Map_Omap__add(_1632970, _1632972, _1632974, _1632976), c_Map_Odom(_1632970, _1632972, _1632976)), -(c_Fun_Oinj__on(_1632970, tc_Option_Ooption(_1632972), _1632976, c_Map_Odom(_1632970, _1632972, _1632976)))], (43045 ^ _784416) ^ [_1633089, _1633091, _1633093, _1633095] : [c_Fun_Oinj__on(_1633089, tc_Option_Ooption(_1633091), _1633095, c_Map_Odom(_1633089, _1633091, _1633095)), -(c_Fun_Oinj__on(_1633089, tc_Option_Ooption(_1633091), c_Map_Omap__add(_1633089, _1633091, _1633093, _1633095), c_Map_Odom(_1633089, _1633091, _1633095)))], (43051 ^ _784416) ^ [_1633214, _1633216, _1633218, _1633220] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1633214, tc_HOL_Obool)), c_Map_Odom(_1633214, _1633216, _1633218)), c_Map_Odom(_1633214, _1633216, _1633220)) = c_Orderings_Obot__class_Obot(tc_fun(_1633214, tc_HOL_Obool)), -(c_Map_Omap__add(_1633214, _1633216, _1633218, _1633220) = c_Map_Omap__add(_1633214, _1633216, _1633220, _1633218))], (43057 ^ _784416) ^ [_1633363, _1633365, _1633367, _1633369] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1633363)), hAPP(c_Set_Oimage(_1633365, tc_Option_Ooption(_1633363), _1633367), c_Orderings_Otop__class_Otop(tc_fun(_1633365, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1633363)), hAPP(c_Set_Oimage(_1633365, tc_Option_Ooption(_1633363), c_Map_Omap__add(_1633365, _1633363, _1633367, hAPP(c_Map_Omap__of(_1633365, _1633363), _1633369))), c_Orderings_Otop__class_Otop(tc_fun(_1633365, tc_HOL_Obool))))))], (43063 ^ _784416) ^ [_1633546, _1633548, _1633550, _1633552, _1633554, _1633556] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633546, _1633548)), _1633550), hAPP(hAPP(c_Relation_Orel__comp(_1633546, _1633552, _1633548), _1633554), _1633556))), 43069 ^ _784416 : [(43070 ^ _784416) ^ [] : [-(_1633550 = hAPP(hAPP(c_Product__Type_OPair(_1633546, _1633548), 43066 ^ [_1633546, _1633548, _1633550, _1633552, _1633554, _1633556]), 43068 ^ [_1633546, _1633548, _1633550, _1633552, _1633554, _1633556]))], (43072 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633546, _1633552)), hAPP(hAPP(c_Product__Type_OPair(_1633546, _1633552), 43066 ^ [_1633546, _1633548, _1633550, _1633552, _1633554, _1633556]), 43067 ^ [_1633546, _1633548, _1633550, _1633552, _1633554, _1633556])), _1633554)))], (43074 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633552, _1633548)), hAPP(hAPP(c_Product__Type_OPair(_1633552, _1633548), 43067 ^ [_1633546, _1633548, _1633550, _1633552, _1633554, _1633556]), 43068 ^ [_1633546, _1633548, _1633550, _1633552, _1633554, _1633556])), _1633556)))]]], (43076 ^ _784416) ^ [_1633924, _1633926, _1633928] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1633924), c_Map_Odom(_1633924, _1633926, hAPP(c_Map_Omap__of(_1633924, _1633926), _1633928)))))], (43078 ^ _784416) ^ [_1633965, _1633967, _1633969] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1633965)), hAPP(c_Set_Oimage(_1633967, tc_Option_Ooption(_1633965), hAPP(c_Map_Omap__of(_1633967, _1633965), _1633969)), c_Orderings_Otop__class_Otop(tc_fun(_1633967, tc_HOL_Obool))))))], (43080 ^ _784416) ^ [_1634018, _1634020, _1634022, _1634024] : [-(c_Map_Omap__add(_1634018, _1634020, _1634022, hAPP(c_Map_Omap__of(_1634018, _1634020), _1634024)) = c_List_Ofoldr(tc_prod(_1634018, _1634020), tc_fun(_1634018, tc_Option_Ooption(_1634020)), hAPP(c_Product__Type_Oprod_Oprod__case(_1634018, _1634020, tc_fun(tc_fun(_1634018, tc_Option_Ooption(_1634020)), tc_fun(_1634018, tc_Option_Ooption(_1634020)))), hAPP(hAPP(c_COMBC(_1634018, tc_fun(_1634020, tc_Option_Ooption(_1634020)), tc_fun(_1634020, tc_fun(tc_fun(_1634018, tc_Option_Ooption(_1634020)), tc_fun(_1634018, tc_Option_Ooption(_1634020))))), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1634020), tc_fun(tc_fun(_1634018, tc_Option_Ooption(_1634020)), tc_fun(_1634018, tc_Option_Ooption(_1634020)))), tc_fun(tc_fun(_1634020, tc_Option_Ooption(_1634020)), tc_fun(_1634020, tc_fun(tc_fun(_1634018, tc_Option_Ooption(_1634020)), tc_fun(_1634018, tc_Option_Ooption(_1634020))))), _1634018), c_COMBB(tc_Option_Ooption(_1634020), tc_fun(tc_fun(_1634018, tc_Option_Ooption(_1634020)), tc_fun(_1634018, tc_Option_Ooption(_1634020))), _1634020)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1634018, tc_Option_Ooption(_1634020)), tc_fun(tc_Option_Ooption(_1634020), tc_fun(_1634018, tc_Option_Ooption(_1634020)))), tc_fun(tc_Option_Ooption(_1634020), tc_fun(tc_fun(_1634018, tc_Option_Ooption(_1634020)), tc_fun(_1634018, tc_Option_Ooption(_1634020)))), _1634018), c_COMBC(tc_fun(_1634018, tc_Option_Ooption(_1634020)), tc_Option_Ooption(_1634020), tc_fun(_1634018, tc_Option_Ooption(_1634020)))), hAPP(c_COMBC(tc_fun(_1634018, tc_Option_Ooption(_1634020)), _1634018, tc_fun(tc_Option_Ooption(_1634020), tc_fun(_1634018, tc_Option_Ooption(_1634020)))), c_Fun_Ofun__upd(_1634018, tc_Option_Ooption(_1634020)))))), c_Option_Ooption_OSome(_1634020))), _1634024, _1634022))], (43082 ^ _784416) ^ [_1634285, _1634287, _1634289] : [-(c_Smallcheck_Oorelse(_1634285, _1634287, _1634289) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1634285), _1634285, _1634289, c_Option_Ooption_OSome(_1634285)), _1634287))], (43084 ^ _784416) ^ [_1634328, _1634330] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint, _1634328, _1634330) = c_Smallcheck_Ofull__small_H(_1634328, hAPP(c_Code__Numeral_Oint__of, _1634330), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1634330))))], (43086 ^ _784416) ^ [_1634382, _1634384, _1634386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1634382), _1634384)), -(c_Smallcheck_Osmall_H(_1634386, _1634382, _1634384) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (43092 ^ _784416) ^ [_1634473, _1634475, _1634477] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1634473), _1634475))), -(c_Smallcheck_Osmall_H(_1634477, _1634473, _1634475) = 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(_1634477, _1634473, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1634475), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1634477, _1634475)))], (43098 ^ _784416) ^ [_1634543, _1634545, _1634547] : [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)), _1634543), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1634545), _1634547)))), 43101 ^ _784416 : [(43102 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1634545), _1634547)), -(c_Smallcheck_Osmall_H(_1634543, _1634545, _1634547) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (43108 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1634545), _1634547))), -(c_Smallcheck_Osmall_H(_1634543, _1634545, _1634547) = 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(_1634543, _1634545, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1634547), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1634543, _1634547)))]]], (43114 ^ _784416) ^ [_1634829, _1634831] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint), _1634829), _1634831) = c_Smallcheck_Osmall_H(_1634829, hAPP(c_Code__Numeral_Oint__of, _1634831), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1634831))))], (43116 ^ _784416) ^ [_1634873, _1634875, _1634877, _1634879] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(_1634875, _1634873)), _1634877), _1634879) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(_1634875), hAPP(hAPP(c_COMBC(_1634875, tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(hAPP(c_COMBB(tc_fun(_1634873, 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))), _1634875), c_Smallcheck_Osmall__class_Osmall(_1634873)), hAPP(hAPP(c_COMBB(tc_fun(_1634873, tc_prod(_1634875, _1634873)), tc_fun(_1634873, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1634875), hAPP(c_COMBB(tc_prod(_1634875, _1634873), tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), _1634873), _1634877)), c_Product__Type_OPair(_1634875, _1634873)))), _1634879)), _1634879)), class_Smallcheck_Osmall(_1634873), class_Smallcheck_Osmall(_1634875)], (43126 ^ _784416) ^ [_1635158, _1635160, _1635162, _1635164] : [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)), _1635158), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1635160), _1635162)))), -(hBOOL(hAPP(hAPP(hAPP(_1635164, _1635158), _1635160), _1635162))), 43134 ^ _784416 : [(43135 ^ _784416) ^ [] : [-(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)), 43131 ^ [_1635158, _1635160, _1635162, _1635164]), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 43132 ^ [_1635158, _1635160, _1635162, _1635164]), 43133 ^ [_1635158, _1635160, _1635162, _1635164])))))], (43147 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1635164, 43131 ^ [_1635158, _1635160, _1635162, _1635164]), 43132 ^ [_1635158, _1635160, _1635162, _1635164]), 43133 ^ [_1635158, _1635160, _1635162, _1635164]))], (43137 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 43132 ^ [_1635158, _1635160, _1635162, _1635164]), 43133 ^ [_1635158, _1635160, _1635162, _1635164]))), hAPP(43131 ^ [_1635158, _1635160, _1635162, _1635164], 43133 ^ [_1635158, _1635160, _1635162, _1635164]) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)), -(hBOOL(hAPP(hAPP(hAPP(_1635164, 43131 ^ [_1635158, _1635160, _1635162, _1635164]), 43132 ^ [_1635158, _1635160, _1635162, _1635164]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 43133 ^ [_1635158, _1635160, _1635162, _1635164]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (43151 ^ _784416) ^ [_1635897, _1635899, _1635901, _1635903, _1635905, _1635907, _1635909] : [c_Fun_Oinj__on(_1635897, _1635899, _1635901, c_Orderings_Otop__class_Otop(tc_fun(_1635897, tc_HOL_Obool))), hAPP(hAPP(c_Map_Omap__of(_1635897, _1635903), _1635905), _1635907) = hAPP(c_Option_Ooption_OSome(_1635903), _1635909), -(hAPP(hAPP(c_Map_Omap__of(_1635899, _1635903), hAPP(hAPP(c_List_Omap(tc_prod(_1635897, _1635903), tc_prod(_1635899, _1635903)), hAPP(c_Product__Type_Oprod_Oprod__case(_1635897, _1635903, tc_prod(_1635899, _1635903)), hAPP(hAPP(c_COMBB(_1635899, tc_fun(_1635903, tc_prod(_1635899, _1635903)), _1635897), c_Product__Type_OPair(_1635899, _1635903)), _1635901))), _1635905)), hAPP(_1635901, _1635907)) = hAPP(c_Option_Ooption_OSome(_1635903), _1635909))], (43161 ^ _784416) ^ [_1636210, _1636212, _1636214] : [c_Fun_Oinj__on(_1636210, _1636212, _1636214, c_Orderings_Otop__class_Otop(tc_fun(_1636210, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1636210), tc_List_Olist(_1636212), hAPP(c_List_Omap(_1636210, _1636212), _1636214), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1636210), tc_HOL_Obool))))], (43167 ^ _784416) ^ [_1636341, _1636343, _1636345, _1636347, _1636349, _1636351, _1636353] : [-(c_List_Ofoldr(_1636341, _1636343, _1636345, hAPP(hAPP(c_List_Omap(_1636347, _1636341), _1636349), _1636351), _1636353) = c_List_Ofoldr(_1636347, _1636343, hAPP(c_Fun_Ocomp(_1636341, tc_fun(_1636343, _1636343), _1636347, _1636345), _1636349), _1636351, _1636353))], (43169 ^ _784416) ^ [_1636408, _1636410, _1636412, _1636414, _1636416, _1636418] : [-(hAPP(hAPP(c_List_Omap(_1636408, _1636410), _1636412), hAPP(hAPP(c_List_Omap(_1636414, _1636408), _1636416), _1636418)) = hAPP(hAPP(c_List_Omap(_1636414, _1636410), hAPP(c_Fun_Ocomp(_1636408, _1636410, _1636414, _1636412), _1636416)), _1636418))], (43171 ^ _784416) ^ [_1636476, _1636478, _1636480, _1636482, _1636484, _1636486] : [-(hAPP(hAPP(c_List_Omap(_1636476, _1636478), _1636480), hAPP(hAPP(c_List_Omap(_1636482, _1636476), _1636484), _1636486)) = hAPP(hAPP(c_List_Omap(_1636482, _1636478), hAPP(c_Fun_Ocomp(_1636476, _1636478, _1636482, _1636480), _1636484)), _1636486))], (43173 ^ _784416) ^ [_1636544, _1636546, _1636548, _1636550, _1636552] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1636544), tc_List_Olist(_1636546), tc_List_Olist(_1636548), hAPP(c_List_Omap(_1636544, _1636546), _1636550)), hAPP(c_List_Omap(_1636548, _1636544), _1636552)) = hAPP(c_List_Omap(_1636548, _1636546), hAPP(c_Fun_Ocomp(_1636544, _1636546, _1636548, _1636550), _1636552)))], (43175 ^ _784416) ^ [_1636615, _1636617, _1636619, _1636621, _1636623] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1636615), tc_List_Olist(_1636617), tc_List_Olist(_1636619), hAPP(c_List_Omap(_1636615, _1636617), _1636621)), hAPP(c_List_Omap(_1636619, _1636615), _1636623)) = hAPP(c_List_Omap(_1636619, _1636617), hAPP(c_Fun_Ocomp(_1636615, _1636617, _1636619, _1636621), _1636623)))], (43177 ^ _784416) ^ [_1636686] : [-(hAPP(c_List_Omap(_1636686, _1636686), c_Fun_Oid(_1636686)) = c_Fun_Oid(tc_List_Olist(_1636686)))], (43179 ^ _784416) ^ [_1636721] : [-(hAPP(c_List_Omap(_1636721, _1636721), c_COMBI(_1636721)) = c_Fun_Oid(tc_List_Olist(_1636721)))], (43181 ^ _784416) ^ [_1636756, _1636758] : [-(hAPP(hAPP(c_List_Omap(_1636756, _1636756), c_COMBI(_1636756)), _1636758) = _1636758)], (43183 ^ _784416) ^ [_1636792, _1636794, _1636796, _1636798, _1636800] : [hAPP(hAPP(c_List_Omap(_1636792, _1636794), _1636796), _1636798) = hAPP(hAPP(c_List_Omap(_1636792, _1636794), _1636796), _1636800), c_Fun_Oinj__on(_1636792, _1636794, _1636796, c_Orderings_Otop__class_Otop(tc_fun(_1636792, tc_HOL_Obool))), -(_1636798 = _1636800)], (43193 ^ _784416) ^ [_1636983, _1636985, _1636987] : [c_Fun_Oinj__on(tc_List_Olist(_1636983), tc_List_Olist(_1636985), hAPP(c_List_Omap(_1636983, _1636985), _1636987), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1636983), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1636983, _1636985, _1636987, c_Orderings_Otop__class_Otop(tc_fun(_1636983, tc_HOL_Obool))))], (43199 ^ _784416) ^ [_1637114, _1637116, _1637118, _1637120, _1637122] : [c_Fun_Oinj__on(_1637114, _1637116, _1637118, c_Orderings_Otop__class_Otop(tc_fun(_1637114, tc_HOL_Obool))), 43202 ^ _784416 : [(43203 ^ _784416) ^ [] : [hAPP(hAPP(c_List_Omap(_1637114, _1637116), _1637118), _1637120) = hAPP(hAPP(c_List_Omap(_1637114, _1637116), _1637118), _1637122), -(_1637120 = _1637122)], (43209 ^ _784416) ^ [] : [_1637120 = _1637122, -(hAPP(hAPP(c_List_Omap(_1637114, _1637116), _1637118), _1637120) = hAPP(hAPP(c_List_Omap(_1637114, _1637116), _1637118), _1637122))]]], (43215 ^ _784416) ^ [_1637425, _1637427, _1637429] : [c_Fun_Oinj__on(tc_List_Olist(_1637425), tc_List_Olist(_1637427), hAPP(c_List_Omap(_1637425, _1637427), _1637429), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1637425), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1637425, _1637427, _1637429, c_Orderings_Otop__class_Otop(tc_fun(_1637425, tc_HOL_Obool))))], (43221 ^ _784416) ^ [_1637552, _1637554, _1637556] : [c_Fun_Oinj__on(_1637552, _1637554, _1637556, c_Orderings_Otop__class_Otop(tc_fun(_1637552, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1637552), tc_List_Olist(_1637554), hAPP(c_List_Omap(_1637552, _1637554), _1637556), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1637552), tc_HOL_Obool))))], (43227 ^ _784416) ^ [_1637685, _1637687, _1637689, _1637691, _1637693] : [-(hAPP(c_Map_Omap__of(_1637685, _1637687), hAPP(hAPP(c_List_Omap(tc_prod(_1637685, _1637689), tc_prod(_1637685, _1637687)), hAPP(c_Product__Type_Oprod_Oprod__case(_1637685, _1637689, tc_prod(_1637685, _1637687)), hAPP(hAPP(c_COMBC(_1637685, tc_fun(_1637689, _1637687), tc_fun(_1637689, tc_prod(_1637685, _1637687))), hAPP(hAPP(c_COMBB(tc_fun(_1637687, tc_prod(_1637685, _1637687)), tc_fun(tc_fun(_1637689, _1637687), tc_fun(_1637689, tc_prod(_1637685, _1637687))), _1637685), c_COMBB(_1637687, tc_prod(_1637685, _1637687), _1637689)), c_Product__Type_OPair(_1637685, _1637687))), _1637691))), _1637693)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1637689), tc_Option_Ooption(_1637687), _1637685, hAPP(c_Option_Omap(_1637689, _1637687), _1637691)), hAPP(c_Map_Omap__of(_1637685, _1637689), _1637693)))], (43229 ^ _784416) ^ [_1637828, _1637830, _1637832, _1637834, _1637836, _1637838] : [-(c_Map_Omap__comp(_1637828, _1637830, _1637832, _1637834, _1637836, _1637838) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1637830), _1637828, c_Option_Ooption_ONone(_1637830), _1637834), hAPP(_1637836, _1637838)))], (43231 ^ _784416) ^ [_1637883, _1637885, _1637887, _1637889, _1637891] : [-(hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1637883), tc_Option_Ooption(_1637885), _1637887, hAPP(c_Option_Omap(_1637883, _1637885), _1637889)), hAPP(c_COMBK(tc_Option_Ooption(_1637883), _1637887), c_Option_Ooption_ONone(_1637883))), _1637891) = c_Option_Ooption_ONone(_1637885))], (43233 ^ _784416) ^ [_1637971, _1637973, _1637975, _1637977, _1637979] : [hAPP(hAPP(c_Option_Omap(_1637971, _1637973), _1637975), _1637977) = hAPP(c_Option_Ooption_OSome(_1637973), _1637979), 43237 ^ _784416 : [(43238 ^ _784416) ^ [] : [-(_1637977 = hAPP(c_Option_Ooption_OSome(_1637971), 43236 ^ [_1637971, _1637973, _1637975, _1637977, _1637979]))], (43240 ^ _784416) ^ [] : [-(hAPP(_1637975, 43236 ^ [_1637971, _1637973, _1637975, _1637977, _1637979]) = _1637979)]]], (43242 ^ _784416) ^ [_1638151, _1638153, _1638155, _1638157, _1638159] : [-(hAPP(hAPP(c_Option_Omap(_1638151, _1638153), _1638155), _1638157) = hAPP(c_Option_Ooption_OSome(_1638153), _1638159)), 43243 ^ _784416 : [(43244 ^ _784416) ^ [_1638219] : [_1638157 = hAPP(c_Option_Ooption_OSome(_1638151), _1638219), hAPP(_1638155, _1638219) = _1638159]]], (43252 ^ _784416) ^ [_1638363, _1638365, _1638367, _1638369] : [-(hAPP(hAPP(c_Option_Omap(_1638363, _1638365), _1638367), hAPP(c_Option_Ooption_OSome(_1638363), _1638369)) = hAPP(c_Option_Ooption_OSome(_1638365), hAPP(_1638367, _1638369)))], (43254 ^ _784416) ^ [_1638435, _1638437, _1638439, _1638441] : [hAPP(hAPP(c_Option_Omap(_1638435, _1638437), _1638439), _1638441) = c_Option_Ooption_ONone(_1638437), -(_1638441 = c_Option_Ooption_ONone(_1638435))], (43260 ^ _784416) ^ [_1638538, _1638540, _1638542, _1638544] : [_1638544 = c_Option_Ooption_ONone(_1638538), -(hAPP(hAPP(c_Option_Omap(_1638538, _1638540), _1638542), _1638544) = c_Option_Ooption_ONone(_1638540))], (43266 ^ _784416) ^ [_1638647, _1638649, _1638651] : [-(hAPP(hAPP(c_Option_Omap(_1638647, _1638649), _1638651), c_Option_Ooption_ONone(_1638647)) = c_Option_Ooption_ONone(_1638649))], (43268 ^ _784416) ^ [_1638696] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1638696)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1638696), tc_HOL_Obool))))], (43270 ^ _784416) ^ [_1638732, _1638734, _1638736, _1638738, _1638740] : [-(c_Map_Odom(_1638732, _1638734, hAPP(hAPP(c_COMBS(_1638732, tc_Option_Ooption(_1638736), tc_Option_Ooption(_1638734)), hAPP(hAPP(c_COMBB(tc_fun(_1638736, _1638734), tc_fun(tc_Option_Ooption(_1638736), tc_Option_Ooption(_1638734)), _1638732), c_Option_Omap(_1638736, _1638734)), _1638738)), _1638740)) = c_Map_Odom(_1638732, _1638736, _1638740))], (43272 ^ _784416) ^ [_1638808] : [-(hAPP(c_Option_Omap(_1638808, _1638808), c_Fun_Oid(_1638808)) = c_Fun_Oid(tc_Option_Ooption(_1638808)))], (43274 ^ _784416) ^ [_1638843] : [-(hAPP(c_Option_Omap(_1638843, _1638843), c_COMBI(_1638843)) = c_Fun_Oid(tc_Option_Ooption(_1638843)))], (43276 ^ _784416) ^ [_1638878, _1638880, _1638882, _1638884, _1638886, _1638888] : [-(hAPP(hAPP(c_Option_Omap(_1638878, _1638880), _1638882), hAPP(hAPP(c_Option_Omap(_1638884, _1638878), _1638886), _1638888)) = hAPP(hAPP(c_Option_Omap(_1638884, _1638880), hAPP(c_Fun_Ocomp(_1638878, _1638880, _1638884, _1638882), _1638886)), _1638888))], (43278 ^ _784416) ^ [_1638946, _1638948, _1638950, _1638952, _1638954, _1638956] : [-(hAPP(hAPP(c_Option_Omap(_1638946, _1638948), _1638950), hAPP(hAPP(c_Option_Omap(_1638952, _1638946), _1638954), _1638956)) = hAPP(hAPP(c_Option_Omap(_1638952, _1638948), hAPP(c_Fun_Ocomp(_1638946, _1638948, _1638952, _1638950), _1638954)), _1638956))], (43280 ^ _784416) ^ [_1639014, _1639016, _1639018, _1639020, _1639022] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1639014), tc_Option_Ooption(_1639016), tc_Option_Ooption(_1639018), hAPP(c_Option_Omap(_1639014, _1639016), _1639020)), hAPP(c_Option_Omap(_1639018, _1639014), _1639022)) = hAPP(c_Option_Omap(_1639018, _1639016), hAPP(c_Fun_Ocomp(_1639014, _1639016, _1639018, _1639020), _1639022)))], (43282 ^ _784416) ^ [_1639085, _1639087, _1639089, _1639091, _1639093, _1639095] : [hAPP(_1639085, _1639087) = c_Option_Ooption_ONone(_1639089), -(c_Map_Omap__comp(_1639089, _1639091, _1639093, _1639095, _1639085, _1639087) = c_Option_Ooption_ONone(_1639091))], (43288 ^ _784416) ^ [_1639228, _1639230, _1639232, _1639234, _1639236, _1639238, _1639240] : [c_Map_Omap__comp(_1639228, _1639230, _1639232, _1639234, _1639236, _1639238) = hAPP(c_Option_Ooption_OSome(_1639230), _1639240), 43292 ^ _784416 : [(43293 ^ _784416) ^ [] : [-(hAPP(_1639236, _1639238) = hAPP(c_Option_Ooption_OSome(_1639228), 43291 ^ [_1639228, _1639230, _1639232, _1639234, _1639236, _1639238, _1639240]))], (43295 ^ _784416) ^ [] : [-(hAPP(_1639234, 43291 ^ [_1639228, _1639230, _1639232, _1639234, _1639236, _1639238, _1639240]) = hAPP(c_Option_Ooption_OSome(_1639230), _1639240))]]], (43297 ^ _784416) ^ [_1639432, _1639434, _1639436, _1639438, _1639440, _1639442, _1639444] : [-(c_Map_Omap__comp(_1639432, _1639434, _1639436, _1639438, _1639440, _1639442) = hAPP(c_Option_Ooption_OSome(_1639434), _1639444)), 43298 ^ _784416 : [(43299 ^ _784416) ^ [_1639510] : [hAPP(_1639440, _1639442) = hAPP(c_Option_Ooption_OSome(_1639432), _1639510), hAPP(_1639438, _1639510) = hAPP(c_Option_Ooption_OSome(_1639434), _1639444)]]], (43307 ^ _784416) ^ [_1639672, _1639674, _1639676, _1639678, _1639680, _1639682, _1639684] : [hAPP(_1639672, _1639674) = hAPP(c_Option_Ooption_OSome(_1639676), _1639678), -(c_Map_Omap__comp(_1639676, _1639680, _1639682, _1639684, _1639672, _1639674) = hAPP(_1639684, _1639678))], (43313 ^ _784416) ^ [_1639795, _1639797, _1639799, _1639801, _1639803, _1639805, _1639807] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1639795), tc_Option_Ooption(_1639797), _1639799, hAPP(c_Option_Omap(_1639795, _1639797), _1639801)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1639799, tc_Option_Ooption(_1639795)), _1639803), _1639805), hAPP(c_Option_Ooption_OSome(_1639795), _1639807))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1639799, tc_Option_Ooption(_1639797)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1639795), tc_Option_Ooption(_1639797), _1639799, hAPP(c_Option_Omap(_1639795, _1639797), _1639801)), _1639803)), _1639805), hAPP(c_Option_Ooption_OSome(_1639797), hAPP(_1639801, _1639807))))], (43315 ^ _784416) ^ [_1639907, _1639909, _1639911, _1639913, _1639915] : [-(c_Map_Omap__comp(_1639907, _1639909, _1639911, _1639913, hAPP(c_COMBK(tc_Option_Ooption(_1639907), _1639911), c_Option_Ooption_ONone(_1639907)), _1639915) = c_Option_Ooption_ONone(_1639909))], (43317 ^ _784416) ^ [_1639957, _1639959, _1639961, _1639963, _1639965] : [-(c_Map_Omap__comp(_1639957, _1639959, _1639961, hAPP(c_COMBK(tc_Option_Ooption(_1639959), _1639957), c_Option_Ooption_ONone(_1639959)), _1639963, _1639965) = c_Option_Ooption_ONone(_1639959))], (43319 ^ _784416) ^ [_1640034, _1640036, _1640038, _1640040, _1640042, _1640044] : [c_Map_Omap__comp(_1640034, _1640036, _1640038, _1640040, _1640042, _1640044) = c_Option_Ooption_ONone(_1640036), -(hAPP(_1640042, _1640044) = c_Option_Ooption_ONone(_1640034)), 43327 ^ _784416 : [(43328 ^ _784416) ^ [] : [-(hAPP(_1640042, _1640044) = hAPP(c_Option_Ooption_OSome(_1640034), 43326 ^ [_1640034, _1640036, _1640038, _1640040, _1640042, _1640044]))], (43330 ^ _784416) ^ [] : [-(hAPP(_1640040, 43326 ^ [_1640034, _1640036, _1640038, _1640040, _1640042, _1640044]) = c_Option_Ooption_ONone(_1640036))]]], (43332 ^ _784416) ^ [_1640260, _1640262, _1640264, _1640266, _1640268, _1640270] : [-(c_Map_Omap__comp(_1640260, _1640262, _1640264, _1640266, _1640268, _1640270) = c_Option_Ooption_ONone(_1640262)), 43333 ^ _784416 : [(43334 ^ _784416) ^ [] : [hAPP(_1640268, _1640270) = c_Option_Ooption_ONone(_1640260)], (43336 ^ _784416) ^ [_1640372] : [hAPP(_1640268, _1640270) = hAPP(c_Option_Ooption_OSome(_1640260), _1640372), hAPP(_1640266, _1640372) = c_Option_Ooption_ONone(_1640262)]]], (43344 ^ _784416) ^ [_1640525, _1640527, _1640529] : [-(hAPP(c_Option_Omap(_1640525, _1640527), _1640529) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1640527), _1640525, c_Option_Ooption_ONone(_1640527), hAPP(hAPP(c_COMBB(_1640527, tc_Option_Ooption(_1640527), _1640525), c_Option_Ooption_OSome(_1640527)), _1640529)))], (43346 ^ _784416) ^ [_1640581, _1640583, _1640585, _1640587] : [-(hAPP(c_Map_Omap__of(_1640581, _1640583), hAPP(hAPP(c_List_Omap(_1640581, tc_prod(_1640581, _1640583)), hAPP(hAPP(c_COMBS(_1640581, _1640583, tc_prod(_1640581, _1640583)), c_Product__Type_OPair(_1640581, _1640583)), _1640585)), _1640587)) = c_Map_Orestrict__map(_1640581, _1640583, hAPP(c_Fun_Ocomp(_1640583, tc_Option_Ooption(_1640583), _1640581, c_Option_Ooption_OSome(_1640583)), _1640585), hAPP(c_List_Oset(_1640581), _1640587)))], (43348 ^ _784416) ^ [_1640666, _1640668, _1640670, _1640672] : [-(hAPP(c_Map_Omap__of(_1640666, _1640668), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1640666, _1640668)), _1640670), _1640672)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1640666, tc_Option_Ooption(_1640668)), hAPP(c_Map_Omap__of(_1640666, _1640668), _1640672)), hAPP(c_Product__Type_Ofst(_1640666, _1640668), _1640670)), hAPP(c_Option_Ooption_OSome(_1640668), hAPP(c_Product__Type_Osnd(_1640666, _1640668), _1640670))))], (43350 ^ _784416) ^ [_1640749, _1640751] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1640749), hAPP(c_List_Oset(_1640749), _1640751))))], (43362 ^ _784416) ^ [_1641051, _1641053, _1641055, _1641057, _1641059] : [43364 ^ _784416 : [(43365 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1641051), 43363 ^ [_1641051, _1641053, _1641055, _1641057, _1641059]), hAPP(c_List_Oset(_1641051), _1641057))))], (43367 ^ _784416) ^ [] : [hAPP(_1641055, 43363 ^ [_1641051, _1641053, _1641055, _1641057, _1641059]) = hAPP(_1641059, 43363 ^ [_1641051, _1641053, _1641055, _1641057, _1641059])]], -(hAPP(hAPP(c_List_Omap(_1641051, _1641053), _1641055), _1641057) = hAPP(hAPP(c_List_Omap(_1641051, _1641053), _1641059), _1641057))], (43352 ^ _784416) ^ [_1640807, _1640809, _1640811, _1640813, _1640815] : [hAPP(hAPP(c_List_Omap(_1640807, _1640809), _1640811), _1640813) = hAPP(hAPP(c_List_Omap(_1640807, _1640809), _1640815), _1640813), 43355 ^ _784416 : [(43356 ^ _784416) ^ [_1640930] : [hBOOL(hAPP(hAPP(c_member(_1640807), _1640930), hAPP(c_List_Oset(_1640807), _1640813))), -(hAPP(_1640811, _1640930) = hAPP(_1640815, _1640930))]]], (43371 ^ _784416) ^ [_1641308, _1641310, _1641312, _1641314, _1641316] : [-(hAPP(hAPP(c_List_Omap(_1641308, _1641310), _1641312), hAPP(hAPP(c_List_Olist_OCons(_1641308), _1641314), _1641316)) = hAPP(hAPP(c_List_Olist_OCons(_1641310), hAPP(_1641312, _1641314)), hAPP(hAPP(c_List_Omap(_1641308, _1641310), _1641312), _1641316)))], (43373 ^ _784416) ^ [_1641376, _1641378, _1641380, _1641382] : [-(hAPP(c_List_Oset(_1641376), hAPP(hAPP(c_List_Omap(_1641378, _1641376), _1641380), _1641382)) = hAPP(c_Set_Oimage(_1641378, _1641376, _1641380), hAPP(c_List_Oset(_1641378), _1641382)))], (43375 ^ _784416) ^ [_1641431, _1641433, _1641435, _1641437, _1641439, _1641441] : [-(c_List_Ofoldr(_1641431, _1641433, _1641435, hAPP(hAPP(c_List_Olist_OCons(_1641431), _1641437), _1641439), _1641441) = hAPP(hAPP(_1641435, _1641437), c_List_Ofoldr(_1641431, _1641433, _1641435, _1641439, _1641441)))], (43377 ^ _784416) ^ [_1641490, _1641492, _1641494] : [-(hAPP(c_List_Oset(_1641490), hAPP(hAPP(c_List_Olist_OCons(_1641490), _1641492), _1641494)) = hAPP(hAPP(c_Set_Oinsert(_1641490), _1641492), hAPP(c_List_Oset(_1641490), _1641494)))], (43379 ^ _784416) ^ [_1641567, _1641569, _1641571, _1641573, _1641575] : [hAPP(hAPP(c_List_Olist_OCons(_1641567), _1641569), _1641571) = hAPP(hAPP(c_List_Olist_OCons(_1641567), _1641573), _1641575), 43382 ^ _784416 : [(43383 ^ _784416) ^ [] : [-(_1641569 = _1641573)], (43385 ^ _784416) ^ [] : [-(_1641571 = _1641575)]]], (43387 ^ _784416) ^ [_1641704, _1641706, _1641708, _1641710, _1641712] : [-(hAPP(hAPP(c_List_Olist_OCons(_1641704), _1641706), _1641708) = hAPP(hAPP(c_List_Olist_OCons(_1641704), _1641710), _1641712)), _1641706 = _1641710, _1641708 = _1641712], (43397 ^ _784416) ^ [_1641894, _1641896, _1641898] : [hAPP(hAPP(c_List_Olist_OCons(_1641894), _1641896), _1641898) = _1641898], (43399 ^ _784416) ^ [_1641944, _1641946, _1641948] : [_1641944 = hAPP(hAPP(c_List_Olist_OCons(_1641946), _1641948), _1641944)], (43401 ^ _784416) ^ [_1641979, _1641981, _1641983, _1641985] : [hBOOL(hAPP(hAPP(c_member(_1641979), _1641981), hAPP(c_List_Oset(_1641979), hAPP(hAPP(c_List_Olist_OCons(_1641979), _1641983), _1641985)))), -(_1641981 = _1641983), -(hBOOL(hAPP(hAPP(c_member(_1641979), _1641981), hAPP(c_List_Oset(_1641979), _1641985))))], (43411 ^ _784416) ^ [_1642137, _1642139, _1642141] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1642137, tc_HOL_Obool)), hAPP(c_List_Oset(_1642137), _1642139)), hAPP(c_List_Oset(_1642137), hAPP(hAPP(c_List_Olist_OCons(_1642137), _1642141), _1642139)))))], (43413 ^ _784416) ^ [_1642192, _1642194, _1642196, _1642198, _1642200] : [hAPP(hAPP(c_List_Omap(_1642192, _1642194), _1642196), _1642198) = hAPP(hAPP(c_List_Omap(_1642192, _1642194), _1642196), _1642200), c_Fun_Oinj__on(_1642192, _1642194, _1642196, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1642192, tc_HOL_Obool)), hAPP(c_List_Oset(_1642192), _1642198)), hAPP(c_List_Oset(_1642192), _1642200))), -(_1642198 = _1642200)], (43423 ^ _784416) ^ [_1642415, _1642417, _1642419, _1642421, _1642423] : [c_Fun_Oinj__on(_1642415, _1642417, _1642419, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1642415, tc_HOL_Obool)), hAPP(c_List_Oset(_1642415), _1642421)), hAPP(c_List_Oset(_1642415), _1642423))), 43426 ^ _784416 : [(43427 ^ _784416) ^ [] : [hAPP(hAPP(c_List_Omap(_1642415, _1642417), _1642419), _1642421) = hAPP(hAPP(c_List_Omap(_1642415, _1642417), _1642419), _1642423), -(_1642421 = _1642423)], (43433 ^ _784416) ^ [] : [_1642421 = _1642423, -(hAPP(hAPP(c_List_Omap(_1642415, _1642417), _1642419), _1642421) = hAPP(hAPP(c_List_Omap(_1642415, _1642417), _1642419), _1642423))]]], (43439 ^ _784416) ^ [_1642736, _1642738, _1642740, _1642742, _1642744, _1642746] : [-(hBOOL(hAPP(hAPP(c_member(_1642736), _1642738), hAPP(c_List_Oset(_1642736), _1642740)))), -(hAPP(hAPP(c_List_Omap(_1642736, _1642742), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1642736, _1642742), _1642744), _1642738), _1642746)), _1642740) = hAPP(hAPP(c_List_Omap(_1642736, _1642742), _1642744), _1642740))], (43445 ^ _784416) ^ [_1642843, _1642845, _1642847, _1642849, _1642851, _1642853] : [_1642843 = _1642845, -(hAPP(hAPP(c_Map_Omap__of(_1642847, _1642849), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1642847, _1642849)), hAPP(hAPP(c_Product__Type_OPair(_1642847, _1642849), _1642843), _1642851)), _1642853)), _1642845) = hAPP(c_Option_Ooption_OSome(_1642849), _1642851))], (43451 ^ _784416) ^ [_1642990, _1642992, _1642994, _1642996, _1642998, _1643000] : [-(_1642990 = _1642992), -(hAPP(hAPP(c_Map_Omap__of(_1642994, _1642996), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1642994, _1642996)), hAPP(hAPP(c_Product__Type_OPair(_1642994, _1642996), _1642990), _1642998)), _1643000)), _1642992) = hAPP(hAPP(c_Map_Omap__of(_1642994, _1642996), _1643000), _1642992))], (43457 ^ _784416) ^ [_1643074, _1643076, _1643078, _1643080] : [hAPP(c_Map_Omap__of(_1643074, _1643076), _1643078) = hAPP(c_Map_Omap__of(_1643074, _1643076), _1643080), -(hAPP(c_Set_Oimage(tc_prod(_1643074, _1643076), _1643074, c_Product__Type_Ofst(_1643074, _1643076)), hAPP(c_List_Oset(tc_prod(_1643074, _1643076)), _1643078)) = hAPP(c_Set_Oimage(tc_prod(_1643074, _1643076), _1643074, c_Product__Type_Ofst(_1643074, _1643076)), hAPP(c_List_Oset(tc_prod(_1643074, _1643076)), _1643080)))], (43463 ^ _784416) ^ [_1643263, _1643265, _1643267, _1643269, _1643271] : [hAPP(hAPP(c_Map_Omap__of(_1643263, _1643265), _1643267), _1643269) = hAPP(c_Option_Ooption_OSome(_1643265), _1643271), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1643263, _1643265)), hAPP(hAPP(c_Product__Type_OPair(_1643263, _1643265), _1643269), _1643271)), hAPP(c_List_Oset(tc_prod(_1643263, _1643265)), _1643267))))], (43469 ^ _784416) ^ [_1643428, _1643430, _1643432, _1643434, _1643436] : [hAPP(hAPP(c_Map_Omap__of(_1643428, _1643430), _1643432), _1643434) = hAPP(c_Option_Ooption_OSome(_1643430), _1643436), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1643428, _1643430)), hAPP(hAPP(c_Product__Type_OPair(_1643428, _1643430), _1643434), _1643436)), hAPP(c_List_Oset(tc_prod(_1643428, _1643430)), _1643432))))], (43475 ^ _784416) ^ [_1643593, _1643595, _1643597] : [-(c_Map_Odom(_1643593, _1643595, hAPP(c_Map_Omap__of(_1643593, _1643595), _1643597)) = hAPP(c_Set_Oimage(tc_prod(_1643593, _1643595), _1643593, c_Product__Type_Ofst(_1643593, _1643595)), hAPP(c_List_Oset(tc_prod(_1643593, _1643595)), _1643597)))], (43477 ^ _784416) ^ [_1643651, _1643653, _1643655, _1643657] : [c_Fun_Oinj__on(_1643651, _1643653, _1643655, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1643651, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1643651), tc_fun(_1643651, tc_HOL_Obool), c_List_Oset(_1643651)), _1643657))), -(c_Fun_Oinj__on(tc_List_Olist(_1643651), tc_List_Olist(_1643653), hAPP(c_List_Omap(_1643651, _1643653), _1643655), _1643657))], (43483 ^ _784416) ^ [_1643821, _1643823, _1643825, _1643827] : [hAPP(hAPP(c_Map_Omap__of(_1643821, _1643823), _1643825), _1643827) = c_Option_Ooption_ONone(_1643823), hBOOL(hAPP(hAPP(c_member(_1643821), _1643827), hAPP(c_Set_Oimage(tc_prod(_1643821, _1643823), _1643821, c_Product__Type_Ofst(_1643821, _1643823)), hAPP(c_List_Oset(tc_prod(_1643821, _1643823)), _1643825))))], (43489 ^ _784416) ^ [_1643975, _1643977, _1643979, _1643981] : [-(hBOOL(hAPP(hAPP(c_member(_1643975), _1643981), hAPP(c_Set_Oimage(tc_prod(_1643975, _1643977), _1643975, c_Product__Type_Ofst(_1643975, _1643977)), hAPP(c_List_Oset(tc_prod(_1643975, _1643977)), _1643979))))), -(hAPP(hAPP(c_Map_Omap__of(_1643975, _1643977), _1643979), _1643981) = c_Option_Ooption_ONone(_1643977))], (43495 ^ _784416) ^ [_1644056, _1644058, _1644060, _1644062] : [hAPP(c_List_Oset(_1644056), _1644058) = c_Map_Odom(_1644056, _1644060, _1644062), -(hAPP(c_Map_Omap__of(_1644056, _1644060), hAPP(hAPP(c_List_Omap(_1644056, tc_prod(_1644056, _1644060)), hAPP(hAPP(c_COMBS(_1644056, _1644060, tc_prod(_1644056, _1644060)), c_Product__Type_OPair(_1644056, _1644060)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1644060), _1644060, _1644056), c_Option_Othe(_1644060)), _1644062))), _1644058)) = _1644062)], (43501 ^ _784416) ^ [_1644251, _1644253, _1644255] : [-(c_List_Oset__Cons(_1644251, _1644253, _1644255) = hAPP(c_Set_OCollect(tc_List_Olist(_1644251)), hAPP(hAPP(c_COMBB(tc_fun(_1644251, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1644251)), c_HOL_OEx(_1644251)), hAPP(hAPP(c_COMBB(tc_fun(_1644251, tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool)), tc_fun(_1644251, tc_HOL_Obool), tc_List_Olist(_1644251)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool), tc_HOL_Obool, _1644251), c_HOL_OEx(tc_List_Olist(_1644251)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1644251), tc_fun(_1644251, tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool)), tc_fun(_1644251, tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1644251, tc_fun(tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool), tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool))), tc_fun(tc_fun(_1644251, tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool)), tc_fun(_1644251, tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool))), tc_List_Olist(_1644251)), c_COMBS(_1644251, tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool), tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1644251, tc_fun(tc_List_Olist(_1644251), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1644251, tc_fun(tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool), tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool))), tc_List_Olist(_1644251)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1644251), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool), tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool)), _1644251), c_COMBS(tc_List_Olist(_1644251), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1644251, tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool)), tc_fun(_1644251, tc_fun(tc_List_Olist(_1644251), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1644251)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool), tc_fun(tc_List_Olist(_1644251), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1644251), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1644251)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1644251), tc_fun(_1644251, tc_fun(tc_List_Olist(_1644251), tc_List_Olist(_1644251))), tc_fun(_1644251, tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1644251), tc_List_Olist(_1644251)), tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool)), tc_fun(tc_fun(_1644251, tc_fun(tc_List_Olist(_1644251), tc_List_Olist(_1644251))), tc_fun(_1644251, tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool))), tc_List_Olist(_1644251)), c_COMBB(tc_fun(tc_List_Olist(_1644251), tc_List_Olist(_1644251)), tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool), _1644251)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1644251), tc_List_Olist(_1644251)), tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool)), tc_List_Olist(_1644251)), c_COMBB(tc_List_Olist(_1644251), tc_HOL_Obool, tc_List_Olist(_1644251))), c_fequal))), c_List_Olist_OCons(_1644251)))))), hAPP(hAPP(c_COMBC(_1644251, tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool), tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool), tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool)), _1644251), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1644251))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1644251), c_fconj), hAPP(hAPP(c_COMBC(_1644251, tc_fun(_1644251, tc_HOL_Obool), tc_HOL_Obool), c_member(_1644251)), _1644253)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1644251), tc_fun(tc_List_Olist(_1644251), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1644251))), _1644255)))))))], (43503 ^ _784416) ^ [_1644786, _1644788] : [-(hAPP(c_Option_Othe(_1644786), hAPP(c_Option_Ooption_OSome(_1644786), _1644788)) = _1644788)], (43505 ^ _784416) ^ [_1644821, _1644823] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1644821), tc_fun(_1644821, tc_HOL_Obool), c_List_Oset(_1644821)), hAPP(c_List_Oset(tc_List_Olist(_1644821)), c_Enum_Osublists(_1644821, _1644823))) = hAPP(c_Set_OPow(_1644821), hAPP(c_List_Oset(_1644821), _1644823)))], (43507 ^ _784416) ^ [_1644895, _1644897, _1644899, _1644901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1644895), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1644897), _1644899))), -(hAPP(c_Random_Opick(_1644897, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1644897)), _1644899), _1644901)), _1644895) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1644897), _1644899))], (43513 ^ _784416) ^ [_1645038, _1645040, _1645042, _1645044] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1645038), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1645040), _1645042)))), -(hAPP(c_Random_Opick(_1645040, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1645040)), _1645042), _1645044)), _1645038) = hAPP(c_Random_Opick(_1645040, _1645044), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1645038), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1645040), _1645042))))], (43519 ^ _784416) ^ [_1645126, _1645128, _1645130] : [-(c_Random_Oselect__weight(_1645126, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1645126)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1645126), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1645128)), _1645130)) = c_Random_Oselect__weight(_1645126, _1645130))], (43521 ^ _784416) ^ [_1645179, _1645181, _1645183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1645179), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1645181), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1645181)), _1645183)))), -(hBOOL(hAPP(hAPP(c_member(_1645181), hAPP(c_Random_Opick(_1645181, _1645183), _1645179)), hAPP(c_List_Oset(_1645181), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1645181), _1645181), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1645181)), _1645183)))))], (43527 ^ _784416) ^ [_1645370, _1645372, _1645374] : [class_Groups_Omonoid__add(_1645370), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1645370), hAPP(hAPP(c_List_Olist_OCons(_1645370), _1645372), _1645374)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1645370), _1645372), hAPP(c_List_Omonoid__add__class_Olistsum(_1645370), _1645374)))], (43533 ^ _784416) ^ [_1645499, _1645501, _1645503] : [class_Groups_Omonoid__add(_1645499), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1645499), hAPP(hAPP(c_List_Omap(_1645501, _1645499), hAPP(c_COMBK(_1645499, _1645501), c_Groups_Ozero__class_Ozero(_1645499))), _1645503)) = c_Groups_Ozero__class_Ozero(_1645499))], (43539 ^ _784416) ^ [_1645624, _1645626, _1645628, _1645630, _1645632] : [class_Groups_Ocomm__monoid__add(_1645624), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1645624), hAPP(hAPP(c_List_Omap(_1645626, _1645624), hAPP(hAPP(c_COMBS(_1645626, _1645624, _1645624), hAPP(hAPP(c_COMBB(_1645624, tc_fun(_1645624, _1645624), _1645626), c_Groups_Oplus__class_Oplus(_1645624)), _1645628)), _1645630)), _1645632)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1645624), hAPP(c_List_Omonoid__add__class_Olistsum(_1645624), hAPP(hAPP(c_List_Omap(_1645626, _1645624), _1645628), _1645632))), hAPP(c_List_Omonoid__add__class_Olistsum(_1645624), hAPP(hAPP(c_List_Omap(_1645626, _1645624), _1645630), _1645632))))], (43545 ^ _784416) ^ [_1645855, _1645857, _1645859, _1645861, _1645863] : [class_Rings_Osemiring__0(_1645855), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1645855), hAPP(hAPP(c_List_Omap(_1645857, _1645855), hAPP(hAPP(c_COMBB(_1645855, _1645855, _1645857), hAPP(c_Groups_Otimes__class_Otimes(_1645855), _1645859)), _1645861)), _1645863)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1645855), _1645859), hAPP(c_List_Omonoid__add__class_Olistsum(_1645855), hAPP(hAPP(c_List_Omap(_1645857, _1645855), _1645861), _1645863))))], (43551 ^ _784416) ^ [_1646038, _1646040, _1646042, _1646044, _1646046] : [class_Rings_Osemiring__0(_1646038), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1646038), hAPP(hAPP(c_List_Omap(_1646040, _1646038), hAPP(hAPP(c_COMBC(_1646040, _1646038, _1646038), hAPP(hAPP(c_COMBB(_1646038, tc_fun(_1646038, _1646038), _1646040), c_Groups_Otimes__class_Otimes(_1646038)), _1646042)), _1646044)), _1646046)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1646038), hAPP(c_List_Omonoid__add__class_Olistsum(_1646038), hAPP(hAPP(c_List_Omap(_1646040, _1646038), _1646042), _1646046))), _1646044))], (43557 ^ _784416) ^ [_1646241, _1646243, _1646245, _1646247, _1646249] : [class_Groups_Oab__group__add(_1646241), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1646241), hAPP(hAPP(c_List_Omap(_1646243, _1646241), hAPP(hAPP(c_COMBS(_1646243, _1646241, _1646241), hAPP(hAPP(c_COMBB(_1646241, tc_fun(_1646241, _1646241), _1646243), c_Groups_Ominus__class_Ominus(_1646241)), _1646245)), _1646247)), _1646249)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1646241), hAPP(c_List_Omonoid__add__class_Olistsum(_1646241), hAPP(hAPP(c_List_Omap(_1646243, _1646241), _1646245), _1646249))), hAPP(c_List_Omonoid__add__class_Olistsum(_1646241), hAPP(hAPP(c_List_Omap(_1646243, _1646241), _1646247), _1646249))))], (43563 ^ _784416) ^ [_1646472, _1646474] : [class_Groups_Oordered__ab__group__add__abs(_1646472), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1646472), hAPP(c_Groups_Oabs__class_Oabs(_1646472), hAPP(c_List_Omonoid__add__class_Olistsum(_1646472), _1646474))), hAPP(c_List_Omonoid__add__class_Olistsum(_1646472), hAPP(hAPP(c_List_Omap(_1646472, _1646472), c_Groups_Oabs__class_Oabs(_1646472)), _1646474)))))], (43569 ^ _784416) ^ [_1646613, _1646615, _1646617, _1646619] : [class_Groups_Oab__group__add(_1646613), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1646613), hAPP(c_List_Omonoid__add__class_Olistsum(_1646613), hAPP(hAPP(c_List_Omap(_1646615, _1646613), _1646617), _1646619))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1646613), hAPP(hAPP(c_List_Omap(_1646615, _1646613), hAPP(c_Fun_Ocomp(_1646613, _1646613, _1646615, c_Groups_Ouminus__class_Ouminus(_1646613)), _1646617)), _1646619)))], (43575 ^ _784416) ^ [_1646778, _1646780] : [-(c_Random_Oselect__weight(_1646778, _1646780) = 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(_1646778, 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, _1646778), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1646778)), _1646780)))), hAPP(hAPP(c_COMBB(_1646778, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1646778, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1646778, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1646778, _1646780))))], (43577 ^ _784416) ^ [_1646862, _1646864, _1646866] : [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, _1646862), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1646862)), _1646864)))), -(hBOOL(hAPP(hAPP(c_member(_1646862), hAPP(c_Product__Type_Ofst(_1646862, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1646862, _1646864), _1646866))), hAPP(c_List_Oset(_1646862), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1646862), _1646862), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1646862)), _1646864)))))], (43583 ^ _784416) ^ [_1647059, _1647061, _1647063, _1647065] : [-(hAPP(c_List_Oset(tc_prod(_1647059, _1647061)), c_Enum_Oproduct(_1647059, _1647061, _1647063, _1647065)) = hAPP(hAPP(c_Product__Type_OSigma(_1647059, _1647061), hAPP(c_List_Oset(_1647059), _1647063)), hAPP(c_COMBK(tc_fun(_1647061, tc_HOL_Obool), _1647059), hAPP(c_List_Oset(_1647061), _1647065))))], (43585 ^ _784416) ^ [_1647129, _1647131, _1647133] : [hBOOL(hAPP(c_List_Odistinct(_1647129), hAPP(hAPP(c_List_Omap(tc_prod(_1647129, _1647131), _1647129), c_Product__Type_Ofst(_1647129, _1647131)), _1647133))), -(c_Map_Oran(_1647129, _1647131, hAPP(c_Map_Omap__of(_1647129, _1647131), _1647133)) = hAPP(c_Set_Oimage(tc_prod(_1647129, _1647131), _1647131, c_Product__Type_Osnd(_1647129, _1647131)), hAPP(c_List_Oset(tc_prod(_1647129, _1647131)), _1647133)))], (43591 ^ _784416) ^ [_1647308, _1647310] : [hBOOL(hAPP(c_List_Odistinct(_1647308), _1647310)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1647308, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1647308), tc_fun(_1647308, tc_HOL_Obool)), c_List_Oset(_1647308)), c_Enum_Osublists(_1647308, _1647310)))))], (43607 ^ _784416) ^ [_1647625] : [43609 ^ _784416 : [(43610 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43608 ^ [_1647625]), hAPP(c_List_Oset(tc_Nat_Onat), _1647625))))], (43612 ^ _784416) ^ [] : [43608 ^ [_1647625] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1647625) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43597 ^ _784416) ^ [_1647457] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1647457) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43600 ^ _784416 : [(43601 ^ _784416) ^ [_1647532] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1647532), hAPP(c_List_Oset(tc_Nat_Onat), _1647457))), -(_1647532 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (43616 ^ _784416) ^ [_1647781, _1647783, _1647785, _1647787] : [hBOOL(hAPP(c_List_Odistinct(_1647781), _1647783)), hBOOL(hAPP(c_List_Odistinct(_1647785), _1647787)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1647781, _1647785)), c_Enum_Oproduct(_1647781, _1647785, _1647783, _1647787))))], (43626 ^ _784416) ^ [_1647976, _1647978, _1647980] : [hBOOL(hAPP(c_List_Odistinct(_1647976), hAPP(hAPP(c_List_Olist_OCons(_1647976), _1647978), _1647980))), 43629 ^ _784416 : [(43630 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1647976), _1647978), hAPP(c_List_Oset(_1647976), _1647980)))], (43632 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1647976), _1647980)))]]], (43634 ^ _784416) ^ [_1648143, _1648145, _1648147] : [-(hBOOL(hAPP(c_List_Odistinct(_1648143), hAPP(hAPP(c_List_Olist_OCons(_1648143), _1648145), _1648147)))), -(hBOOL(hAPP(hAPP(c_member(_1648143), _1648145), hAPP(c_List_Oset(_1648143), _1648147)))), hBOOL(hAPP(c_List_Odistinct(_1648143), _1648147))], (43644 ^ _784416) ^ [_1648358, _1648360, _1648362, _1648364] : [hBOOL(hAPP(c_List_Odistinct(_1648358), hAPP(hAPP(c_List_Omap(_1648360, _1648358), _1648362), _1648364))), 43647 ^ _784416 : [(43648 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1648360), _1648364)))], (43650 ^ _784416) ^ [] : [-(c_Fun_Oinj__on(_1648360, _1648358, _1648362, hAPP(c_List_Oset(_1648360), _1648364)))]]], (43652 ^ _784416) ^ [_1648509, _1648511, _1648513, _1648515] : [-(hBOOL(hAPP(c_List_Odistinct(_1648509), hAPP(hAPP(c_List_Omap(_1648511, _1648509), _1648513), _1648515)))), hBOOL(hAPP(c_List_Odistinct(_1648511), _1648515)), c_Fun_Oinj__on(_1648511, _1648509, _1648513, hAPP(c_List_Oset(_1648511), _1648515))], (43662 ^ _784416) ^ [_1648696, _1648698] : [class_Groups_Ocomm__monoid__add(_1648696), hBOOL(hAPP(c_List_Odistinct(_1648696), _1648698)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1648696), _1648698) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1648696, _1648696), c_COMBI(_1648696)), hAPP(c_List_Oset(_1648696), _1648698)))], (43672 ^ _784416) ^ [_1648873, _1648875, _1648877, _1648879] : [class_Groups_Ocomm__monoid__add(_1648873), hBOOL(hAPP(c_List_Odistinct(_1648875), _1648877)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1648873), hAPP(hAPP(c_List_Omap(_1648875, _1648873), _1648879), _1648877)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1648875, _1648873), _1648879), hAPP(c_List_Oset(_1648875), _1648877)))], (43682 ^ _784416) ^ [_1649072, _1649074, _1649076, _1649078] : [hBOOL(hAPP(c_List_Odistinct(_1649072), hAPP(hAPP(c_List_Omap(tc_prod(_1649072, _1649074), _1649072), c_Product__Type_Ofst(_1649072, _1649074)), _1649076))), hBOOL(hAPP(c_List_Odistinct(_1649072), hAPP(hAPP(c_List_Omap(tc_prod(_1649072, _1649074), _1649072), c_Product__Type_Ofst(_1649072, _1649074)), _1649078))), 43689 ^ _784416 : [(43690 ^ _784416) ^ [] : [hAPP(c_Map_Omap__of(_1649072, _1649074), _1649076) = hAPP(c_Map_Omap__of(_1649072, _1649074), _1649078), -(hAPP(c_List_Oset(tc_prod(_1649072, _1649074)), _1649076) = hAPP(c_List_Oset(tc_prod(_1649072, _1649074)), _1649078))], (43696 ^ _784416) ^ [] : [hAPP(c_List_Oset(tc_prod(_1649072, _1649074)), _1649076) = hAPP(c_List_Oset(tc_prod(_1649072, _1649074)), _1649078), -(hAPP(c_Map_Omap__of(_1649072, _1649074), _1649076) = hAPP(c_Map_Omap__of(_1649072, _1649074), _1649078))]]], (43702 ^ _784416) ^ [_1649507, _1649509, _1649511, _1649513, _1649515] : [hBOOL(hAPP(c_List_Odistinct(_1649507), hAPP(hAPP(c_List_Omap(tc_prod(_1649507, _1649509), _1649507), c_Product__Type_Ofst(_1649507, _1649509)), _1649511))), 43705 ^ _784416 : [(43706 ^ _784416) ^ [] : [hAPP(c_Option_Ooption_OSome(_1649509), _1649513) = hAPP(hAPP(c_Map_Omap__of(_1649507, _1649509), _1649511), _1649515), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1649507, _1649509)), hAPP(hAPP(c_Product__Type_OPair(_1649507, _1649509), _1649515), _1649513)), hAPP(c_List_Oset(tc_prod(_1649507, _1649509)), _1649511))))], (43712 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1649507, _1649509)), hAPP(hAPP(c_Product__Type_OPair(_1649507, _1649509), _1649515), _1649513)), hAPP(c_List_Oset(tc_prod(_1649507, _1649509)), _1649511))), -(hAPP(c_Option_Ooption_OSome(_1649509), _1649513) = hAPP(hAPP(c_Map_Omap__of(_1649507, _1649509), _1649511), _1649515))]]], (43718 ^ _784416) ^ [_1649893, _1649895, _1649897, _1649899, _1649901] : [hBOOL(hAPP(c_List_Odistinct(_1649893), hAPP(hAPP(c_List_Omap(tc_prod(_1649893, _1649895), _1649893), c_Product__Type_Ofst(_1649893, _1649895)), _1649897))), 43721 ^ _784416 : [(43722 ^ _784416) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1649893, _1649895), _1649897), _1649899) = hAPP(c_Option_Ooption_OSome(_1649895), _1649901), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1649893, _1649895)), hAPP(hAPP(c_Product__Type_OPair(_1649893, _1649895), _1649899), _1649901)), hAPP(c_List_Oset(tc_prod(_1649893, _1649895)), _1649897))))], (43728 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1649893, _1649895)), hAPP(hAPP(c_Product__Type_OPair(_1649893, _1649895), _1649899), _1649901)), hAPP(c_List_Oset(tc_prod(_1649893, _1649895)), _1649897))), -(hAPP(hAPP(c_Map_Omap__of(_1649893, _1649895), _1649897), _1649899) = hAPP(c_Option_Ooption_OSome(_1649895), _1649901))]]], (43734 ^ _784416) ^ [_1650279, _1650281, _1650283, _1650285, _1650287] : [hBOOL(hAPP(c_List_Odistinct(_1650279), hAPP(hAPP(c_List_Omap(tc_prod(_1650279, _1650281), _1650279), c_Product__Type_Ofst(_1650279, _1650281)), _1650283))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1650279, _1650281)), hAPP(hAPP(c_Product__Type_OPair(_1650279, _1650281), _1650285), _1650287)), hAPP(c_List_Oset(tc_prod(_1650279, _1650281)), _1650283))), -(hAPP(hAPP(c_Map_Omap__of(_1650279, _1650281), _1650283), _1650285) = hAPP(c_Option_Ooption_OSome(_1650281), _1650287))], (43744 ^ _784416) ^ [_1650540, _1650542, _1650544] : [hBOOL(hAPP(c_List_Odistinct(_1650540), hAPP(hAPP(c_List_Omap(tc_prod(_1650540, _1650542), _1650540), c_Product__Type_Ofst(_1650540, _1650542)), _1650544))), -(hAPP(c_List_Oset(tc_prod(_1650540, _1650542)), _1650544) = hAPP(c_Set_OCollect(tc_prod(_1650540, _1650542)), hAPP(c_Product__Type_Oprod_Oprod__case(_1650540, _1650542, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1650540, tc_fun(_1650542, tc_Option_Ooption(_1650542)), tc_fun(_1650542, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1650542), tc_HOL_Obool), tc_fun(tc_fun(_1650542, tc_Option_Ooption(_1650542)), tc_fun(_1650542, tc_HOL_Obool)), _1650540), c_COMBB(tc_Option_Ooption(_1650542), tc_HOL_Obool, _1650542)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1650542), tc_fun(tc_Option_Ooption(_1650542), tc_HOL_Obool), _1650540), c_fequal), hAPP(c_Map_Omap__of(_1650540, _1650542), _1650544)))), c_Option_Ooption_OSome(_1650542)))))], (43750 ^ _784416) ^ [_1650853, _1650855, _1650857, _1650859] : [class_Groups_Ocomm__monoid__add(_1650853), 43753 ^ _784416 : [(43754 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1650855), _1650857)), -(c_Nitpick_Osetsum_H(_1650855, _1650853, _1650859, _1650857) = hAPP(c_List_Omonoid__add__class_Olistsum(_1650853), hAPP(hAPP(c_List_Omap(_1650855, _1650853), _1650859), c_Hilbert__Choice_OEps(tc_List_Olist(_1650855), hAPP(hAPP(c_COMBS(tc_List_Olist(_1650855), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1650855)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1650855), tc_fun(_1650855, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1650855, tc_HOL_Obool), tc_fun(tc_fun(_1650855, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1650855)), c_fequal), c_List_Oset(_1650855))), _1650857))), c_List_Odistinct(_1650855))))))], (43760 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1650855), _1650857))), -(c_Nitpick_Osetsum_H(_1650855, _1650853, _1650859, _1650857) = c_Groups_Ozero__class_Ozero(_1650853))]]], (43766 ^ _784416) ^ [_1651241, _1651243, _1651245] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1651241), _1651243)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1651241)), hAPP(c_Set_OCollect(tc_List_Olist(_1651241)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1651241), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1651241)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1651241), tc_fun(_1651241, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1651241, tc_HOL_Obool), tc_fun(tc_fun(_1651241, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1651241)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1651241, tc_HOL_Obool))), c_List_Oset(_1651241))), _1651243))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1651241), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1651241)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1651241)))), _1651245))))))], (43772 ^ _784416) ^ [_1651544, _1651546, _1651548, _1651550, _1651552, _1651554, _1651556] : [hAPP(hAPP(c_List_Omap(_1651544, _1651546), _1651548), _1651550) = hAPP(hAPP(c_List_Omap(_1651552, _1651546), _1651554), _1651556), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651544)), _1651550) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651552)), _1651556))], (43778 ^ _784416) ^ [_1651695, _1651697, _1651699, _1651701] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651695)), hAPP(hAPP(c_List_Omap(_1651697, _1651695), _1651699), _1651701)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651697)), _1651701))], (43780 ^ _784416) ^ [_1651747, _1651749, _1651751, _1651753, _1651755] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651747), tc_List_Olist(_1651747))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651747), tc_List_Olist(_1651747)), _1651749), _1651751)), hAPP(c_List_Olexn(_1651747, _1651753), _1651755))), 43783 ^ _784416 : [(43784 ^ _784416) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651747)), _1651749) = _1651755)], (43786 ^ _784416) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651747)), _1651751) = _1651755)]]], (43788 ^ _784416) ^ [_1651950, _1651952, _1651954, _1651956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651950)), _1651952)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651950)), _1651954))), _1651952 = hAPP(hAPP(c_List_Olist_OCons(_1651950), _1651956), _1651954)], (43794 ^ _784416) ^ [_1652086, _1652088] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1652086))), c_Enum_Osublists(_1652086, _1652088)) = 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(_1652086)), _1652088)))], (43796 ^ _784416) ^ [_1652132, _1652134, _1652136] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652132)), _1652134) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652132)), _1652136)), _1652134 = _1652136], (43802 ^ _784416) ^ [_1652224, _1652226] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1652224), hAPP(c_List_Oset(_1652224), _1652226))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652224)), _1652226))))], (43804 ^ _784416) ^ [_1652271, _1652273] : [hBOOL(hAPP(c_List_Odistinct(_1652271), _1652273)), -(hAPP(c_Finite__Set_Ocard(_1652271), hAPP(c_List_Oset(_1652271), _1652273)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652271)), _1652273))], (43810 ^ _784416) ^ [_1652390, _1652392] : [hAPP(c_Finite__Set_Ocard(_1652390), hAPP(c_List_Oset(_1652390), _1652392)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652390)), _1652392), -(hBOOL(hAPP(c_List_Odistinct(_1652390), _1652392)))], (43816 ^ _784416) ^ [_1652509, _1652511, _1652513] : [-(hAPP(c_List_Olexn(_1652509, _1652511), hAPP(c_Nat_OSuc, _1652513)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1652509), tc_List_Olist(_1652509)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1652509, tc_List_Olist(_1652509)), tc_prod(_1652509, tc_List_Olist(_1652509))), tc_prod(tc_List_Olist(_1652509), tc_List_Olist(_1652509)), c_Product__Type_Omap__pair(tc_prod(_1652509, tc_List_Olist(_1652509)), tc_List_Olist(_1652509), tc_prod(_1652509, tc_List_Olist(_1652509)), tc_List_Olist(_1652509), hAPP(c_Product__Type_Oprod_Oprod__case(_1652509, tc_List_Olist(_1652509), tc_List_Olist(_1652509)), c_List_Olist_OCons(_1652509)), hAPP(c_Product__Type_Oprod_Oprod__case(_1652509, tc_List_Olist(_1652509), tc_List_Olist(_1652509)), c_List_Olist_OCons(_1652509)))), c_Wellfounded_Olex__prod(_1652509, tc_List_Olist(_1652509), _1652511, hAPP(c_List_Olexn(_1652509, _1652511), _1652513)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1652509), tc_List_Olist(_1652509))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1652509), tc_List_Olist(_1652509), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1652509), tc_fun(tc_List_Olist(_1652509), tc_HOL_Obool), tc_fun(tc_List_Olist(_1652509), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1652509), tc_HOL_Obool), tc_fun(tc_List_Olist(_1652509), tc_HOL_Obool)), tc_List_Olist(_1652509)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1652509))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1652509)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1652509), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1652509)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1652509)))), hAPP(c_Nat_OSuc, _1652513))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1652509), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1652509)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1652509)))), hAPP(c_Nat_OSuc, _1652513)))))))], (43818 ^ _784416) ^ [_1652800, _1652802, _1652804] : [hBOOL(hAPP(hAPP(c_member(_1652800), _1652802), hAPP(c_List_Oset(_1652800), _1652804))), -(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(_1652800)), _1652804))))], (43824 ^ _784416) ^ [_1652921, _1652923, _1652925] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652921)), hAPP(hAPP(c_List_Olist_OCons(_1652921), _1652923), _1652925)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652921)), _1652925)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43826 ^ _784416) ^ [_1653003, _1653005, _1653007, _1653009, _1653011, _1653013] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1653003), tc_List_Olist(_1653003))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653003), tc_List_Olist(_1653003)), hAPP(hAPP(c_List_Olist_OCons(_1653003), _1653005), _1653007)), hAPP(hAPP(c_List_Olist_OCons(_1653003), _1653009), _1653011))), c_List_Olex(_1653003, _1653013))), 43831 ^ _784416 : [(43832 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1653003, _1653003)), hAPP(hAPP(c_Product__Type_OPair(_1653003, _1653003), _1653005), _1653009)), _1653013)))], (43834 ^ _784416) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653003)), _1653007) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653003)), _1653011))]], 43835 ^ _784416 : [(43836 ^ _784416) ^ [] : [-(_1653005 = _1653009)], (43838 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1653003), tc_List_Olist(_1653003))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653003), tc_List_Olist(_1653003)), _1653007), _1653011)), c_List_Olex(_1653003, _1653013))))]]], (43840 ^ _784416) ^ [_1653401, _1653403, _1653405, _1653407, _1653409, _1653411] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1653401), tc_List_Olist(_1653401))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653401), tc_List_Olist(_1653401)), hAPP(hAPP(c_List_Olist_OCons(_1653401), _1653403), _1653405)), hAPP(hAPP(c_List_Olist_OCons(_1653401), _1653407), _1653409))), c_List_Olex(_1653401, _1653411)))), 43841 ^ _784416 : [(43842 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1653401, _1653401)), hAPP(hAPP(c_Product__Type_OPair(_1653401, _1653401), _1653403), _1653407)), _1653411)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653401)), _1653405) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653401)), _1653409)], (43848 ^ _784416) ^ [] : [_1653403 = _1653407, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1653401), tc_List_Olist(_1653401))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1653401), tc_List_Olist(_1653401)), _1653405), _1653409)), c_List_Olex(_1653401, _1653411)))]]], (43856 ^ _784416) ^ [_1653857, _1653859, _1653861, _1653863] : [class_Rings_Osemiring__1(_1653857), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1653857), hAPP(hAPP(c_List_Omap(_1653859, _1653857), hAPP(c_COMBK(_1653857, _1653859), _1653861)), _1653863)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1653857), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1653857), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653859)), _1653863))), _1653861))], (43862 ^ _784416) ^ [_1654016, _1654018] : [-(c_List_Olenlex(_1654016, _1654018) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1654016), tc_List_Olist(_1654016))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1654016), tc_List_Olist(_1654016), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1654016), tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool), tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1654016), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool), tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool)), tc_List_Olist(_1654016)), c_COMBS(tc_List_Olist(_1654016), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool), tc_fun(tc_List_Olist(_1654016), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1654016)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1654016)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1654016), tc_fun(tc_List_Olist(_1654016), tc_Nat_Onat), tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1654016), tc_Nat_Onat), tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool)), tc_List_Olist(_1654016)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1654016))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1654016)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1654016))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1654016)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1654016), tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool), tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1654016), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool), tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool)), tc_List_Olist(_1654016)), c_COMBS(tc_List_Olist(_1654016), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool), tc_fun(tc_List_Olist(_1654016), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1654016)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1654016)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1654016), tc_fun(tc_List_Olist(_1654016), tc_Nat_Onat), tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1654016), tc_Nat_Onat), tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool)), tc_List_Olist(_1654016)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1654016))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1654016)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1654016))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1654016)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1654016), tc_fun(tc_prod(tc_List_Olist(_1654016), tc_List_Olist(_1654016)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1654016), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1654016), tc_List_Olist(_1654016)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1654016), tc_List_Olist(_1654016)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1654016), tc_HOL_Obool)), tc_List_Olist(_1654016)), c_COMBC(tc_List_Olist(_1654016), tc_fun(tc_prod(tc_List_Olist(_1654016), tc_List_Olist(_1654016)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1654016), tc_prod(tc_List_Olist(_1654016), tc_List_Olist(_1654016))), tc_fun(tc_List_Olist(_1654016), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1654016), tc_List_Olist(_1654016)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1654016)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1654016), tc_List_Olist(_1654016)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1654016), tc_List_Olist(_1654016)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1654016)), c_member(tc_prod(tc_List_Olist(_1654016), tc_List_Olist(_1654016))))), c_Product__Type_OPair(tc_List_Olist(_1654016), tc_List_Olist(_1654016))))), c_List_Olex(_1654016, _1654018)))))))], (43864 ^ _784416) ^ [_1654572, _1654574] : [-(c_List_Olenlex(_1654572, _1654574) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1654572)), tc_List_Olist(_1654572)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1654572), c_Wellfounded_Oless__than, c_List_Olex(_1654572, _1654574))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1654572), tc_List_Olist(_1654572), tc_prod(tc_Nat_Onat, tc_List_Olist(_1654572))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1654572), tc_prod(tc_Nat_Onat, tc_List_Olist(_1654572))), tc_List_Olist(_1654572)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1654572))), c_Nat_Osize__class_Osize(tc_List_Olist(_1654572)))), c_COMBI(tc_List_Olist(_1654572)))))], (43866 ^ _784416) ^ [_1654680, _1654682, _1654684] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1654680), _1654682)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1654680)), hAPP(c_Set_OCollect(tc_List_Olist(_1654680)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1654680), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1654680)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1654680), tc_fun(_1654680, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1654680, tc_HOL_Obool), tc_fun(tc_fun(_1654680, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1654680)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1654680, tc_HOL_Obool))), c_List_Oset(_1654680))), _1654682))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1654680), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1654680)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1654680)))), _1654684))))))], (43872 ^ _784416) ^ [_1654992, _1654994] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1654992), _1654994)), -(c_Nitpick_Ocard_H(_1654992, _1654994) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654992)), c_Hilbert__Choice_OEps(tc_List_Olist(_1654992), hAPP(hAPP(c_COMBS(tc_List_Olist(_1654992), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1654992)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1654992), tc_fun(_1654992, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1654992, tc_HOL_Obool), tc_fun(tc_fun(_1654992, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1654992)), c_fequal), c_List_Oset(_1654992))), _1654994))), c_List_Odistinct(_1654992)))))], (43878 ^ _784416) ^ [_1655229, _1655231] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1655229), _1655231))), -(c_Nitpick_Ocard_H(_1655229, _1655231) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43884 ^ _784416) ^ [_1655274, _1655276, _1655278] : [-(hAPP(c_List_Oset(tc_List_Olist(_1655274)), c_Enum_On__lists(_1655274, _1655276, _1655278)) = hAPP(c_Set_OCollect(tc_List_Olist(_1655274)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1655274), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1655274)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1655274), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1655274)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1655274)))), _1655276))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1655274), tc_fun(_1655274, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1655274, tc_HOL_Obool), tc_fun(tc_fun(_1655274, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1655274)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1655274, tc_HOL_Obool))), c_List_Oset(_1655274))), hAPP(c_List_Oset(_1655274), _1655278)))))], (43886 ^ _784416) ^ [_1655419, _1655421, _1655423] : [hBOOL(hAPP(c_List_Odistinct(_1655419), _1655421)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1655419)), c_Enum_On__lists(_1655419, _1655423, _1655421))))], (43892 ^ _784416) ^ [_1655526, _1655528, _1655530] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1655526))), c_Enum_On__lists(_1655526, _1655528, _1655530)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655526)), _1655530)), _1655528))], (43894 ^ _784416) ^ [_1655579, _1655581, _1655583, _1655585] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1655579)), _1655581), hAPP(c_List_Oset(tc_List_Olist(_1655579)), c_Enum_On__lists(_1655579, _1655583, _1655585)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655579)), _1655581) = _1655583)], (43900 ^ _784416) ^ [_1655714, _1655716, _1655718] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655714)), c_List_Osublist(_1655714, _1655716, _1655718)) = 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(_1655714)), _1655716)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1655718)))))], (43902 ^ _784416) ^ [_1655807, _1655809, _1655811, _1655813, _1655815, _1655817] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655807), tc_List_Olist(_1655807))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655807), tc_List_Olist(_1655807)), hAPP(hAPP(c_List_Olist_OCons(_1655807), _1655809), _1655811)), hAPP(hAPP(c_List_Olist_OCons(_1655807), _1655813), _1655815))), c_List_Olexord(_1655807, _1655817))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1655807, _1655807)), hAPP(hAPP(c_Product__Type_OPair(_1655807, _1655807), _1655809), _1655813)), _1655817))), 43909 ^ _784416 : [(43910 ^ _784416) ^ [] : [-(_1655809 = _1655813)], (43912 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655807), tc_List_Olist(_1655807))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655807), tc_List_Olist(_1655807)), _1655811), _1655815)), c_List_Olexord(_1655807, _1655817))))]]], (43914 ^ _784416) ^ [_1656134, _1656136, _1656138, _1656140, _1656142, _1656144] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656134), tc_List_Olist(_1656134))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656134), tc_List_Olist(_1656134)), hAPP(hAPP(c_List_Olist_OCons(_1656134), _1656136), _1656138)), hAPP(hAPP(c_List_Olist_OCons(_1656134), _1656140), _1656142))), c_List_Olexord(_1656134, _1656144)))), 43915 ^ _784416 : [(43916 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1656134, _1656134)), hAPP(hAPP(c_Product__Type_OPair(_1656134, _1656134), _1656136), _1656140)), _1656144))], (43918 ^ _784416) ^ [] : [_1656136 = _1656140, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656134), tc_List_Olist(_1656134))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656134), tc_List_Olist(_1656134)), _1656138), _1656142)), c_List_Olexord(_1656134, _1656144)))]]], (43926 ^ _784416) ^ [_1656507, _1656509, _1656511] : [hBOOL(hAPP(c_List_Odistinct(_1656507), _1656509)), -(hBOOL(hAPP(c_List_Odistinct(_1656507), c_List_Osublist(_1656507, _1656509, _1656511))))], (43932 ^ _784416) ^ [_1656610, _1656612, _1656614, _1656616] : [hBOOL(hAPP(hAPP(c_member(_1656610), _1656612), hAPP(c_List_Oset(_1656610), c_List_Osublist(_1656610, _1656614, _1656616)))), -(hBOOL(hAPP(hAPP(c_member(_1656610), _1656612), hAPP(c_List_Oset(_1656610), _1656614))))], (43938 ^ _784416) ^ [_1656746, _1656748, _1656750, _1656752] : [-(hBOOL(hAPP(hAPP(c_member(_1656746), _1656748), hAPP(c_List_Oset(_1656746), _1656750)))), hBOOL(hAPP(hAPP(c_member(_1656746), _1656748), hAPP(c_List_Oset(_1656746), c_List_Osublist(_1656746, _1656750, _1656752))))], (43944 ^ _784416) ^ [_1656870, _1656872, _1656874] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1656870, tc_HOL_Obool)), hAPP(c_List_Oset(_1656870), c_List_Osublist(_1656870, _1656872, _1656874))), hAPP(c_List_Oset(_1656870), _1656872))))], (43946 ^ _784416) ^ [_1656942, _1656944, _1656946, _1656948] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656942), tc_List_Olist(_1656942))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656942), tc_List_Olist(_1656942)), _1656944), _1656946)), c_List_Olex(_1656942, _1656948))), 43949 ^ _784416 : [(43950 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656942), tc_List_Olist(_1656942))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656942), tc_List_Olist(_1656942)), _1656944), _1656946)), c_List_Olexord(_1656942, _1656948))))], (43952 ^ _784416) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656942)), _1656944) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656942)), _1656946))]]], (43954 ^ _784416) ^ [_1657193, _1657195, _1657197, _1657199] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657193), tc_List_Olist(_1657193))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657193), tc_List_Olist(_1657193)), _1657195), _1657197)), c_List_Olex(_1657193, _1657199)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657193), tc_List_Olist(_1657193))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657193), tc_List_Olist(_1657193)), _1657195), _1657197)), c_List_Olexord(_1657193, _1657199))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657193)), _1657195) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657193)), _1657197)], (43964 ^ _784416) ^ [_1657480, _1657482, _1657484, _1657486, _1657488, _1657490] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1657480, _1657480)), hAPP(hAPP(c_Product__Type_OPair(_1657480, _1657480), _1657482), _1657484)), c_Transitive__Closure_Ortrancl(_1657480, _1657486))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657480), tc_List_Olist(_1657480))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657480), tc_List_Olist(_1657480)), _1657488), _1657490)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1657480), c_List_Olistrel1(_1657480, _1657486)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1657480), tc_List_Olist(_1657480))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1657480), tc_List_Olist(_1657480)), hAPP(hAPP(c_List_Olist_OCons(_1657480), _1657482), _1657488)), hAPP(hAPP(c_List_Olist_OCons(_1657480), _1657484), _1657490))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1657480), c_List_Olistrel1(_1657480, _1657486)))))], (43974 ^ _784416) ^ [_1657841, _1657843, _1657845, _1657847] : [-(c_List_Olist_Olist__size(_1657841, _1657843, hAPP(hAPP(c_List_Olist_OCons(_1657841), _1657845), _1657847)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1657843, _1657845)), c_List_Olist_Olist__size(_1657841, _1657843, _1657847))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43976 ^ _784416) ^ [_1657901, _1657903, _1657905, _1657907] : [hBOOL(hAPP(hAPP(c_member(_1657901), _1657903), c_Wellfounded_Oacc(_1657901, _1657905))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1657901)), _1657907), c_Wellfounded_Oacc(tc_List_Olist(_1657901), c_List_Olistrel1(_1657901, _1657905)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1657901)), hAPP(hAPP(c_List_Olist_OCons(_1657901), _1657903), _1657907)), c_Wellfounded_Oacc(tc_List_Olist(_1657901), c_List_Olistrel1(_1657901, _1657905)))))], (43986 ^ _784416) ^ [_1658142, _1658144, _1658146, _1658148, _1658150] : [-(c_List_Olist_Olist__size(_1658142, _1658144, hAPP(hAPP(c_List_Omap(_1658146, _1658142), _1658148), _1658150)) = c_List_Olist_Olist__size(_1658146, hAPP(c_Fun_Ocomp(_1658142, tc_Nat_Onat, _1658146, _1658144), _1658148), _1658150))], (43988 ^ _784416) ^ [_1658198, _1658200, _1658202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1658198, _1658198), tc_HOL_Obool)), _1658200), _1658202)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1658198), tc_List_Olist(_1658198)), tc_HOL_Obool)), c_List_Olistrel1(_1658198, _1658200)), c_List_Olistrel1(_1658198, _1658202))))], (43994 ^ _784416) ^ [_1658349, _1658351] : [-(c_List_Olistrel1(_1658349, hAPP(c_Relation_Oconverse(_1658349, _1658349), _1658351)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1658349), tc_List_Olist(_1658349)), c_List_Olistrel1(_1658349, _1658351)))], (43996 ^ _784416) ^ [_1658396, _1658398] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1658396), tc_List_Olist(_1658396)), tc_HOL_Obool)), c_List_Olistrel1(_1658396, c_Transitive__Closure_Ortrancl(_1658396, _1658398))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1658396), c_List_Olistrel1(_1658396, _1658398)))))], (43998 ^ _784416) ^ [_1658452, _1658454, _1658456, _1658458, _1658460] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658452), tc_List_Olist(_1658452))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658452), tc_List_Olist(_1658452)), _1658454), _1658456)), c_List_Olistrel1(_1658452, _1658458))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658452), tc_List_Olist(_1658452))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658452), tc_List_Olist(_1658452)), hAPP(hAPP(c_List_Olist_OCons(_1658452), _1658460), _1658454)), hAPP(hAPP(c_List_Olist_OCons(_1658452), _1658460), _1658456))), c_List_Olistrel1(_1658452, _1658458))))], (44004 ^ _784416) ^ [_1658687, _1658689, _1658691, _1658693, _1658695] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658687), tc_List_Olist(_1658687))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658687), tc_List_Olist(_1658687)), _1658689), _1658691)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1658687), c_List_Olistrel1(_1658687, _1658693)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658687), tc_List_Olist(_1658687))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658687), tc_List_Olist(_1658687)), hAPP(hAPP(c_List_Olist_OCons(_1658687), _1658695), _1658689)), hAPP(hAPP(c_List_Olist_OCons(_1658687), _1658695), _1658691))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1658687), c_List_Olistrel1(_1658687, _1658693)))))], (44010 ^ _784416) ^ [_1658942, _1658944, _1658946, _1658948] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658942), tc_List_Olist(_1658942))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658942), tc_List_Olist(_1658942)), _1658944), _1658946)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1658942), c_List_Olistrel1(_1658942, _1658948)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658942)), _1658944) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658942)), _1658946))], (44016 ^ _784416) ^ [_1659121, _1659123, _1659125, _1659127] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659121), tc_List_Olist(_1659121))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659121), tc_List_Olist(_1659121)), _1659123), _1659125)), c_List_Olistrel1(_1659121, _1659127))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659121)), _1659123) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659121)), _1659125))], (44022 ^ _784416) ^ [_1659311, _1659313, _1659315, _1659317] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659311), tc_List_Olist(_1659311))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659311), tc_List_Olist(_1659311)), _1659313), _1659315)), c_List_Olistrel1(_1659311, hAPP(c_Relation_Oconverse(_1659311, _1659311), _1659317)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659311), tc_List_Olist(_1659311))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659311), tc_List_Olist(_1659311)), _1659313), _1659315)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1659311), tc_List_Olist(_1659311)), c_List_Olistrel1(_1659311, _1659317)))))], (44028 ^ _784416) ^ [_1659540, _1659542, _1659544, _1659546] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659540), tc_List_Olist(_1659540))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659540), tc_List_Olist(_1659540)), _1659542), _1659544)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1659540), tc_List_Olist(_1659540)), c_List_Olistrel1(_1659540, _1659546)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659540), tc_List_Olist(_1659540))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659540), tc_List_Olist(_1659540)), _1659542), _1659544)), c_List_Olistrel1(_1659540, hAPP(c_Relation_Oconverse(_1659540, _1659540), _1659546)))))], (44034 ^ _784416) ^ [_1659775, _1659777, _1659779, _1659781, _1659783] : [hBOOL(hAPP(hAPP(c_member(_1659775), _1659777), hAPP(c_List_Oset(_1659775), _1659779))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1659781), hAPP(_1659783, _1659777))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1659781), c_List_Olist_Olist__size(_1659775, _1659783, _1659779))))], (44044 ^ _784416) ^ [_1659974, _1659976, _1659978, _1659980, _1659982] : [hBOOL(hAPP(hAPP(c_member(_1659974), _1659976), hAPP(c_List_Oset(_1659974), _1659978))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1659980), hAPP(_1659982, _1659976))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1659980), c_List_Olist_Olist__size(_1659974, _1659982, _1659978))))], (44054 ^ _784416) ^ [_1660173, _1660175, _1660177, _1660179, _1660181] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1660173, _1660173)), hAPP(hAPP(c_Product__Type_OPair(_1660173, _1660173), _1660175), _1660177)), _1660179)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1660173), tc_List_Olist(_1660173))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1660173), tc_List_Olist(_1660173)), hAPP(hAPP(c_List_Olist_OCons(_1660173), _1660175), _1660181)), hAPP(hAPP(c_List_Olist_OCons(_1660173), _1660177), _1660181))), c_List_Olistrel1(_1660173, _1660179))))], (44060 ^ _784416) ^ [_1660413, _1660415, _1660417, _1660419, _1660421, _1660423] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1660413), tc_List_Olist(_1660413))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1660413), tc_List_Olist(_1660413)), hAPP(hAPP(c_List_Olist_OCons(_1660413), _1660415), _1660417)), hAPP(hAPP(c_List_Olist_OCons(_1660413), _1660419), _1660421))), c_List_Olistrel1(_1660413, _1660423))), 44065 ^ _784416 : [(44066 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1660413, _1660413)), hAPP(hAPP(c_Product__Type_OPair(_1660413, _1660413), _1660415), _1660419)), _1660423)))], (44068 ^ _784416) ^ [] : [-(_1660417 = _1660421)]], 44069 ^ _784416 : [(44070 ^ _784416) ^ [] : [-(_1660415 = _1660419)], (44072 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1660413), tc_List_Olist(_1660413))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1660413), tc_List_Olist(_1660413)), _1660417), _1660421)), c_List_Olistrel1(_1660413, _1660423))))]]], (44074 ^ _784416) ^ [_1660783, _1660785, _1660787, _1660789, _1660791, _1660793] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1660783), tc_List_Olist(_1660783))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1660783), tc_List_Olist(_1660783)), hAPP(hAPP(c_List_Olist_OCons(_1660783), _1660785), _1660787)), hAPP(hAPP(c_List_Olist_OCons(_1660783), _1660789), _1660791))), c_List_Olistrel1(_1660783, _1660793)))), 44075 ^ _784416 : [(44076 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1660783, _1660783)), hAPP(hAPP(c_Product__Type_OPair(_1660783, _1660783), _1660785), _1660789)), _1660793)), _1660787 = _1660791], (44082 ^ _784416) ^ [] : [_1660785 = _1660789, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1660783), tc_List_Olist(_1660783))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1660783), tc_List_Olist(_1660783)), _1660787), _1660791)), c_List_Olistrel1(_1660783, _1660793)))]]], (44090 ^ _784416) ^ [_1661211, _1661213, _1661215] : [-(c_List_Olist_Olist__size(_1661211, _1661213, _1661215) = 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(_1661211, tc_Nat_Onat), _1661213), _1661215))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661211)), _1661215)))], (44092 ^ _784416) ^ [_1661267, _1661269, _1661271, _1661273] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1661267), tc_List_Olist(_1661267), c_List_Olistrel(_1661267, _1661269)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1661267)), hAPP(hAPP(c_List_Olist_OCons(_1661267), _1661271), _1661273)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1661267), tc_HOL_Obool)))) = c_List_Oset__Cons(_1661267, hAPP(c_Relation_OImage(_1661267, _1661267, _1661269), hAPP(hAPP(c_Set_Oinsert(_1661267), _1661271), c_Orderings_Obot__class_Obot(tc_fun(_1661267, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1661267), tc_List_Olist(_1661267), c_List_Olistrel(_1661267, _1661269)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1661267)), _1661273), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1661267), tc_HOL_Obool))))))], (44094 ^ _784416) ^ [_1661390, _1661392] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1661390, _1661392) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1661390), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1661392), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (44096 ^ _784416) ^ [_1661437, _1661439, _1661441] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1661437), tc_List_Olist(_1661437))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1661437), tc_List_Olist(_1661437)), _1661439), _1661439)), c_List_Olistrel(_1661437, c_Transitive__Closure_Ortrancl(_1661437, _1661441)))))], (44098 ^ _784416) ^ [_1661497, _1661499, _1661501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1661497, _1661497), tc_HOL_Obool)), _1661499), _1661501)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1661497), tc_List_Olist(_1661497)), tc_HOL_Obool)), c_List_Olistrel(_1661497, _1661499)), c_List_Olistrel(_1661497, _1661501))))], (44104 ^ _784416) ^ [_1661648, _1661650] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1661648, _1661650)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1661648, _1661650))], (44106 ^ _784416) ^ [_1661683, _1661685] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1661683, _1661685) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1661683, _1661685)))], (44108 ^ _784416) ^ [_1661718, _1661720] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1661718, _1661720))))], (44110 ^ _784416) ^ [_1661748, _1661750] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1661748), tc_List_Olist(_1661748)), tc_HOL_Obool)), c_List_Olistrel(_1661748, _1661750)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1661748), c_List_Olistrel1(_1661748, _1661750)))))], (44112 ^ _784416) ^ [_1661801, _1661803, _1661805, _1661807] : [class_Groups_Ocomm__monoid__add(_1661801), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1661801), _1661803), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1661805, _1661807))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1661801), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1661801), _1661803), c_List_Oupto(_1661805, _1661807))))], (44118 ^ _784416) ^ [_1661944, _1661946, _1661948, _1661950] : [class_Groups_Ocomm__monoid__add(_1661944), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1661944), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1661944), _1661946), c_List_Oupto(_1661948, _1661950))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1661944), _1661946), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1661948, _1661950))))], (44124 ^ _784416) ^ [_1662087, _1662089, _1662091, _1662093] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662087), tc_List_Olist(_1662087))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662087), tc_List_Olist(_1662087)), _1662089), _1662091)), c_List_Olistrel(_1662087, _1662093))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662087)), _1662089) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662087)), _1662091))], (44130 ^ _784416) ^ [_1662256, _1662258, _1662260, _1662262, _1662264] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662256), tc_List_Olist(_1662256))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662256), tc_List_Olist(_1662256)), _1662258), _1662260)), c_List_Olistrel(_1662256, c_Transitive__Closure_Ortrancl(_1662256, _1662262)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662256), tc_List_Olist(_1662256))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662256), tc_List_Olist(_1662256)), _1662260), _1662264)), c_List_Olistrel(_1662256, c_Transitive__Closure_Ortrancl(_1662256, _1662262)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662256), tc_List_Olist(_1662256))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662256), tc_List_Olist(_1662256)), _1662258), _1662264)), c_List_Olistrel(_1662256, c_Transitive__Closure_Ortrancl(_1662256, _1662262)))))], (44140 ^ _784416) ^ [_1662595, _1662597] : [-(c_List_Olistrel(_1662595, c_Transitive__Closure_Ortrancl(_1662595, _1662597)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1662595), c_List_Olistrel1(_1662595, _1662597)))], (44142 ^ _784416) ^ [_1662634, _1662636] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1662634), _1662636) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1662634, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1662636), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (44144 ^ _784416) ^ [_1662677, _1662679, _1662681, _1662683] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662677), tc_List_Olist(_1662677))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662677), tc_List_Olist(_1662677)), _1662679), _1662681)), c_List_Olistrel1(_1662677, _1662683))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1662677), tc_List_Olist(_1662677))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1662677), tc_List_Olist(_1662677)), _1662679), _1662681)), c_List_Olistrel(_1662677, c_Transitive__Closure_Ortrancl(_1662677, _1662683)))))], (44150 ^ _784416) ^ [_1662884, _1662886, _1662888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1662884, _1662884), tc_HOL_Obool)), _1662886), _1662888)), c_Relation_Orefl__on(_1662884, c_Orderings_Otop__class_Otop(tc_fun(_1662884, tc_HOL_Obool)), _1662888), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1662884), tc_List_Olist(_1662884)), tc_HOL_Obool)), c_List_Olistrel1(_1662884, _1662886)), c_List_Olistrel(_1662884, _1662888))))], (44160 ^ _784416) ^ [_1663101, _1663103] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1663101, _1663103) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1663101), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1663103)))], (44162 ^ _784416) ^ [_1663142, _1663144, _1663146, _1663148] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663142), tc_List_Olist(_1663142))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663142), tc_List_Olist(_1663142)), _1663144), _1663146)), c_List_Olistrel(_1663142, _1663148))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663142), tc_List_Olist(_1663142))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663142), tc_List_Olist(_1663142)), _1663144), _1663146)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1663142), c_List_Olistrel1(_1663142, _1663148)))))], (44168 ^ _784416) ^ [_1663353, _1663355, _1663357, _1663359, _1663361, _1663363] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1663353, _1663353)), hAPP(hAPP(c_Product__Type_OPair(_1663353, _1663353), _1663355), _1663357)), _1663359)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663353), tc_List_Olist(_1663353))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663353), tc_List_Olist(_1663353)), _1663361), _1663363)), c_List_Olistrel(_1663353, _1663359))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663353), tc_List_Olist(_1663353))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663353), tc_List_Olist(_1663353)), hAPP(hAPP(c_List_Olist_OCons(_1663353), _1663355), _1663361)), hAPP(hAPP(c_List_Olist_OCons(_1663353), _1663357), _1663363))), c_List_Olistrel(_1663353, _1663359))))], (44178 ^ _784416) ^ [_1663700] : [c_List_Onat__list(_1663700), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1663700)))], (44184 ^ _784416) ^ [_1663773] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1663773)), -(c_List_Onat__list(_1663773))], (44190 ^ _784416) ^ [_1663873, _1663875, _1663877, _1663879] : [c_List_Olistrelp(_1663873, hAPP(hAPP(c_COMBC(_1663873, tc_fun(tc_prod(_1663873, _1663873), tc_HOL_Obool), tc_fun(_1663873, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1663873, tc_fun(tc_fun(tc_prod(_1663873, _1663873), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1663873, _1663873), tc_HOL_Obool), tc_fun(_1663873, tc_HOL_Obool)), _1663873), c_COMBC(_1663873, tc_fun(tc_prod(_1663873, _1663873), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1663873, tc_prod(_1663873, _1663873)), tc_fun(_1663873, tc_fun(tc_fun(tc_prod(_1663873, _1663873), tc_HOL_Obool), tc_HOL_Obool)), _1663873), hAPP(c_COMBB(tc_prod(_1663873, _1663873), tc_fun(tc_fun(tc_prod(_1663873, _1663873), tc_HOL_Obool), tc_HOL_Obool), _1663873), c_member(tc_prod(_1663873, _1663873)))), c_Product__Type_OPair(_1663873, _1663873)))), _1663875), _1663877, _1663879), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1663873), tc_List_Olist(_1663873))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1663873), tc_List_Olist(_1663873)), _1663877), _1663879)), c_List_Olistrel(_1663873, _1663875))))], (44196 ^ _784416) ^ [_1664250, _1664252, _1664254, _1664256] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1664250), tc_List_Olist(_1664250))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1664250), tc_List_Olist(_1664250)), _1664254), _1664256)), c_List_Olistrel(_1664250, _1664252))), -(c_List_Olistrelp(_1664250, hAPP(hAPP(c_COMBC(_1664250, tc_fun(tc_prod(_1664250, _1664250), tc_HOL_Obool), tc_fun(_1664250, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1664250, tc_fun(tc_fun(tc_prod(_1664250, _1664250), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1664250, _1664250), tc_HOL_Obool), tc_fun(_1664250, tc_HOL_Obool)), _1664250), c_COMBC(_1664250, tc_fun(tc_prod(_1664250, _1664250), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1664250, tc_prod(_1664250, _1664250)), tc_fun(_1664250, tc_fun(tc_fun(tc_prod(_1664250, _1664250), tc_HOL_Obool), tc_HOL_Obool)), _1664250), hAPP(c_COMBB(tc_prod(_1664250, _1664250), tc_fun(tc_fun(tc_prod(_1664250, _1664250), tc_HOL_Obool), tc_HOL_Obool), _1664250), c_member(tc_prod(_1664250, _1664250)))), c_Product__Type_OPair(_1664250, _1664250)))), _1664252), _1664254, _1664256))], (44202 ^ _784416) ^ [_1664660, _1664662, _1664664, _1664666, _1664668, _1664670] : [c_List_Olistrelp(_1664660, _1664662, hAPP(hAPP(c_List_Olist_OCons(_1664660), _1664664), _1664666), hAPP(hAPP(c_List_Olist_OCons(_1664660), _1664668), _1664670)), 44205 ^ _784416 : [(44206 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1664662, _1664664), _1664668)))], (44208 ^ _784416) ^ [] : [-(c_List_Olistrelp(_1664660, _1664662, _1664666, _1664670))]]], (44210 ^ _784416) ^ [_1664817, _1664819, _1664821, _1664823, _1664825, _1664827] : [-(c_List_Olistrelp(_1664817, _1664819, hAPP(hAPP(c_List_Olist_OCons(_1664817), _1664821), _1664823), hAPP(hAPP(c_List_Olist_OCons(_1664817), _1664825), _1664827))), hBOOL(hAPP(hAPP(_1664819, _1664821), _1664825)), c_List_Olistrelp(_1664817, _1664819, _1664823, _1664827)], (44220 ^ _784416) ^ [_1665014, _1665016, _1665018, _1665020, _1665022, _1665024] : [hBOOL(hAPP(hAPP(_1665014, _1665016), _1665018)), c_List_Olistrelp(_1665020, _1665014, _1665022, _1665024), -(c_List_Olistrelp(_1665020, _1665014, hAPP(hAPP(c_List_Olist_OCons(_1665020), _1665016), _1665022), hAPP(hAPP(c_List_Olist_OCons(_1665020), _1665018), _1665024)))], (44230 ^ _784416) ^ [_1665230, _1665232, _1665234, _1665236] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1665230), tc_List_Olist(_1665230))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1665230), tc_List_Olist(_1665230)), _1665232), _1665234)), c_List_Olistrel(_1665230, _1665236))), 44233 ^ _784416 : [(44234 ^ _784416) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665230)), _1665232) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665230)), _1665234))], (44236 ^ _784416) ^ [_1665566] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1665230, _1665230)), _1665566), hAPP(c_List_Oset(tc_prod(_1665230, _1665230)), hAPP(hAPP(c_List_Ozip(_1665230, _1665230), _1665232), _1665234)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1665230, _1665230, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1665230, tc_fun(tc_prod(_1665230, _1665230), tc_HOL_Obool), tc_fun(_1665230, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1665230, tc_fun(tc_fun(tc_prod(_1665230, _1665230), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1665230, _1665230), tc_HOL_Obool), tc_fun(_1665230, tc_HOL_Obool)), _1665230), c_COMBC(_1665230, tc_fun(tc_prod(_1665230, _1665230), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1665230, tc_prod(_1665230, _1665230)), tc_fun(_1665230, tc_fun(tc_fun(tc_prod(_1665230, _1665230), tc_HOL_Obool), tc_HOL_Obool)), _1665230), hAPP(c_COMBB(tc_prod(_1665230, _1665230), tc_fun(tc_fun(tc_prod(_1665230, _1665230), tc_HOL_Obool), tc_HOL_Obool), _1665230), c_member(tc_prod(_1665230, _1665230)))), c_Product__Type_OPair(_1665230, _1665230)))), _1665236)), _1665566)))]]], (44242 ^ _784416) ^ [_1665959, _1665961, _1665963, _1665965] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1665959), tc_List_Olist(_1665959))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1665959), tc_List_Olist(_1665959)), _1665961), _1665963)), c_List_Olistrel(_1665959, _1665965)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665959)), _1665961) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665959)), _1665963), 44248 ^ _784416 : [(44249 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1665959, _1665959)), 44247 ^ [_1665959, _1665961, _1665963, _1665965]), hAPP(c_List_Oset(tc_prod(_1665959, _1665959)), hAPP(hAPP(c_List_Ozip(_1665959, _1665959), _1665961), _1665963)))))], (44251 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1665959, _1665959, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1665959, tc_fun(tc_prod(_1665959, _1665959), tc_HOL_Obool), tc_fun(_1665959, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1665959, tc_fun(tc_fun(tc_prod(_1665959, _1665959), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1665959, _1665959), tc_HOL_Obool), tc_fun(_1665959, tc_HOL_Obool)), _1665959), c_COMBC(_1665959, tc_fun(tc_prod(_1665959, _1665959), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1665959, tc_prod(_1665959, _1665959)), tc_fun(_1665959, tc_fun(tc_fun(tc_prod(_1665959, _1665959), tc_HOL_Obool), tc_HOL_Obool)), _1665959), hAPP(c_COMBB(tc_prod(_1665959, _1665959), tc_fun(tc_fun(tc_prod(_1665959, _1665959), tc_HOL_Obool), tc_HOL_Obool), _1665959), c_member(tc_prod(_1665959, _1665959)))), c_Product__Type_OPair(_1665959, _1665959)))), _1665965)), 44247 ^ [_1665959, _1665961, _1665963, _1665965]))]]], (44255 ^ _784416) ^ [_1666697, _1666699, _1666701, _1666703, _1666705] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1666697), tc_List_Olist(_1666697))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1666697), tc_List_Olist(_1666697)), _1666699), hAPP(hAPP(c_List_Olist_OCons(_1666697), _1666701), _1666703))), c_List_Olistrel(_1666697, _1666705))), 44260 ^ _784416 : [(44261 ^ _784416) ^ [] : [-(_1666699 = hAPP(hAPP(c_List_Olist_OCons(_1666697), 44258 ^ [_1666697, _1666699, _1666701, _1666703, _1666705]), 44259 ^ [_1666697, _1666699, _1666701, _1666703, _1666705]))], (44263 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1666697, _1666697)), hAPP(hAPP(c_Product__Type_OPair(_1666697, _1666697), 44258 ^ [_1666697, _1666699, _1666701, _1666703, _1666705]), _1666701)), _1666705)))], (44265 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1666697), tc_List_Olist(_1666697))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1666697), tc_List_Olist(_1666697)), 44259 ^ [_1666697, _1666699, _1666701, _1666703, _1666705]), _1666703)), c_List_Olistrel(_1666697, _1666705))))]]], (44267 ^ _784416) ^ [_1667086, _1667088, _1667090, _1667092] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1667086, _1667088))), hAPP(hAPP(c_List_Ozip(_1667086, _1667088), _1667090), _1667092)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667086)), _1667090)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667088)), _1667092)))], (44269 ^ _784416) ^ [_1667154, _1667156] : [-(hAPP(hAPP(c_List_Ozip(_1667154, _1667154), _1667156), _1667156) = hAPP(hAPP(c_List_Omap(_1667154, tc_prod(_1667154, _1667154)), hAPP(hAPP(c_COMBS(_1667154, _1667154, tc_prod(_1667154, _1667154)), c_Product__Type_OPair(_1667154, _1667154)), c_COMBI(_1667154))), _1667156))], (44271 ^ _784416) ^ [_1667218, _1667220, _1667222, _1667224] : [hBOOL(hAPP(c_List_Odistinct(_1667218), _1667220)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1667222, _1667218)), hAPP(hAPP(c_List_Ozip(_1667222, _1667218), _1667224), _1667220))))], (44277 ^ _784416) ^ [_1667339, _1667341, _1667343, _1667345] : [hBOOL(hAPP(c_List_Odistinct(_1667339), _1667341)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1667339, _1667343)), hAPP(hAPP(c_List_Ozip(_1667339, _1667343), _1667341), _1667345))))], (44283 ^ _784416) ^ [_1667460, _1667462, _1667464, _1667466, _1667468] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667460)), _1667462) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667464)), _1667466), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667460)), _1667468) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667464)), _1667466), hBOOL(hAPP(c_List_Odistinct(_1667464), _1667466)), hAPP(c_Map_Omap__of(_1667464, _1667460), hAPP(hAPP(c_List_Ozip(_1667464, _1667460), _1667466), _1667462)) = hAPP(c_Map_Omap__of(_1667464, _1667460), hAPP(hAPP(c_List_Ozip(_1667464, _1667460), _1667466), _1667468)), -(_1667462 = _1667468)], (44301 ^ _784416) ^ [_1667841, _1667843, _1667845, _1667847] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667841)), _1667843) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667845)), _1667847), -(hAPP(hAPP(c_List_Omap(tc_prod(_1667841, _1667845), _1667841), c_Product__Type_Ofst(_1667841, _1667845)), hAPP(hAPP(c_List_Ozip(_1667841, _1667845), _1667843), _1667847)) = _1667843)], (44307 ^ _784416) ^ [_1667998, _1668000, _1668002, _1668004] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667998)), _1668000) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668002)), _1668004), -(hAPP(hAPP(c_List_Omap(tc_prod(_1667998, _1668002), _1668002), c_Product__Type_Osnd(_1667998, _1668002)), hAPP(hAPP(c_List_Ozip(_1667998, _1668002), _1668000), _1668004)) = _1668004)], (44313 ^ _784416) ^ [_1668155, _1668157, _1668159] : [-(hAPP(hAPP(c_List_Ozip(_1668155, _1668157), hAPP(hAPP(c_List_Omap(tc_prod(_1668155, _1668157), _1668155), c_Product__Type_Ofst(_1668155, _1668157)), _1668159)), hAPP(hAPP(c_List_Omap(tc_prod(_1668155, _1668157), _1668157), c_Product__Type_Osnd(_1668155, _1668157)), _1668159)) = _1668159)], (44315 ^ _784416) ^ [_1668221, _1668223, _1668225, _1668227, _1668229, _1668231] : [-(hAPP(hAPP(c_List_Ozip(_1668221, _1668223), hAPP(hAPP(c_List_Olist_OCons(_1668221), _1668225), _1668227)), hAPP(hAPP(c_List_Olist_OCons(_1668223), _1668229), _1668231)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1668221, _1668223)), hAPP(hAPP(c_Product__Type_OPair(_1668221, _1668223), _1668225), _1668229)), hAPP(hAPP(c_List_Ozip(_1668221, _1668223), _1668227), _1668231)))], (44317 ^ _784416) ^ [_1668308, _1668310, _1668312, _1668314, _1668316] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668308)), _1668310) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1668312)), _1668314), 44320 ^ _784416 : [(44321 ^ _784416) ^ [] : [hAPP(hAPP(c_List_Ozip(_1668308, _1668312), _1668310), _1668314) = _1668316, 44324 ^ _784416 : [(44325 ^ _784416) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1668308, _1668312), _1668308), c_Product__Type_Ofst(_1668308, _1668312)), _1668316) = _1668310)], (44327 ^ _784416) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1668308, _1668312), _1668312), c_Product__Type_Osnd(_1668308, _1668312)), _1668316) = _1668314)]]], (44329 ^ _784416) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1668308, _1668312), _1668310), _1668314) = _1668316), hAPP(hAPP(c_List_Omap(tc_prod(_1668308, _1668312), _1668308), c_Product__Type_Ofst(_1668308, _1668312)), _1668316) = _1668310, hAPP(hAPP(c_List_Omap(tc_prod(_1668308, _1668312), _1668312), c_Product__Type_Osnd(_1668308, _1668312)), _1668316) = _1668314]]], (44339 ^ _784416) ^ [_1668756, _1668758, _1668760, _1668762, _1668764, _1668766, _1668768, _1668770] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1668756, _1668758), _1668760), _1668762), hAPP(hAPP(c_List_Ozip(_1668756, _1668758), _1668764), hAPP(hAPP(c_List_Omap(_1668766, _1668758), _1668768), _1668770))) = hAPP(hAPP(c_List_Omap(tc_prod(_1668756, _1668766), _1668760), hAPP(c_Product__Type_Oprod_Oprod__case(_1668756, _1668766, _1668760), hAPP(hAPP(c_COMBB(tc_fun(_1668766, tc_prod(_1668756, _1668758)), tc_fun(_1668766, _1668760), _1668756), hAPP(c_COMBB(tc_prod(_1668756, _1668758), _1668760, _1668766), _1668762)), hAPP(hAPP(c_COMBC(_1668756, tc_fun(_1668766, _1668758), tc_fun(_1668766, tc_prod(_1668756, _1668758))), hAPP(hAPP(c_COMBB(tc_fun(_1668758, tc_prod(_1668756, _1668758)), tc_fun(tc_fun(_1668766, _1668758), tc_fun(_1668766, tc_prod(_1668756, _1668758))), _1668756), c_COMBB(_1668758, tc_prod(_1668756, _1668758), _1668766)), c_Product__Type_OPair(_1668756, _1668758))), _1668768)))), hAPP(hAPP(c_List_Ozip(_1668756, _1668766), _1668764), _1668770)))], (44341 ^ _784416) ^ [_1668937, _1668939, _1668941, _1668943, _1668945, _1668947, _1668949, _1668951] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1668937, _1668939), _1668941), _1668943), hAPP(hAPP(c_List_Ozip(_1668937, _1668939), hAPP(hAPP(c_List_Omap(_1668945, _1668937), _1668947), _1668949)), _1668951)) = hAPP(hAPP(c_List_Omap(tc_prod(_1668945, _1668939), _1668941), hAPP(c_Product__Type_Oprod_Oprod__case(_1668945, _1668939, _1668941), hAPP(hAPP(c_COMBB(tc_fun(_1668939, tc_prod(_1668937, _1668939)), tc_fun(_1668939, _1668941), _1668945), hAPP(c_COMBB(tc_prod(_1668937, _1668939), _1668941, _1668939), _1668943)), hAPP(hAPP(c_COMBB(_1668937, tc_fun(_1668939, tc_prod(_1668937, _1668939)), _1668945), c_Product__Type_OPair(_1668937, _1668939)), _1668947)))), hAPP(hAPP(c_List_Ozip(_1668945, _1668939), _1668949), _1668951)))], (44343 ^ _784416) ^ [_1669098, _1669100, _1669102] : [_1669098 = _1669100, 44346 ^ _784416 : [(44347 ^ _784416) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669102)), _1669098) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669102)), _1669100))], (44349 ^ _784416) ^ [_1669254] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1669102, _1669102)), _1669254), hAPP(c_List_Oset(tc_prod(_1669102, _1669102)), hAPP(hAPP(c_List_Ozip(_1669102, _1669102), _1669098), _1669100)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1669102, _1669102, tc_HOL_Obool), c_fequal), _1669254)))]]], (44355 ^ _784416) ^ [_1669409, _1669411, _1669413] : [-(_1669409 = _1669411), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669413)), _1669409) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669413)), _1669411), 44361 ^ _784416 : [(44362 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1669413, _1669413)), 44360 ^ [_1669409, _1669411, _1669413]), hAPP(c_List_Oset(tc_prod(_1669413, _1669413)), hAPP(hAPP(c_List_Ozip(_1669413, _1669413), _1669409), _1669411)))))], (44364 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1669413, _1669413, tc_HOL_Obool), c_fequal), 44360 ^ [_1669409, _1669411, _1669413]))]]], (44368 ^ _784416) ^ [_1669744, _1669746, _1669748, _1669750] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1669744, _1669744)), hAPP(hAPP(c_Product__Type_OPair(_1669744, _1669744), _1669746), _1669748)), hAPP(c_List_Oset(tc_prod(_1669744, _1669744)), hAPP(hAPP(c_List_Ozip(_1669744, _1669744), _1669750), _1669750)))), 44371 ^ _784416 : [(44372 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1669744), _1669746), hAPP(c_List_Oset(_1669744), _1669750))))], (44374 ^ _784416) ^ [] : [-(_1669746 = _1669748)]]], (44376 ^ _784416) ^ [_1669943, _1669945, _1669947, _1669949] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1669943, _1669943)), hAPP(hAPP(c_Product__Type_OPair(_1669943, _1669943), _1669945), _1669947)), hAPP(c_List_Oset(tc_prod(_1669943, _1669943)), hAPP(hAPP(c_List_Ozip(_1669943, _1669943), _1669949), _1669949))))), hBOOL(hAPP(hAPP(c_member(_1669943), _1669945), hAPP(c_List_Oset(_1669943), _1669949))), _1669945 = _1669947], (44386 ^ _784416) ^ [_1670178, _1670180, _1670182, _1670184, _1670186, _1670188] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1670178, _1670180)), hAPP(hAPP(c_Product__Type_OPair(_1670178, _1670180), _1670182), _1670184)), hAPP(c_List_Oset(tc_prod(_1670178, _1670180)), hAPP(hAPP(c_List_Ozip(_1670178, _1670180), _1670186), _1670188)))), -(hBOOL(hAPP(hAPP(c_member(_1670178), _1670182), hAPP(c_List_Oset(_1670178), _1670186))))], (44392 ^ _784416) ^ [_1670359, _1670361, _1670363, _1670365, _1670367, _1670369] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1670359, _1670361)), hAPP(hAPP(c_Product__Type_OPair(_1670359, _1670361), _1670363), _1670365)), hAPP(c_List_Oset(tc_prod(_1670359, _1670361)), hAPP(hAPP(c_List_Ozip(_1670359, _1670361), _1670367), _1670369)))), -(hBOOL(hAPP(hAPP(c_member(_1670361), _1670365), hAPP(c_List_Oset(_1670361), _1670369))))], (44398 ^ _784416) ^ [_1670540, _1670542, _1670544, _1670546, _1670548, _1670550] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1670540, _1670542)), hAPP(hAPP(c_Product__Type_OPair(_1670540, _1670542), _1670544), _1670546)), hAPP(c_List_Oset(tc_prod(_1670540, _1670542)), hAPP(hAPP(c_List_Ozip(_1670540, _1670542), _1670548), _1670550)))), 44401 ^ _784416 : [(44402 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1670540), _1670544), hAPP(c_List_Oset(_1670540), _1670548))))], (44404 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1670542), _1670546), hAPP(c_List_Oset(_1670542), _1670550))))]]], (44406 ^ _784416) ^ [_1670775, _1670777, _1670779, _1670781, _1670783] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670775)), _1670777) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670779)), _1670781), 44409 ^ _784416 : [(44410 ^ _784416) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1670775, _1670779), hAPP(hAPP(c_List_Ozip(_1670775, _1670779), _1670777), _1670781)), _1670783) = c_Option_Ooption_ONone(_1670779), hBOOL(hAPP(hAPP(c_member(_1670775), _1670783), hAPP(c_List_Oset(_1670775), _1670777)))], (44416 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1670775), _1670783), hAPP(c_List_Oset(_1670775), _1670777)))), -(hAPP(hAPP(c_Map_Omap__of(_1670775, _1670779), hAPP(hAPP(c_List_Ozip(_1670775, _1670779), _1670777), _1670781)), _1670783) = c_Option_Ooption_ONone(_1670779))]]], (44422 ^ _784416) ^ [_1671080, _1671082, _1671084, _1671086, _1671088] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671080)), _1671082) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671084)), _1671086), 44425 ^ _784416 : [(44426 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1671080), _1671088), hAPP(c_List_Oset(_1671080), _1671082))), -(hAPP(hAPP(c_Map_Omap__of(_1671080, _1671084), hAPP(hAPP(c_List_Ozip(_1671080, _1671084), _1671082), _1671086)), _1671088) = hAPP(c_Option_Ooption_OSome(_1671084), 44429 ^ [_1671080, _1671082, _1671084, _1671086, _1671088]))], (44433 ^ _784416) ^ [] : [44434 ^ _784416 : [(44435 ^ _784416) ^ [_1671372] : [hAPP(hAPP(c_Map_Omap__of(_1671080, _1671084), hAPP(hAPP(c_List_Ozip(_1671080, _1671084), _1671082), _1671086)), _1671088) = hAPP(c_Option_Ooption_OSome(_1671084), _1671372)]], -(hBOOL(hAPP(hAPP(c_member(_1671080), _1671088), hAPP(c_List_Oset(_1671080), _1671082))))]]], (44439 ^ _784416) ^ [_1671464, _1671466, _1671468, _1671470, _1671472, _1671474] : [-(hAPP(hAPP(c_List_Ozip(_1671464, _1671466), _1671468), hAPP(hAPP(c_List_Omap(_1671470, _1671466), _1671472), _1671474)) = hAPP(hAPP(c_List_Omap(tc_prod(_1671464, _1671470), tc_prod(_1671464, _1671466)), hAPP(c_Product__Type_Oprod_Oprod__case(_1671464, _1671470, tc_prod(_1671464, _1671466)), hAPP(hAPP(c_COMBC(_1671464, tc_fun(_1671470, _1671466), tc_fun(_1671470, tc_prod(_1671464, _1671466))), hAPP(hAPP(c_COMBB(tc_fun(_1671466, tc_prod(_1671464, _1671466)), tc_fun(tc_fun(_1671470, _1671466), tc_fun(_1671470, tc_prod(_1671464, _1671466))), _1671464), c_COMBB(_1671466, tc_prod(_1671464, _1671466), _1671470)), c_Product__Type_OPair(_1671464, _1671466))), _1671472))), hAPP(hAPP(c_List_Ozip(_1671464, _1671470), _1671468), _1671474)))], (44441 ^ _784416) ^ [_1671606, _1671608, _1671610, _1671612, _1671614, _1671616] : [-(hAPP(hAPP(c_List_Ozip(_1671606, _1671608), hAPP(hAPP(c_List_Omap(_1671610, _1671606), _1671612), _1671614)), _1671616) = hAPP(hAPP(c_List_Omap(tc_prod(_1671610, _1671608), tc_prod(_1671606, _1671608)), hAPP(c_Product__Type_Oprod_Oprod__case(_1671610, _1671608, tc_prod(_1671606, _1671608)), hAPP(hAPP(c_COMBB(_1671606, tc_fun(_1671608, tc_prod(_1671606, _1671608)), _1671610), c_Product__Type_OPair(_1671606, _1671608)), _1671612))), hAPP(hAPP(c_List_Ozip(_1671610, _1671608), _1671614), _1671616)))], (44443 ^ _784416) ^ [_1671710, _1671712, _1671714, _1671716, _1671718, _1671720, _1671722, _1671724] : [-(hAPP(hAPP(c_List_Ozip(_1671710, _1671712), hAPP(hAPP(c_List_Omap(_1671714, _1671710), _1671716), _1671718)), hAPP(hAPP(c_List_Omap(_1671720, _1671712), _1671722), _1671724)) = hAPP(hAPP(c_List_Omap(tc_prod(_1671714, _1671720), tc_prod(_1671710, _1671712)), hAPP(c_Product__Type_Oprod_Oprod__case(_1671714, _1671720, tc_prod(_1671710, _1671712)), hAPP(hAPP(c_COMBC(_1671714, tc_fun(_1671720, _1671712), tc_fun(_1671720, tc_prod(_1671710, _1671712))), hAPP(hAPP(c_COMBB(tc_fun(_1671712, tc_prod(_1671710, _1671712)), tc_fun(tc_fun(_1671720, _1671712), tc_fun(_1671720, tc_prod(_1671710, _1671712))), _1671714), c_COMBB(_1671712, tc_prod(_1671710, _1671712), _1671720)), hAPP(hAPP(c_COMBB(_1671710, tc_fun(_1671712, tc_prod(_1671710, _1671712)), _1671714), c_Product__Type_OPair(_1671710, _1671712)), _1671716))), _1671722))), hAPP(hAPP(c_List_Ozip(_1671714, _1671720), _1671718), _1671724)))], (44445 ^ _784416) ^ [_1671881, _1671883, _1671885, _1671887] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671881)), _1671883) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671885)), _1671887), hBOOL(hAPP(c_List_Odistinct(_1671881), _1671883)), -(c_Map_Odom(_1671881, _1671885, hAPP(c_Map_Omap__of(_1671881, _1671885), hAPP(hAPP(c_List_Ozip(_1671881, _1671885), _1671883), _1671887))) = hAPP(c_List_Oset(_1671881), _1671883))], (44455 ^ _784416) ^ [_1672102, _1672104, _1672106, _1672108, _1672110, _1672112, _1672114, _1672116] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672102)), _1672104) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672106)), _1672108), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672102)), _1672110) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672106)), _1672108), -(hBOOL(hAPP(hAPP(c_member(_1672106), _1672112), hAPP(c_List_Oset(_1672106), _1672108)))), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1672106, tc_Option_Ooption(_1672102)), hAPP(c_Map_Omap__of(_1672106, _1672102), hAPP(hAPP(c_List_Ozip(_1672106, _1672102), _1672108), _1672104))), _1672112), hAPP(c_Option_Ooption_OSome(_1672102), _1672114)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1672106, tc_Option_Ooption(_1672102)), hAPP(c_Map_Omap__of(_1672106, _1672102), hAPP(hAPP(c_List_Ozip(_1672106, _1672102), _1672108), _1672110))), _1672112), hAPP(c_Option_Ooption_OSome(_1672102), _1672116)), -(hAPP(c_Map_Omap__of(_1672106, _1672102), hAPP(hAPP(c_List_Ozip(_1672106, _1672102), _1672108), _1672104)) = hAPP(c_Map_Omap__of(_1672106, _1672102), hAPP(hAPP(c_List_Ozip(_1672106, _1672102), _1672108), _1672110)))], (44473 ^ _784416) ^ [_1672680, _1672682, _1672684, _1672686, _1672688] : [hBOOL(hAPP(hAPP(c_member(_1672680), _1672682), hAPP(c_List_Oset(_1672680), _1672684))), -(hAPP(hAPP(c_Map_Omap__of(_1672680, _1672686), hAPP(hAPP(c_List_Ozip(_1672680, _1672686), _1672684), hAPP(hAPP(c_List_Omap(_1672680, _1672686), _1672688), _1672684))), _1672682) = hAPP(c_Option_Ooption_OSome(_1672686), hAPP(_1672688, _1672682)))], (44479 ^ _784416) ^ [_1672851, _1672853, _1672855, _1672857, _1672859] : [-(hBOOL(hAPP(hAPP(c_member(_1672851), _1672853), hAPP(c_List_Oset(_1672851), _1672855)))), -(hAPP(hAPP(c_Map_Omap__of(_1672851, _1672857), hAPP(hAPP(c_List_Ozip(_1672851, _1672857), _1672855), hAPP(hAPP(c_List_Omap(_1672851, _1672857), _1672859), _1672855))), _1672853) = c_Option_Ooption_ONone(_1672857))], (44485 ^ _784416) ^ [_1672936, _1672938, _1672940, _1672942, _1672944] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1672936), tc_List_Olist(_1672936))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1672936), tc_List_Olist(_1672936)), hAPP(hAPP(c_List_Olist_OCons(_1672936), _1672938), _1672940)), _1672942)), c_List_Olistrel(_1672936, _1672944))), 44490 ^ _784416 : [(44491 ^ _784416) ^ [] : [-(_1672942 = hAPP(hAPP(c_List_Olist_OCons(_1672936), 44488 ^ [_1672936, _1672938, _1672940, _1672942, _1672944]), 44489 ^ [_1672936, _1672938, _1672940, _1672942, _1672944]))], (44493 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1672936, _1672936)), hAPP(hAPP(c_Product__Type_OPair(_1672936, _1672936), _1672938), 44488 ^ [_1672936, _1672938, _1672940, _1672942, _1672944])), _1672944)))], (44495 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1672936), tc_List_Olist(_1672936))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1672936), tc_List_Olist(_1672936)), _1672940), 44489 ^ [_1672936, _1672938, _1672940, _1672942, _1672944])), c_List_Olistrel(_1672936, _1672944))))]]], (44497 ^ _784416) ^ [_1673325, _1673327, _1673329, _1673331] : [class_Enum_Oenum(_1673325), class_Enum_Oenum(_1673327), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673327)), _1673329) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673325)), c_Enum_Oenum__class_Oenum(_1673325)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673327)), _1673331) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673325)), c_Enum_Oenum__class_Oenum(_1673325)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1673327), _1673327, _1673325, c_Option_Othe(_1673327)), hAPP(c_Map_Omap__of(_1673325, _1673327), hAPP(hAPP(c_List_Ozip(_1673325, _1673327), c_Enum_Oenum__class_Oenum(_1673325)), _1673329))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1673327), _1673327, _1673325, c_Option_Othe(_1673327)), hAPP(c_Map_Omap__of(_1673325, _1673327), hAPP(hAPP(c_List_Ozip(_1673325, _1673327), c_Enum_Oenum__class_Oenum(_1673325)), _1673331))), -(_1673329 = _1673331)], (44519 ^ _784416) ^ [_1673808, _1673810] : [-(c_Enum_Oenum__class_Oenum(tc_prod(_1673808, _1673810)) = c_Enum_Oproduct(_1673808, _1673810, c_Enum_Oenum__class_Oenum(_1673808), c_Enum_Oenum__class_Oenum(_1673810))), class_Enum_Oenum(_1673808), class_Enum_Oenum(_1673810)], (44529 ^ _784416) ^ [_1673961] : [class_Enum_Oenum(_1673961), -(hBOOL(hAPP(c_List_Odistinct(_1673961), c_Enum_Oenum__class_Oenum(_1673961))))], (44535 ^ _784416) ^ [_1674046] : [class_Enum_Oenum(_1674046), -(c_Enum_Oenum__class_Oenum(tc_Option_Ooption(_1674046)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(_1674046)), c_Option_Ooption_ONone(_1674046)), hAPP(hAPP(c_List_Omap(_1674046, tc_Option_Ooption(_1674046)), c_Option_Ooption_OSome(_1674046)), c_Enum_Oenum__class_Oenum(_1674046))))], (44541 ^ _784416) ^ [_1674181, _1674183] : [class_Enum_Oenum(_1674181), -(hBOOL(hAPP(hAPP(c_member(_1674181), _1674183), hAPP(c_List_Oset(_1674181), c_Enum_Oenum__class_Oenum(_1674181)))))], (44547 ^ _784416) ^ [_1674284] : [class_Enum_Oenum(_1674284), -(c_Orderings_Otop__class_Otop(tc_fun(_1674284, tc_HOL_Obool)) = hAPP(c_List_Oset(_1674284), c_Enum_Oenum__class_Oenum(_1674284)))], (44553 ^ _784416) ^ [_1674381] : [class_Enum_Oenum(_1674381), -(hAPP(c_List_Oset(_1674381), c_Enum_Oenum__class_Oenum(_1674381)) = c_Orderings_Otop__class_Otop(tc_fun(_1674381, tc_HOL_Obool)))], (44559 ^ _784416) ^ [_1674478, _1674480] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1674478, _1674480)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1674480), tc_fun(_1674478, _1674480)), hAPP(hAPP(c_COMBB(tc_fun(_1674478, tc_Option_Ooption(_1674480)), tc_fun(_1674478, _1674480), tc_List_Olist(_1674480)), c_Fun_Ocomp(tc_Option_Ooption(_1674480), _1674480, _1674478, c_Option_Othe(_1674480))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1674478, _1674480)), tc_fun(_1674478, tc_Option_Ooption(_1674480)), tc_List_Olist(_1674480)), c_Map_Omap__of(_1674478, _1674480)), hAPP(c_List_Ozip(_1674478, _1674480), c_Enum_Oenum__class_Oenum(_1674478))))), c_Enum_On__lists(_1674480, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674478)), c_Enum_Oenum__class_Oenum(_1674478)), c_Enum_Oenum__class_Oenum(_1674480)))), class_Enum_Oenum(_1674478), class_HOL_Oequal(_1674478), class_Enum_Oenum(_1674480)], (44573 ^ _784416) ^ [_1674845, _1674847] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1674845, _1674847)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1674847), tc_fun(_1674845, _1674847)), hAPP(hAPP(c_COMBB(tc_fun(_1674845, tc_Option_Ooption(_1674847)), tc_fun(_1674845, _1674847), tc_List_Olist(_1674847)), c_Fun_Ocomp(tc_Option_Ooption(_1674847), _1674847, _1674845, c_Option_Othe(_1674847))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1674845, _1674847)), tc_fun(_1674845, tc_Option_Ooption(_1674847)), tc_List_Olist(_1674847)), c_Map_Omap__of(_1674845, _1674847)), hAPP(c_List_Ozip(_1674845, _1674847), c_Enum_Oenum__class_Oenum(_1674845))))), c_Enum_On__lists(_1674847, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674845)), c_Enum_Oenum__class_Oenum(_1674845)), c_Enum_Oenum__class_Oenum(_1674847)))), class_Enum_Oenum(_1674845), class_Enum_Oenum(_1674847)], (44583 ^ _784416) ^ [_1675162, _1675164, _1675166] : [class_Enum_Oenum(_1675162), class_Enum_Oenum(_1675164), 44590 ^ _784416 : [(44591 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1675164, _1675162)), _1675166)), -(c_Enum_Oex__n__lists(_1675162, hAPP(hAPP(c_COMBB(tc_fun(_1675164, _1675162), tc_HOL_Obool, tc_List_Olist(_1675162)), _1675166), hAPP(hAPP(c_COMBB(tc_fun(_1675164, tc_Option_Ooption(_1675162)), tc_fun(_1675164, _1675162), tc_List_Olist(_1675162)), c_Fun_Ocomp(tc_Option_Ooption(_1675162), _1675162, _1675164, c_Option_Othe(_1675162))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1675164, _1675162)), tc_fun(_1675164, tc_Option_Ooption(_1675162)), tc_List_Olist(_1675162)), c_Map_Omap__of(_1675164, _1675162)), hAPP(c_List_Ozip(_1675164, _1675162), c_Enum_Oenum__class_Oenum(_1675164))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675164)), c_Enum_Oenum__class_Oenum(_1675164))))], (44597 ^ _784416) ^ [] : [c_Enum_Oex__n__lists(_1675162, hAPP(hAPP(c_COMBB(tc_fun(_1675164, _1675162), tc_HOL_Obool, tc_List_Olist(_1675162)), _1675166), hAPP(hAPP(c_COMBB(tc_fun(_1675164, tc_Option_Ooption(_1675162)), tc_fun(_1675164, _1675162), tc_List_Olist(_1675162)), c_Fun_Ocomp(tc_Option_Ooption(_1675162), _1675162, _1675164, c_Option_Othe(_1675162))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1675164, _1675162)), tc_fun(_1675164, tc_Option_Ooption(_1675162)), tc_List_Olist(_1675162)), c_Map_Omap__of(_1675164, _1675162)), hAPP(c_List_Ozip(_1675164, _1675162), c_Enum_Oenum__class_Oenum(_1675164))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675164)), c_Enum_Oenum__class_Oenum(_1675164))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1675164, _1675162)), _1675166)))]]], (44603 ^ _784416) ^ [_1675709, _1675711, _1675713] : [class_Enum_Oenum(_1675709), class_Enum_Oenum(_1675711), class_HOL_Oequal(_1675711), 44614 ^ _784416 : [(44615 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1675711, _1675709)), _1675713)), -(c_Enum_Oex__n__lists(_1675709, hAPP(hAPP(c_COMBB(tc_fun(_1675711, _1675709), tc_HOL_Obool, tc_List_Olist(_1675709)), _1675713), hAPP(hAPP(c_COMBB(tc_fun(_1675711, tc_Option_Ooption(_1675709)), tc_fun(_1675711, _1675709), tc_List_Olist(_1675709)), c_Fun_Ocomp(tc_Option_Ooption(_1675709), _1675709, _1675711, c_Option_Othe(_1675709))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1675711, _1675709)), tc_fun(_1675711, tc_Option_Ooption(_1675709)), tc_List_Olist(_1675709)), c_Map_Omap__of(_1675711, _1675709)), hAPP(c_List_Ozip(_1675711, _1675709), c_Enum_Oenum__class_Oenum(_1675711))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675711)), c_Enum_Oenum__class_Oenum(_1675711))))], (44621 ^ _784416) ^ [] : [c_Enum_Oex__n__lists(_1675709, hAPP(hAPP(c_COMBB(tc_fun(_1675711, _1675709), tc_HOL_Obool, tc_List_Olist(_1675709)), _1675713), hAPP(hAPP(c_COMBB(tc_fun(_1675711, tc_Option_Ooption(_1675709)), tc_fun(_1675711, _1675709), tc_List_Olist(_1675709)), c_Fun_Ocomp(tc_Option_Ooption(_1675709), _1675709, _1675711, c_Option_Othe(_1675709))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1675711, _1675709)), tc_fun(_1675711, tc_Option_Ooption(_1675709)), tc_List_Olist(_1675709)), c_Map_Omap__of(_1675711, _1675709)), hAPP(c_List_Ozip(_1675711, _1675709), c_Enum_Oenum__class_Oenum(_1675711))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675711)), c_Enum_Oenum__class_Oenum(_1675711))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1675711, _1675709)), _1675713)))]]], (44627 ^ _784416) ^ [_1676310, _1676312, _1676314] : [class_Enum_Oenum(_1676310), 44630 ^ _784416 : [(44631 ^ _784416) ^ [] : [c_Enum_Oex__n__lists(_1676310, _1676312, _1676314), 44635 ^ _784416 : [(44636 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1676310)), 44634 ^ [_1676310, _1676312, _1676314]), hAPP(c_List_Oset(tc_List_Olist(_1676310)), c_Enum_On__lists(_1676310, _1676314, c_Enum_Oenum__class_Oenum(_1676310))))))], (44638 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1676312, 44634 ^ [_1676310, _1676312, _1676314])))]]], (44640 ^ _784416) ^ [] : [-(c_Enum_Oex__n__lists(_1676310, _1676312, _1676314)), 44641 ^ _784416 : [(44642 ^ _784416) ^ [_1676566] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1676310)), _1676566), hAPP(c_List_Oset(tc_List_Olist(_1676310)), c_Enum_On__lists(_1676310, _1676314, c_Enum_Oenum__class_Oenum(_1676310))))), hBOOL(hAPP(_1676312, _1676566))]]]]], (44650 ^ _784416) ^ [_1676729, _1676731, _1676733] : [class_Enum_Oenum(_1676729), class_Enum_Oenum(_1676731), 44657 ^ _784416 : [(44658 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1676731, _1676729)), _1676733)), -(c_Enum_Oall__n__lists(_1676729, hAPP(hAPP(c_COMBB(tc_fun(_1676731, _1676729), tc_HOL_Obool, tc_List_Olist(_1676729)), _1676733), hAPP(hAPP(c_COMBB(tc_fun(_1676731, tc_Option_Ooption(_1676729)), tc_fun(_1676731, _1676729), tc_List_Olist(_1676729)), c_Fun_Ocomp(tc_Option_Ooption(_1676729), _1676729, _1676731, c_Option_Othe(_1676729))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1676731, _1676729)), tc_fun(_1676731, tc_Option_Ooption(_1676729)), tc_List_Olist(_1676729)), c_Map_Omap__of(_1676731, _1676729)), hAPP(c_List_Ozip(_1676731, _1676729), c_Enum_Oenum__class_Oenum(_1676731))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676731)), c_Enum_Oenum__class_Oenum(_1676731))))], (44664 ^ _784416) ^ [] : [c_Enum_Oall__n__lists(_1676729, hAPP(hAPP(c_COMBB(tc_fun(_1676731, _1676729), tc_HOL_Obool, tc_List_Olist(_1676729)), _1676733), hAPP(hAPP(c_COMBB(tc_fun(_1676731, tc_Option_Ooption(_1676729)), tc_fun(_1676731, _1676729), tc_List_Olist(_1676729)), c_Fun_Ocomp(tc_Option_Ooption(_1676729), _1676729, _1676731, c_Option_Othe(_1676729))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1676731, _1676729)), tc_fun(_1676731, tc_Option_Ooption(_1676729)), tc_List_Olist(_1676729)), c_Map_Omap__of(_1676731, _1676729)), hAPP(c_List_Ozip(_1676731, _1676729), c_Enum_Oenum__class_Oenum(_1676731))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676731)), c_Enum_Oenum__class_Oenum(_1676731))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1676731, _1676729)), _1676733)))]]], (44670 ^ _784416) ^ [_1677276, _1677278, _1677280] : [class_Enum_Oenum(_1677276), class_Enum_Oenum(_1677278), class_HOL_Oequal(_1677278), 44681 ^ _784416 : [(44682 ^ _784416) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1677278, _1677276)), _1677280)), -(c_Enum_Oall__n__lists(_1677276, hAPP(hAPP(c_COMBB(tc_fun(_1677278, _1677276), tc_HOL_Obool, tc_List_Olist(_1677276)), _1677280), hAPP(hAPP(c_COMBB(tc_fun(_1677278, tc_Option_Ooption(_1677276)), tc_fun(_1677278, _1677276), tc_List_Olist(_1677276)), c_Fun_Ocomp(tc_Option_Ooption(_1677276), _1677276, _1677278, c_Option_Othe(_1677276))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1677278, _1677276)), tc_fun(_1677278, tc_Option_Ooption(_1677276)), tc_List_Olist(_1677276)), c_Map_Omap__of(_1677278, _1677276)), hAPP(c_List_Ozip(_1677278, _1677276), c_Enum_Oenum__class_Oenum(_1677278))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677278)), c_Enum_Oenum__class_Oenum(_1677278))))], (44688 ^ _784416) ^ [] : [c_Enum_Oall__n__lists(_1677276, hAPP(hAPP(c_COMBB(tc_fun(_1677278, _1677276), tc_HOL_Obool, tc_List_Olist(_1677276)), _1677280), hAPP(hAPP(c_COMBB(tc_fun(_1677278, tc_Option_Ooption(_1677276)), tc_fun(_1677278, _1677276), tc_List_Olist(_1677276)), c_Fun_Ocomp(tc_Option_Ooption(_1677276), _1677276, _1677278, c_Option_Othe(_1677276))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1677278, _1677276)), tc_fun(_1677278, tc_Option_Ooption(_1677276)), tc_List_Olist(_1677276)), c_Map_Omap__of(_1677278, _1677276)), hAPP(c_List_Ozip(_1677278, _1677276), c_Enum_Oenum__class_Oenum(_1677278))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1677278)), c_Enum_Oenum__class_Oenum(_1677278))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1677278, _1677276)), _1677280)))]]], (44694 ^ _784416) ^ [_1677877, _1677879, _1677881] : [class_Enum_Oenum(_1677877), 44697 ^ _784416 : [(44708 ^ _784416) ^ [] : [44710 ^ _784416 : [(44711 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1677877)), 44709 ^ [_1677877, _1677879, _1677881]), hAPP(c_List_Oset(tc_List_Olist(_1677877)), c_Enum_On__lists(_1677877, _1677881, c_Enum_Oenum__class_Oenum(_1677877))))))], (44713 ^ _784416) ^ [] : [hBOOL(hAPP(_1677879, 44709 ^ [_1677877, _1677879, _1677881]))]], -(c_Enum_Oall__n__lists(_1677877, _1677879, _1677881))], (44698 ^ _784416) ^ [] : [c_Enum_Oall__n__lists(_1677877, _1677879, _1677881), 44701 ^ _784416 : [(44702 ^ _784416) ^ [_1678027] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1677877)), _1678027), hAPP(c_List_Oset(tc_List_Olist(_1677877)), c_Enum_On__lists(_1677877, _1677881, c_Enum_Oenum__class_Oenum(_1677877))))), -(hBOOL(hAPP(_1677879, _1678027)))]]]]], (44717 ^ _784416) ^ [_1678318, _1678320, _1678322, _1678324] : [-(hAPP(c_List_Oset(tc_prod(_1678318, _1678320)), hAPP(hAPP(c_List_Ozip(_1678318, _1678320), _1678322), _1678324)) = hAPP(c_Set_OCollect(tc_prod(_1678318, _1678320)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1678318, _1678320)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1678318, _1678320), 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(_1678318, _1678320)), 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(_1678318, _1678320)), 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(_1678318, _1678320), tc_fun(tc_Nat_Onat, tc_prod(_1678318, _1678320)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1678318, _1678320), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1678318, _1678320)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1678318, _1678320)), c_COMBB(tc_prod(_1678318, _1678320), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1678320, tc_prod(_1678318, _1678320)), hAPP(hAPP(c_COMBB(_1678318, tc_fun(_1678320, tc_prod(_1678318, _1678320)), tc_Nat_Onat), c_Product__Type_OPair(_1678318, _1678320)), hAPP(c_List_Onth(_1678318), _1678322))), hAPP(c_List_Onth(_1678320), _1678324)))))), 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(_1678318)), _1678322)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678320)), _1678324)))))))], (44719 ^ _784416) ^ [_1678543, _1678545, _1678547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1678543, _1678543), tc_HOL_Obool)), _1678545), hAPP(hAPP(c_Product__Type_OSigma(_1678543, _1678543), _1678547), hAPP(c_COMBK(tc_fun(_1678543, tc_HOL_Obool), _1678543), _1678547)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1678543), tc_List_Olist(_1678543)), tc_HOL_Obool)), c_List_Olistrel(_1678543, _1678545)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1678543), tc_List_Olist(_1678543)), c_List_Olists(_1678543, _1678547)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1678543), tc_HOL_Obool), tc_List_Olist(_1678543)), c_List_Olists(_1678543, _1678547))))))], (44725 ^ _784416) ^ [_1678788, _1678790, _1678792, _1678794, _1678796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678788), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678790)), _1678792))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678788), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678794)), _1678796))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1678790, _1678794)), hAPP(hAPP(c_List_Ozip(_1678790, _1678794), _1678792), _1678796)), _1678788) = hAPP(hAPP(c_Product__Type_OPair(_1678790, _1678794), hAPP(hAPP(c_List_Onth(_1678790), _1678792), _1678788)), hAPP(hAPP(c_List_Onth(_1678794), _1678796), _1678788)))], (44735 ^ _784416) ^ [_1679085, _1679087, _1679089] : [_1679085 = _1679087, 44738 ^ _784416 : [(44739 ^ _784416) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679089)), _1679085) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679089)), _1679087))], (44741 ^ _784416) ^ [_1679233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1679233), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679089)), _1679085))), -(hAPP(hAPP(c_List_Onth(_1679089), _1679085), _1679233) = hAPP(hAPP(c_List_Onth(_1679089), _1679087), _1679233))]]], (44747 ^ _784416) ^ [_1679372, _1679374, _1679376] : [-(_1679372 = _1679374), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679376)), _1679372) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679376)), _1679374), 44753 ^ _784416 : [(44754 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44752 ^ [_1679372, _1679374, _1679376]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679376)), _1679372))))], (44756 ^ _784416) ^ [] : [hAPP(hAPP(c_List_Onth(_1679376), _1679372), 44752 ^ [_1679372, _1679374, _1679376]) = hAPP(hAPP(c_List_Onth(_1679376), _1679374), 44752 ^ [_1679372, _1679374, _1679376])]]], (44760 ^ _784416) ^ [_1679687, _1679689, _1679691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1679687, tc_HOL_Obool)), _1679689), _1679691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1679687), tc_HOL_Obool)), c_List_Olists(_1679687, _1679689)), c_List_Olists(_1679687, _1679691))))], (44766 ^ _784416) ^ [_1679822, _1679824, _1679826, _1679828] : [-(hAPP(hAPP(c_List_Onth(_1679822), hAPP(hAPP(c_List_Olist_OCons(_1679822), _1679824), _1679826)), _1679828) = c_Nat_Onat_Onat__case(_1679822, _1679824, hAPP(c_List_Onth(_1679822), _1679826), _1679828))], (44768 ^ _784416) ^ [_1679877, _1679879, _1679881, _1679883] : [-(hAPP(hAPP(c_List_Onth(_1679877), hAPP(hAPP(c_List_Olist_OCons(_1679877), _1679879), _1679881)), hAPP(c_Nat_OSuc, _1679883)) = hAPP(hAPP(c_List_Onth(_1679877), _1679881), _1679883))], (44770 ^ _784416) ^ [_1679933, _1679935, _1679937] : [-(hAPP(hAPP(c_List_Onth(_1679933), hAPP(hAPP(c_List_Olist_OCons(_1679933), _1679935), _1679937)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1679935)], (44772 ^ _784416) ^ [_1679994, _1679996, _1679998] : [44774 ^ _784416 : [(44775 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1679994), 44773 ^ [_1679994, _1679996, _1679998]), hAPP(c_List_Oset(_1679994), _1679996))))], (44777 ^ _784416) ^ [] : [hBOOL(hAPP(_1679998, 44773 ^ [_1679994, _1679996, _1679998]))]], 44778 ^ _784416 : [(44779 ^ _784416) ^ [_1680178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1680178), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679994)), _1679996))), -(hBOOL(hAPP(_1679998, hAPP(hAPP(c_List_Onth(_1679994), _1679996), _1680178))))]]], (44785 ^ _784416) ^ [_1680305, _1680307, _1680309] : [44787 ^ _784416 : [(44788 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44786 ^ [_1680305, _1680307, _1680309]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680305)), _1680307))))], (44790 ^ _784416) ^ [] : [hBOOL(hAPP(_1680309, hAPP(hAPP(c_List_Onth(_1680305), _1680307), 44786 ^ [_1680305, _1680307, _1680309])))]], 44791 ^ _784416 : [(44792 ^ _784416) ^ [_1680507] : [hBOOL(hAPP(hAPP(c_member(_1680305), _1680507), hAPP(c_List_Oset(_1680305), _1680307))), -(hBOOL(hAPP(_1680309, _1680507)))]]], (44798 ^ _784416) ^ [_1680624, _1680626, _1680628, _1680630, _1680632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1680624), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680626)), _1680628))), -(hAPP(hAPP(c_List_Onth(_1680630), hAPP(hAPP(c_List_Omap(_1680626, _1680630), _1680632), _1680628)), _1680624) = hAPP(_1680632, hAPP(hAPP(c_List_Onth(_1680626), _1680628), _1680624)))], (44822 ^ _784416) ^ [_1681262, _1681264] : [44824 ^ _784416 : [(44825 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44823 ^ [_1681262, _1681264]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681262)), _1681264))))], (44828 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44826 ^ [_1681262, _1681264]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681262)), _1681264))))], (44830 ^ _784416) ^ [] : [44823 ^ [_1681262, _1681264] = 44826 ^ [_1681262, _1681264]], (44832 ^ _784416) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1681262), _1681264), 44823 ^ [_1681262, _1681264]) = hAPP(hAPP(c_List_Onth(_1681262), _1681264), 44826 ^ [_1681262, _1681264]))]], -(hBOOL(hAPP(c_List_Odistinct(_1681262), _1681264)))], (44804 ^ _784416) ^ [_1680802, _1680804] : [hBOOL(hAPP(c_List_Odistinct(_1680802), _1680804)), 44807 ^ _784416 : [(44808 ^ _784416) ^ [_1680934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1680934), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680802)), _1680804))), 44811 ^ _784416 : [(44812 ^ _784416) ^ [_1681061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681061), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680802)), _1680804))), -(_1680934 = _1681061), hAPP(hAPP(c_List_Onth(_1680802), _1680804), _1680934) = hAPP(hAPP(c_List_Onth(_1680802), _1680804), _1681061)]]]]], (44836 ^ _784416) ^ [_1681694, _1681696, _1681698, _1681700] : [hBOOL(hAPP(c_List_Odistinct(_1681694), _1681696)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681698), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681694)), _1681696))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681700), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681694)), _1681696))), 44847 ^ _784416 : [(44848 ^ _784416) ^ [] : [hAPP(hAPP(c_List_Onth(_1681694), _1681696), _1681698) = hAPP(hAPP(c_List_Onth(_1681694), _1681696), _1681700), -(_1681698 = _1681700)], (44854 ^ _784416) ^ [] : [_1681698 = _1681700, -(hAPP(hAPP(c_List_Onth(_1681694), _1681696), _1681698) = hAPP(hAPP(c_List_Onth(_1681694), _1681696), _1681700))]]], (44860 ^ _784416) ^ [_1682129] : [-(c_List_Olists(_1682129, c_Orderings_Otop__class_Otop(tc_fun(_1682129, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1682129), tc_HOL_Obool)))], (44862 ^ _784416) ^ [_1682167, _1682169, _1682171] : [c_Equiv__Relations_Oequiv(_1682167, _1682169, _1682171), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1682167), c_List_Olists(_1682167, _1682169), c_List_Olistrel(_1682167, _1682171)))], (44868 ^ _784416) ^ [_1682266, _1682268, _1682270] : [c_Relation_Orefl__on(_1682266, _1682268, _1682270), -(c_Relation_Orefl__on(tc_List_Olist(_1682266), c_List_Olists(_1682266, _1682268), c_List_Olistrel(_1682266, _1682270)))], (44874 ^ _784416) ^ [_1682365, _1682367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682365), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1682367))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1682367), _1682365)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1682367))))], (44880 ^ _784416) ^ [_1682504, _1682506, _1682508] : [hBOOL(hAPP(hAPP(c_member(_1682504), _1682506), hAPP(c_List_Oset(_1682504), _1682508))), 44884 ^ _784416 : [(44885 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44883 ^ [_1682504, _1682506, _1682508]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682504)), _1682508))))], (44887 ^ _784416) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1682504), _1682508), 44883 ^ [_1682504, _1682506, _1682508]) = _1682506)]]], (44889 ^ _784416) ^ [_1682692, _1682694, _1682696] : [-(hBOOL(hAPP(hAPP(c_member(_1682692), _1682694), hAPP(c_List_Oset(_1682692), _1682696)))), 44890 ^ _784416 : [(44891 ^ _784416) ^ [_1682766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682766), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682692)), _1682696))), hAPP(hAPP(c_List_Onth(_1682692), _1682696), _1682766) = _1682694]]], (44899 ^ _784416) ^ [_1682928, _1682930, _1682932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682928), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682930)), _1682932))), -(hBOOL(hAPP(hAPP(c_member(_1682930), hAPP(hAPP(c_List_Onth(_1682930), _1682932), _1682928)), hAPP(c_List_Oset(_1682930), _1682932))))], (44905 ^ _784416) ^ [_1683086, _1683088, _1683090, _1683092] : [_1683086 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1683088), hAPP(hAPP(c_List_Olist_OCons(_1683088), _1683090), _1683092)), _1683086) = _1683090)], (44911 ^ _784416) ^ [_1683193, _1683195, _1683197, _1683199] : [-(_1683193 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1683195), hAPP(hAPP(c_List_Olist_OCons(_1683195), _1683197), _1683199)), _1683193) = hAPP(hAPP(c_List_Onth(_1683195), _1683199), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1683193), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (44917 ^ _784416) ^ [_1683265, _1683267] : [-(hAPP(c_List_Oset(_1683265), _1683267) = hAPP(c_Set_OCollect(_1683265), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1683265), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1683265, 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)), _1683265), 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)), _1683265), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1683265, tc_fun(tc_Nat_Onat, _1683265), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1683265, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1683265), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1683265), c_COMBB(_1683265, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1683265), _1683267))))), 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(_1683265)), _1683267))))))], (44919 ^ _784416) ^ [_1683412, _1683414, _1683416, _1683418] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1683412)), hAPP(hAPP(c_List_Olist_OCons(_1683412), _1683414), _1683416)), c_List_Olists(_1683412, _1683418))), 44922 ^ _784416 : [(44923 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1683412), _1683414), _1683418)))], (44925 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1683412)), _1683416), c_List_Olists(_1683412, _1683418))))]]], (44927 ^ _784416) ^ [_1683593, _1683595, _1683597, _1683599] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1683593)), hAPP(hAPP(c_List_Olist_OCons(_1683593), _1683595), _1683597)), c_List_Olists(_1683593, _1683599)))), hBOOL(hAPP(hAPP(c_member(_1683593), _1683595), _1683599)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1683593)), _1683597), c_List_Olists(_1683593, _1683599)))], (44947 ^ _784416) ^ [_1684055, _1684057, _1684059] : [44949 ^ _784416 : [(44950 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1684055), 44948 ^ [_1684055, _1684057, _1684059]), hAPP(c_List_Oset(_1684055), _1684057))))], (44952 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1684055), 44948 ^ [_1684055, _1684057, _1684059]), _1684059))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1684055)), _1684057), c_List_Olists(_1684055, _1684059))))], (44937 ^ _784416) ^ [_1683828, _1683830, _1683832] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1683828)), _1683830), c_List_Olists(_1683828, _1683832))), 44940 ^ _784416 : [(44941 ^ _784416) ^ [_1683936] : [hBOOL(hAPP(hAPP(c_member(_1683828), _1683936), hAPP(c_List_Oset(_1683828), _1683830))), -(hBOOL(hAPP(hAPP(c_member(_1683828), _1683936), _1683832)))]]], (44956 ^ _784416) ^ [_1684290, _1684292, _1684294, _1684296] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1684290) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1684292), hAPP(hAPP(c_List_Olist_OCons(_1684292), _1684294), _1684296)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1684290)) = _1684294)], (44962 ^ _784416) ^ [_1684409, _1684411, _1684413, _1684415] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1684409) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1684411), hAPP(hAPP(c_List_Olist_OCons(_1684411), _1684413), _1684415)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1684409)) = hAPP(hAPP(c_List_Onth(_1684411), _1684415), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1684409)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (44968 ^ _784416) ^ [_1684490, _1684492] : [-(c_List_Olists(_1684490, _1684492) = hAPP(c_Set_OCollect(tc_List_Olist(_1684490)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1684490), tc_fun(_1684490, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1684490, tc_HOL_Obool), tc_fun(tc_fun(_1684490, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1684490)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1684490, tc_HOL_Obool))), c_List_Oset(_1684490))), _1684492)))], (44970 ^ _784416) ^ [_1684568, _1684570] : [class_Groups_Ocomm__monoid__add(_1684568), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1684568), _1684570) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1684568), hAPP(c_List_Onth(_1684568), _1684570)), 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(_1684568)), _1684570))))], (44976 ^ _784416) ^ [_1684701, _1684703, _1684705] : [-(hAPP(c_List_Oset(_1684701), c_List_Osublist(_1684701, _1684703, _1684705)) = hAPP(c_Set_OCollect(_1684701), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1684701), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1684701, 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)), _1684701), 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)), _1684701), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1684701, tc_fun(tc_Nat_Onat, _1684701), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1684701, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1684701), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1684701), c_COMBB(_1684701, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1684701), _1684703))))), 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(_1684701)), _1684703)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1684705))))))], (44978 ^ _784416) ^ [_1684866, _1684868, _1684870, _1684872] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1684866), tc_List_Olist(_1684866))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1684866), tc_List_Olist(_1684866)), _1684868), _1684870)), c_List_Olistrel(_1684866, _1684872))), 44981 ^ _784416 : [(44982 ^ _784416) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684866)), _1684868) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684866)), _1684870))], (44984 ^ _784416) ^ [_1685095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685095), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684866)), _1684868))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1684866, _1684866)), hAPP(hAPP(c_Product__Type_OPair(_1684866, _1684866), hAPP(hAPP(c_List_Onth(_1684866), _1684868), _1685095)), hAPP(hAPP(c_List_Onth(_1684866), _1684870), _1685095))), _1684872)))]]], (44990 ^ _784416) ^ [_1685274, _1685276, _1685278, _1685280] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1685274), tc_List_Olist(_1685274))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1685274), tc_List_Olist(_1685274)), _1685276), _1685278)), c_List_Olistrel(_1685274, _1685280)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685274)), _1685276) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685274)), _1685278), 44996 ^ _784416 : [(44997 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44995 ^ [_1685274, _1685276, _1685278, _1685280]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685274)), _1685276))))], (44999 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1685274, _1685274)), hAPP(hAPP(c_Product__Type_OPair(_1685274, _1685274), hAPP(hAPP(c_List_Onth(_1685274), _1685276), 44995 ^ [_1685274, _1685276, _1685278, _1685280])), hAPP(hAPP(c_List_Onth(_1685274), _1685278), 44995 ^ [_1685274, _1685276, _1685278, _1685280]))), _1685280))]]], (45003 ^ _784416) ^ [_1685718, _1685720, _1685722] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1685718)), _1685720), c_List_Olists(_1685718, c_Wellfounded_Oacc(_1685718, _1685722)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1685718)), _1685720), c_Wellfounded_Oacc(tc_List_Olist(_1685718), c_List_Olistrel1(_1685718, _1685722)))))], (45009 ^ _784416) ^ [_1685861, _1685863, _1685865] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1685861)), _1685863), c_Wellfounded_Oacc(tc_List_Olist(_1685861), c_List_Olistrel1(_1685861, _1685865)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1685861)), _1685863), c_List_Olists(_1685861, c_Wellfounded_Oacc(_1685861, _1685865)))))], (45015 ^ _784416) ^ [_1686025, _1686027, _1686029, _1686031] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1686025), tc_List_Olist(_1686025))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1686025), tc_List_Olist(_1686025)), _1686027), _1686029)), c_List_Olexord(_1686025, _1686031))), 45020 ^ _784416 : [(45021 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686025)), _1686027)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686025)), _1686029))))], (45023 ^ _784416) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1686025), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686025)), _1686027)), _1686029) = _1686027)]], 45025 ^ _784416 : [(45026 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45024 ^ [_1686025, _1686027, _1686029, _1686031]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686025)), _1686027)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686025)), _1686029)))))], (45028 ^ _784416) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1686025), 45024 ^ [_1686025, _1686027, _1686029, _1686031]), _1686027) = hAPP(hAPP(c_List_Otake(_1686025), 45024 ^ [_1686025, _1686027, _1686029, _1686031]), _1686029))], (45030 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1686025, _1686025)), hAPP(hAPP(c_Product__Type_OPair(_1686025, _1686025), hAPP(hAPP(c_List_Onth(_1686025), _1686027), 45024 ^ [_1686025, _1686027, _1686029, _1686031])), hAPP(hAPP(c_List_Onth(_1686025), _1686029), 45024 ^ [_1686025, _1686027, _1686029, _1686031]))), _1686031)))]]], (45032 ^ _784416) ^ [_1686565, _1686567, _1686569, _1686571] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1686565), tc_List_Olist(_1686565))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1686565), tc_List_Olist(_1686565)), _1686567), _1686569)), c_List_Olexord(_1686565, _1686571)))), 45033 ^ _784416 : [(45034 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686565)), _1686567)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686565)), _1686569))), hAPP(hAPP(c_List_Otake(_1686565), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686565)), _1686567)), _1686569) = _1686567], (45040 ^ _784416) ^ [_1686872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686872), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686565)), _1686567)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686565)), _1686569)))), hAPP(hAPP(c_List_Otake(_1686565), _1686872), _1686567) = hAPP(hAPP(c_List_Otake(_1686565), _1686872), _1686569), hBOOL(hAPP(hAPP(c_member(tc_prod(_1686565, _1686565)), hAPP(hAPP(c_Product__Type_OPair(_1686565, _1686565), hAPP(hAPP(c_List_Onth(_1686565), _1686567), _1686872)), hAPP(hAPP(c_List_Onth(_1686565), _1686569), _1686872))), _1686571))]]], (45052 ^ _784416) ^ [_1687226, _1687228, _1687230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1687226), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687228)), _1687230))), -(hAPP(c_Random_Opick(_1687228, hAPP(hAPP(c_List_Omap(_1687228, tc_prod(tc_Code__Numeral_Ocode__numeral, _1687228)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1687228), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1687230)), hAPP(c_Code__Numeral_Oof__nat, _1687226)) = hAPP(hAPP(c_List_Onth(_1687228), _1687230), _1687226))], (45058 ^ _784416) ^ [_1687399, _1687401, _1687403, _1687405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1687399), _1687401)), -(hAPP(hAPP(c_List_Onth(_1687403), hAPP(hAPP(c_List_Otake(_1687403), _1687401), _1687405)), _1687399) = hAPP(hAPP(c_List_Onth(_1687403), _1687405), _1687399))], (45064 ^ _784416) ^ [_1687538, _1687540, _1687542, _1687544, _1687546] : [-(hAPP(hAPP(c_List_Otake(_1687538), _1687540), hAPP(hAPP(c_List_Omap(_1687542, _1687538), _1687544), _1687546)) = hAPP(hAPP(c_List_Omap(_1687542, _1687538), _1687544), hAPP(hAPP(c_List_Otake(_1687542), _1687540), _1687546)))], (45066 ^ _784416) ^ [_1687603, _1687605, _1687607, _1687609] : [-(hAPP(hAPP(c_List_Otake(_1687603), hAPP(c_Nat_OSuc, _1687605)), hAPP(hAPP(c_List_Olist_OCons(_1687603), _1687607), _1687609)) = hAPP(hAPP(c_List_Olist_OCons(_1687603), _1687607), hAPP(hAPP(c_List_Otake(_1687603), _1687605), _1687609)))], (45068 ^ _784416) ^ [_1687667, _1687669, _1687671, _1687673, _1687675] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1687667, _1687669)), _1687671), hAPP(hAPP(c_List_Ozip(_1687667, _1687669), _1687673), _1687675)) = hAPP(hAPP(c_List_Ozip(_1687667, _1687669), hAPP(hAPP(c_List_Otake(_1687667), _1687671), _1687673)), hAPP(hAPP(c_List_Otake(_1687669), _1687671), _1687675)))], (45070 ^ _784416) ^ [_1687743, _1687745, _1687747, _1687749] : [hBOOL(hAPP(hAPP(c_member(_1687743), _1687745), hAPP(c_List_Oset(_1687743), hAPP(hAPP(c_List_Otake(_1687743), _1687747), _1687749)))), -(hBOOL(hAPP(hAPP(c_member(_1687743), _1687745), hAPP(c_List_Oset(_1687743), _1687749))))], (45076 ^ _784416) ^ [_1687888, _1687890, _1687892] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1687888, tc_HOL_Obool)), hAPP(c_List_Oset(_1687888), hAPP(hAPP(c_List_Otake(_1687888), _1687890), _1687892))), hAPP(c_List_Oset(_1687888), _1687892))))], (45078 ^ _784416) ^ [_1687943, _1687945, _1687947] : [-(c_List_Osublist(_1687943, _1687945, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1687947)) = hAPP(hAPP(c_List_Otake(_1687943), _1687947), _1687945))], (45080 ^ _784416) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (45082 ^ _784416) ^ [_1688003, _1688005] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1688003)), hAPP(c_Code__Numeral_Oof__nat, _1688005)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1688003), _1688005)))], (45084 ^ _784416) ^ [_1688064, _1688066] : [hAPP(c_Code__Numeral_Oof__nat, _1688064) = hAPP(c_Code__Numeral_Oof__nat, _1688066), -(_1688064 = _1688066)], (45090 ^ _784416) ^ [_1688149, _1688151] : [_1688149 = _1688151, -(hAPP(c_Code__Numeral_Oof__nat, _1688149) = hAPP(c_Code__Numeral_Oof__nat, _1688151))], (45096 ^ _784416) ^ [_1688240, _1688242, _1688244, _1688246] : [-(hAPP(hAPP(c_List_Otake(_1688240), _1688242), hAPP(hAPP(c_List_Otake(_1688240), _1688244), _1688246)) = hAPP(hAPP(c_List_Otake(_1688240), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1688242), _1688244)), _1688246))], (45098 ^ _784416) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45100 ^ _784416) ^ [_1688317, _1688319, _1688321] : [hBOOL(hAPP(c_List_Odistinct(_1688317), _1688319)), -(hBOOL(hAPP(c_List_Odistinct(_1688317), hAPP(hAPP(c_List_Otake(_1688317), _1688321), _1688319))))], (45106 ^ _784416) ^ [_1688428, _1688430, _1688432] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688428)), hAPP(hAPP(c_List_Otake(_1688428), _1688430), _1688432)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688428)), _1688432)), _1688430))], (45108 ^ _784416) ^ [_1688483, _1688485, _1688487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688483)), _1688485)), _1688487)), -(hAPP(hAPP(c_List_Otake(_1688483), _1688487), _1688485) = _1688485)], (45114 ^ _784416) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (45116 ^ _784416) ^ [_1688635, _1688637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1688635)), hAPP(c_Code__Numeral_Oof__nat, _1688637))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688635), _1688637)))], (45122 ^ _784416) ^ [_1688740, _1688742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688740), _1688742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1688740)), hAPP(c_Code__Numeral_Oof__nat, _1688742))))], (45128 ^ _784416) ^ [_1688851, _1688853] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1688851), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1688853), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 45135 ^ _784416 : [(45136 ^ _784416) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1688851) = hAPP(c_Code__Numeral_Oof__nat, _1688853), -(_1688851 = _1688853)], (45142 ^ _784416) ^ [] : [_1688851 = _1688853, -(hAPP(c_Code__Numeral_Oof__nat, _1688851) = hAPP(c_Code__Numeral_Oof__nat, _1688853))]]], (45148 ^ _784416) ^ [] : [-(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))], (45150 ^ _784416) ^ [_1689166, _1689168, _1689170, _1689172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1689166), _1689168)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1689170, tc_HOL_Obool)), hAPP(c_List_Oset(_1689170), hAPP(hAPP(c_List_Otake(_1689170), _1689166), _1689172))), hAPP(c_List_Oset(_1689170), hAPP(hAPP(c_List_Otake(_1689170), _1689168), _1689172)))))], (45156 ^ _784416) ^ [_1689329, _1689331] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1689329)), hAPP(c_Code__Numeral_Oof__nat, _1689331)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1689329), _1689331)))], (45158 ^ _784416) ^ [_1689390, _1689392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1689390)), hAPP(c_Code__Numeral_Oof__nat, _1689392))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1689390), _1689392)))], (45164 ^ _784416) ^ [_1689495, _1689497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1689495), _1689497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1689495)), hAPP(c_Code__Numeral_Oof__nat, _1689497))))], (45170 ^ _784416) ^ [_1689612] : [-(_1689612 = 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)), _1689612)))], (45176 ^ _784416) ^ [_1689644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1689644)), _1689644 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45182 ^ _784416) ^ [_1689726, _1689728, _1689730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1689726), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1689728))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1689728), _1689726), _1689730)) = 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), _1689728)), _1689730)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1689728), _1689726)))], (45188 ^ _784416) ^ [_1689887, _1689889, _1689891, _1689893] : [hBOOL(hAPP(c_List_Odistinct(_1689887), _1689889)), -(hBOOL(hAPP(hAPP(c_member(_1689887), _1689891), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1689887, tc_HOL_Obool)), hAPP(c_List_Oset(_1689887), _1689889)), hAPP(hAPP(c_Set_Oinsert(_1689887), hAPP(hAPP(c_List_Onth(_1689887), _1689889), _1689893)), c_Orderings_Obot__class_Obot(tc_fun(_1689887, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1689887), hAPP(hAPP(c_List_Olist__update(_1689887, _1689889), _1689893), _1689891))))], (45198 ^ _784416) ^ [_1690105, _1690107, _1690109] : [-(hAPP(hAPP(c_List_Olist__update(_1690105, _1690107), _1690109), hAPP(hAPP(c_List_Onth(_1690105), _1690107), _1690109)) = _1690107)], (45200 ^ _784416) ^ [_1690145, _1690147, _1690149, _1690151, _1690153] : [-(_1690145 = _1690147), -(hAPP(hAPP(c_List_Onth(_1690149), hAPP(hAPP(c_List_Olist__update(_1690149, _1690151), _1690145), _1690153)), _1690147) = hAPP(hAPP(c_List_Onth(_1690149), _1690151), _1690147))], (45206 ^ _784416) ^ [_1690212, _1690214, _1690216, _1690218, _1690220, _1690222] : [-(hAPP(hAPP(c_List_Omap(_1690212, _1690214), _1690216), hAPP(hAPP(c_List_Olist__update(_1690212, _1690218), _1690220), _1690222)) = hAPP(hAPP(c_List_Olist__update(_1690214, hAPP(hAPP(c_List_Omap(_1690212, _1690214), _1690216), _1690218)), _1690220), hAPP(_1690216, _1690222)))], (45208 ^ _784416) ^ [_1690284, _1690286, _1690288, _1690290] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690284)), hAPP(hAPP(c_List_Olist__update(_1690284, _1690286), _1690288), _1690290)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690284)), _1690286))], (45210 ^ _784416) ^ [_1690336, _1690338, _1690340, _1690342] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690336)), _1690338)), _1690340)), -(hAPP(hAPP(c_List_Olist__update(_1690336, _1690338), _1690340), _1690342) = _1690338)], (45216 ^ _784416) ^ [_1690459, _1690461, _1690463, _1690465, _1690467] : [-(hAPP(hAPP(c_List_Olist__update(_1690459, hAPP(hAPP(c_List_Olist__update(_1690459, _1690461), _1690463), _1690465)), _1690463), _1690467) = hAPP(hAPP(c_List_Olist__update(_1690459, _1690461), _1690463), _1690467))], (45218 ^ _784416) ^ [_1690513, _1690515, _1690517, _1690519, _1690521, _1690523] : [-(_1690513 = _1690515), -(hAPP(hAPP(c_List_Olist__update(_1690517, hAPP(hAPP(c_List_Olist__update(_1690517, _1690519), _1690513), _1690521)), _1690515), _1690523) = hAPP(hAPP(c_List_Olist__update(_1690517, hAPP(hAPP(c_List_Olist__update(_1690517, _1690519), _1690515), _1690523)), _1690513), _1690521))], (45224 ^ _784416) ^ [_1690593, _1690595, _1690597, _1690599, _1690601, _1690603] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1690593, _1690595), hAPP(hAPP(c_List_Ozip(_1690593, _1690595), _1690597), _1690599)), _1690601), _1690603) = hAPP(hAPP(c_List_Ozip(_1690593, _1690595), hAPP(hAPP(c_List_Olist__update(_1690593, _1690597), _1690601), hAPP(c_Product__Type_Ofst(_1690593, _1690595), _1690603))), hAPP(hAPP(c_List_Olist__update(_1690595, _1690599), _1690601), hAPP(c_Product__Type_Osnd(_1690593, _1690595), _1690603))))], (45226 ^ _784416) ^ [_1690686, _1690688, _1690690, _1690692, _1690694, _1690696, _1690698] : [-(hAPP(hAPP(c_List_Ozip(_1690686, _1690688), hAPP(hAPP(c_List_Olist__update(_1690686, _1690690), _1690692), _1690694)), hAPP(hAPP(c_List_Olist__update(_1690688, _1690696), _1690692), _1690698)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1690686, _1690688), hAPP(hAPP(c_List_Ozip(_1690686, _1690688), _1690690), _1690696)), _1690692), hAPP(hAPP(c_Product__Type_OPair(_1690686, _1690688), _1690694), _1690698)))], (45228 ^ _784416) ^ [_1690778, _1690780, _1690782, _1690784, _1690786] : [-(hAPP(hAPP(c_List_Olist__update(_1690778, hAPP(hAPP(c_List_Olist_OCons(_1690778), _1690780), _1690782)), _1690784), _1690786) = c_Nat_Onat_Onat__case(tc_List_Olist(_1690778), hAPP(hAPP(c_List_Olist_OCons(_1690778), _1690786), _1690782), hAPP(hAPP(c_COMBB(tc_List_Olist(_1690778), tc_List_Olist(_1690778), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1690778), _1690780)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1690778, tc_List_Olist(_1690778)), c_List_Olist__update(_1690778, _1690782)), _1690786)), _1690784))], (45230 ^ _784416) ^ [_1690875, _1690877, _1690879, _1690881, _1690883] : [-(hAPP(hAPP(c_List_Olist__update(_1690875, hAPP(hAPP(c_List_Olist_OCons(_1690875), _1690877), _1690879)), hAPP(c_Nat_OSuc, _1690881)), _1690883) = hAPP(hAPP(c_List_Olist_OCons(_1690875), _1690877), hAPP(hAPP(c_List_Olist__update(_1690875, _1690879), _1690881), _1690883)))], (45232 ^ _784416) ^ [_1690943, _1690945, _1690947, _1690949] : [-(hAPP(hAPP(c_List_Olist__update(_1690943, hAPP(hAPP(c_List_Olist_OCons(_1690943), _1690945), _1690947)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1690949) = hAPP(hAPP(c_List_Olist_OCons(_1690943), _1690949), _1690947))], (45234 ^ _784416) ^ [_1690997, _1690999, _1691001, _1691003, _1691005] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1690997, tc_HOL_Obool)), hAPP(c_List_Oset(_1690997), _1690999)), _1691001)), hBOOL(hAPP(hAPP(c_member(_1690997), _1691003), _1691001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1690997, tc_HOL_Obool)), hAPP(c_List_Oset(_1690997), hAPP(hAPP(c_List_Olist__update(_1690997, _1690999), _1691005), _1691003))), _1691001)))], (45244 ^ _784416) ^ [_1691230, _1691232, _1691234, _1691236] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1691230, tc_HOL_Obool)), hAPP(c_List_Oset(_1691230), hAPP(hAPP(c_List_Olist__update(_1691230, _1691232), _1691234), _1691236))), hAPP(hAPP(c_Set_Oinsert(_1691230), _1691236), hAPP(c_List_Oset(_1691230), _1691232)))))], (45246 ^ _784416) ^ [_1691296, _1691298, _1691300, _1691302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1691296), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691298)), _1691300))), -(hAPP(hAPP(c_List_Onth(_1691298), hAPP(hAPP(c_List_Olist__update(_1691298, _1691300), _1691296), _1691302)), _1691296) = _1691302)], (45252 ^ _784416) ^ [_1691435, _1691437, _1691439, _1691441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1691435), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691437)), _1691439))), 45255 ^ _784416 : [(45256 ^ _784416) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1691437, _1691439), _1691435), _1691441) = _1691439, -(hAPP(hAPP(c_List_Onth(_1691437), _1691439), _1691435) = _1691441)], (45262 ^ _784416) ^ [] : [hAPP(hAPP(c_List_Onth(_1691437), _1691439), _1691435) = _1691441, -(hAPP(hAPP(c_List_Olist__update(_1691437, _1691439), _1691435), _1691441) = _1691439)]]], (45268 ^ _784416) ^ [_1691729, _1691731, _1691733, _1691735, _1691737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1691729), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691731)), _1691733))), 45271 ^ _784416 : [(45272 ^ _784416) ^ [] : [_1691729 = _1691735, -(hAPP(hAPP(c_List_Onth(_1691731), hAPP(hAPP(c_List_Olist__update(_1691731, _1691733), _1691729), _1691737)), _1691735) = _1691737)], (45278 ^ _784416) ^ [] : [-(_1691729 = _1691735), -(hAPP(hAPP(c_List_Onth(_1691731), hAPP(hAPP(c_List_Olist__update(_1691731, _1691733), _1691729), _1691737)), _1691735) = hAPP(hAPP(c_List_Onth(_1691731), _1691733), _1691735))]]], (45284 ^ _784416) ^ [_1692025, _1692027, _1692029, _1692031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1692025), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692027)), _1692029))), -(hBOOL(hAPP(hAPP(c_member(_1692027), _1692031), hAPP(c_List_Oset(_1692027), hAPP(hAPP(c_List_Olist__update(_1692027, _1692029), _1692025), _1692031)))))], (45290 ^ _784416) ^ [_1692193, _1692195, _1692197, _1692199] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1692193), tc_List_Olist(_1692193))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1692193), tc_List_Olist(_1692193)), _1692195), _1692197)), c_List_Olistrel1(_1692193, _1692199))), 45295 ^ _784416 : [(45296 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1692193, _1692193)), hAPP(hAPP(c_Product__Type_OPair(_1692193, _1692193), hAPP(hAPP(c_List_Onth(_1692193), _1692195), 45294 ^ [_1692193, _1692195, _1692197, _1692199])), 45293 ^ [_1692193, _1692195, _1692197, _1692199])), _1692199)))], (45298 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45294 ^ [_1692193, _1692195, _1692197, _1692199]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692193)), _1692195))))], (45300 ^ _784416) ^ [] : [-(_1692197 = hAPP(hAPP(c_List_Olist__update(_1692193, _1692195), 45294 ^ [_1692193, _1692195, _1692197, _1692199]), 45293 ^ [_1692193, _1692195, _1692197, _1692199]))]]], (45302 ^ _784416) ^ [_1692541, _1692543, _1692545, _1692547] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1692541), tc_List_Olist(_1692541))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1692541), tc_List_Olist(_1692541)), _1692543), _1692545)), c_List_Olistrel1(_1692541, _1692547)))), 45303 ^ _784416 : [(45304 ^ _784416) ^ [_1692674, _1692676] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1692541, _1692541)), hAPP(hAPP(c_Product__Type_OPair(_1692541, _1692541), hAPP(hAPP(c_List_Onth(_1692541), _1692543), _1692674)), _1692676)), _1692547)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1692674), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692541)), _1692543))), _1692545 = hAPP(hAPP(c_List_Olist__update(_1692541, _1692543), _1692674), _1692676)]]], (45316 ^ _784416) ^ [_1692998, _1693000, _1693002, _1693004, _1693006, _1693008, _1693010] : [hBOOL(hAPP(hAPP(c_member(_1692998), _1693000), hAPP(c_List_Oset(_1692998), hAPP(hAPP(c_List_Otake(_1692998), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693002)), _1693004)), _1693006)))), -(c_Map_Omap__upds(_1692998, _1693002, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1692998, tc_Option_Ooption(_1693002)), _1693008), _1693000), hAPP(c_Option_Ooption_OSome(_1693002), _1693010)), _1693006, _1693004) = c_Map_Omap__upds(_1692998, _1693002, _1693008, _1693006, _1693004))], (45322 ^ _784416) ^ [_1693195, _1693197, _1693199, _1693201, _1693203, _1693205, _1693207] : [-(hBOOL(hAPP(hAPP(c_member(_1693195), _1693197), hAPP(c_List_Oset(_1693195), hAPP(hAPP(c_List_Otake(_1693195), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693199)), _1693201)), _1693203))))), -(c_Map_Omap__upds(_1693195, _1693199, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1693195, tc_Option_Ooption(_1693199)), _1693205), _1693197), hAPP(c_Option_Ooption_OSome(_1693199), _1693207)), _1693203, _1693201) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1693195, tc_Option_Ooption(_1693199)), c_Map_Omap__upds(_1693195, _1693199, _1693205, _1693203, _1693201)), _1693197), hAPP(c_Option_Ooption_OSome(_1693199), _1693207)))], (45328 ^ _784416) ^ [_1693316, _1693318, _1693320, _1693322, _1693324, _1693326] : [-(hBOOL(hAPP(hAPP(c_member(_1693316), _1693318), hAPP(c_List_Oset(_1693316), _1693320)))), -(hAPP(c_Map_Omap__upds(_1693316, _1693322, _1693324, _1693320, _1693326), _1693318) = hAPP(_1693324, _1693318))], (45334 ^ _784416) ^ [_1693384, _1693386, _1693388, _1693390, _1693392, _1693394] : [-(c_Map_Omap__add(_1693384, _1693386, _1693388, c_Map_Omap__upds(_1693384, _1693386, _1693390, _1693392, _1693394)) = c_Map_Omap__upds(_1693384, _1693386, c_Map_Omap__add(_1693384, _1693386, _1693388, _1693390), _1693392, _1693394))], (45336 ^ _784416) ^ [_1693439, _1693441, _1693443, _1693445, _1693447, _1693449, _1693451] : [-(c_Map_Omap__upds(_1693439, _1693441, _1693443, hAPP(hAPP(c_List_Olist_OCons(_1693439), _1693445), _1693447), hAPP(hAPP(c_List_Olist_OCons(_1693441), _1693449), _1693451)) = c_Map_Omap__upds(_1693439, _1693441, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1693439, tc_Option_Ooption(_1693441)), _1693443), _1693445), hAPP(c_Option_Ooption_OSome(_1693441), _1693449)), _1693447, _1693451))], (45338 ^ _784416) ^ [_1693521, _1693523, _1693525, _1693527, _1693529, _1693531, _1693533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693521)), _1693523)), _1693525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1693525), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693527)), _1693529))), -(c_Map_Omap__upds(_1693521, _1693527, _1693531, _1693523, hAPP(hAPP(c_List_Olist__update(_1693527, _1693529), _1693525), _1693533)) = c_Map_Omap__upds(_1693521, _1693527, _1693531, _1693523, _1693529))], (45348 ^ _784416) ^ [_1693756, _1693758, _1693760, _1693762, _1693764, _1693766, _1693768] : [-(hBOOL(hAPP(hAPP(c_member(_1693756), _1693758), hAPP(c_List_Oset(_1693756), _1693760)))), -(c_Map_Omap__upds(_1693756, _1693762, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1693756, tc_Option_Ooption(_1693762)), _1693764), _1693758), hAPP(c_Option_Ooption_OSome(_1693762), _1693766)), _1693760, _1693768) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1693756, tc_Option_Ooption(_1693762)), c_Map_Omap__upds(_1693756, _1693762, _1693764, _1693760, _1693768)), _1693758), hAPP(c_Option_Ooption_OSome(_1693762), _1693766)))], (45354 ^ _784416) ^ [_1693864, _1693866, _1693868, _1693870, _1693872, _1693874] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693864)), _1693866) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693868)), _1693870), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1693864, tc_HOL_Obool)), hAPP(c_List_Oset(_1693864), _1693866)), _1693872)), -(c_Map_Orestrict__map(_1693864, _1693868, c_Map_Omap__upds(_1693864, _1693868, _1693874, _1693866, _1693870), _1693872) = c_Map_Omap__upds(_1693864, _1693868, c_Map_Orestrict__map(_1693864, _1693868, _1693874, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1693864, tc_HOL_Obool)), _1693872), hAPP(c_List_Oset(_1693864), _1693866))), _1693866, _1693870))], (45364 ^ _784416) ^ [_1694143, _1694145, _1694147, _1694149, _1694151] : [-(c_Map_Odom(_1694143, _1694145, c_Map_Omap__upds(_1694143, _1694145, _1694147, _1694149, _1694151)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1694143, tc_HOL_Obool)), hAPP(c_List_Oset(_1694143), hAPP(hAPP(c_List_Otake(_1694143), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694145)), _1694151)), _1694149))), c_Map_Odom(_1694143, _1694145, _1694147)))], (45366 ^ _784416) ^ [_1694219, _1694221] : [-(c_Random_Oselect(_1694219, _1694221) = 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(_1694219, 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(_1694219)), _1694221)))), hAPP(hAPP(c_COMBB(_1694219, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1694219, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1694219, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1694219, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1694219), _1694221)), c_Code__Numeral_Onat__of))))], (45368 ^ _784416) ^ [_1694307, _1694309] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1694307)), hAPP(c_Code__Numeral_Oof__nat, _1694309)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1694307), _1694309)))], (45370 ^ _784416) ^ [_1694353] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1694353)) = _1694353)], (45372 ^ _784416) ^ [_1694382] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1694382)) = _1694382)], (45374 ^ _784416) ^ [_1694411] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1694411)) = _1694411)], (45376 ^ _784416) ^ [_1694455, _1694457] : [hAPP(c_Code__Numeral_Onat__of, _1694455) = hAPP(c_Code__Numeral_Onat__of, _1694457), -(_1694455 = _1694457)], (45382 ^ _784416) ^ [_1694540, _1694542] : [_1694540 = _1694542, -(hAPP(c_Code__Numeral_Onat__of, _1694540) = hAPP(c_Code__Numeral_Onat__of, _1694542))], (45388 ^ _784416) ^ [_1694646, _1694648] : [hAPP(c_Code__Numeral_Onat__of, _1694646) = hAPP(c_Code__Numeral_Onat__of, _1694648), -(_1694646 = _1694648)], (45394 ^ _784416) ^ [_1694731, _1694733] : [_1694731 = _1694733, -(hAPP(c_Code__Numeral_Onat__of, _1694731) = hAPP(c_Code__Numeral_Onat__of, _1694733))], (45400 ^ _784416) ^ [] : [-(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))))], (45402 ^ _784416) ^ [_1694855, _1694857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1694855), _1694857)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1694855)), hAPP(c_Code__Numeral_Onat__of, _1694857))))], (45408 ^ _784416) ^ [_1694960, _1694962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1694960)), hAPP(c_Code__Numeral_Onat__of, _1694962))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1694960), _1694962)))], (45414 ^ _784416) ^ [_1695071] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1695071)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (45416 ^ _784416) ^ [_1695102] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1695102)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1695102))], (45418 ^ _784416) ^ [] : [-(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))], (45420 ^ _784416) ^ [_1695167, _1695169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1695167), _1695169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1695167)), hAPP(c_Code__Numeral_Onat__of, _1695169))))], (45426 ^ _784416) ^ [_1695272, _1695274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1695272)), hAPP(c_Code__Numeral_Onat__of, _1695274))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1695272), _1695274)))], (45432 ^ _784416) ^ [_1695383] : [-(hAPP(c_Code__Numeral_Onat__of, _1695383) = c_Code__Numeral_Onat__of__aux(_1695383, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45434 ^ _784416) ^ [_1695412, _1695414] : [-(c_Code__Numeral_Onat__of__aux(_1695412, _1695414) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1695412)), _1695414))], (45436 ^ _784416) ^ [_1695449] : [-(c_Code__Numeral_OSuc__code__numeral(_1695449) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1695449))))], (45438 ^ _784416) ^ [_1695483, _1695485] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1695483), _1695485) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1695483)), hAPP(c_Code__Numeral_Onat__of, _1695485))))], (45440 ^ _784416) ^ [_1695529] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1695529), 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, _1695529)) = _1695529)], (45446 ^ _784416) ^ [_1695626, _1695628] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1695626), _1695628) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1695626)), hAPP(c_Code__Numeral_Onat__of, _1695628))))], (45448 ^ _784416) ^ [_1695672, _1695674] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1695672), _1695674) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1695672)), hAPP(c_Code__Numeral_Onat__of, _1695674))))], (45450 ^ _784416) ^ [_1695718, _1695720] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1695718), _1695720) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1695718), _1695720))], (45452 ^ _784416) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (45454 ^ _784416) ^ [_1695773, _1695775] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1695773), _1695775) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1695773)), hAPP(c_Code__Numeral_Onat__of, _1695775))))], (45456 ^ _784416) ^ [_1695819, _1695821] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1695819, _1695821) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1695819), hAPP(c_Code__Numeral_Onat__of, _1695821))))], (45458 ^ _784416) ^ [_1695857] : [-(_1695857 = 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, _1695857)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1695857))))], (45464 ^ _784416) ^ [_1695904, _1695906] : [-(_1695904 = c_List_Olist_ONil(_1695906)), -(c_Random_Oselect__weight(_1695906, hAPP(hAPP(c_List_Omap(_1695906, tc_prod(tc_Code__Numeral_Ocode__numeral, _1695906)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1695906), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1695904)) = c_Random_Oselect(_1695906, _1695904))], (45470 ^ _784416) ^ [_1695966, _1695968, _1695970, _1695972, _1695974] : [class_Groups_Omonoid__add(_1695966), class_Groups_Oordered__ab__semigroup__add(_1695966), 45480 ^ _784416 : [(45481 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1695968), 45479 ^ [_1695966, _1695968, _1695970, _1695972, _1695974]), hAPP(c_List_Oset(_1695968), _1695970))))], (45483 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1695966), hAPP(_1695972, 45479 ^ [_1695966, _1695968, _1695970, _1695972, _1695974])), hAPP(_1695974, 45479 ^ [_1695966, _1695968, _1695970, _1695972, _1695974])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1695966), hAPP(c_List_Omonoid__add__class_Olistsum(_1695966), hAPP(hAPP(c_List_Omap(_1695968, _1695966), _1695972), _1695970))), hAPP(c_List_Omonoid__add__class_Olistsum(_1695966), hAPP(hAPP(c_List_Omap(_1695968, _1695966), _1695974), _1695970)))))], (45487 ^ _784416) ^ [_1696390, _1696392] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1696390)), c_List_Olist_ONil(_1696390)), c_List_Olists(_1696390, _1696392))))], (45489 ^ _784416) ^ [_1696429, _1696431, _1696433] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1696429), tc_List_Olist(_1696429))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1696429), tc_List_Olist(_1696429)), _1696431), c_List_Olist_ONil(_1696429))), c_List_Olistrel(_1696429, _1696433))), -(_1696431 = c_List_Olist_ONil(_1696429))], (45495 ^ _784416) ^ [_1696576, _1696578, _1696580] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1696576), tc_List_Olist(_1696576))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1696576), tc_List_Olist(_1696576)), c_List_Olist_ONil(_1696576)), _1696578)), c_List_Olistrel(_1696576, _1696580))), -(_1696578 = c_List_Olist_ONil(_1696576))], (45511 ^ _784416) ^ [_1696853, _1696855, _1696857] : [45512 ^ _784416 : [(45513 ^ _784416) ^ [] : [_1696855 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (45515 ^ _784416) ^ [] : [_1696857 = c_List_Olist_ONil(_1696853)]], -(hAPP(hAPP(c_List_Otake(_1696853), _1696855), _1696857) = c_List_Olist_ONil(_1696853))], (45501 ^ _784416) ^ [_1696741, _1696743, _1696745] : [hAPP(hAPP(c_List_Otake(_1696741), _1696743), _1696745) = c_List_Olist_ONil(_1696741), -(_1696743 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1696745 = c_List_Olist_ONil(_1696741))], (45519 ^ _784416) ^ [_1696996, _1696998] : [-(hAPP(hAPP(c_List_Otake(_1696996), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1696998) = c_List_Olist_ONil(_1696996))], (45521 ^ _784416) ^ [_1697031, _1697033] : [-(hAPP(hAPP(c_List_Otake(_1697031), _1697033), c_List_Olist_ONil(_1697031)) = c_List_Olist_ONil(_1697031))], (45523 ^ _784416) ^ [_1697068, _1697070] : [-(c_Enum_On__lists(_1697068, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1697070) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1697068)), c_List_Olist_ONil(_1697068)), c_List_Olist_ONil(tc_List_Olist(_1697068))))], (45525 ^ _784416) ^ [_1697122, _1697124] : [_1697122 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1697124, _1697122, c_List_Olist_ONil(_1697124)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1697124)), c_List_Olist_ONil(_1697124)), c_List_Olist_ONil(tc_List_Olist(_1697124))))], (45531 ^ _784416) ^ [_1697237, _1697239] : [-(_1697237 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1697239, _1697237, c_List_Olist_ONil(_1697239)) = c_List_Olist_ONil(tc_List_Olist(_1697239)))], (45537 ^ _784416) ^ [_1697285] : [-(c_Enum_Osublists(_1697285, c_List_Olist_ONil(_1697285)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1697285)), c_List_Olist_ONil(_1697285)), c_List_Olist_ONil(tc_List_Olist(_1697285))))], (45539 ^ _784416) ^ [_1697344, _1697346, _1697348] : [hAPP(hAPP(c_List_Olist_OCons(_1697344), _1697346), _1697348) = c_List_Olist_ONil(_1697344)], (45541 ^ _784416) ^ [_1697396, _1697398, _1697400] : [c_List_Olist_ONil(_1697396) = hAPP(hAPP(c_List_Olist_OCons(_1697396), _1697398), _1697400)], (45543 ^ _784416) ^ [_1697433, _1697435, _1697437] : [-(hAPP(hAPP(c_List_Ozip(_1697433, _1697435), c_List_Olist_ONil(_1697433)), _1697437) = c_List_Olist_ONil(tc_prod(_1697433, _1697435)))], (45545 ^ _784416) ^ [_1697476, _1697478, _1697480] : [-(hAPP(hAPP(c_List_Ozip(_1697476, _1697478), _1697480), c_List_Olist_ONil(_1697478)) = c_List_Olist_ONil(tc_prod(_1697476, _1697478)))], (45547 ^ _784416) ^ [_1697519, _1697521] : [-(c_List_Osublist(_1697519, _1697521, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1697519))], (45549 ^ _784416) ^ [_1697550, _1697552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1697550), _1697552)), -(c_List_Oupto(_1697552, _1697550) = c_List_Olist_ONil(tc_Int_Oint))], (45555 ^ _784416) ^ [_1697658, _1697660] : [hAPP(c_List_Oset(_1697658), _1697660) = c_Orderings_Obot__class_Obot(tc_fun(_1697658, tc_HOL_Obool)), -(_1697660 = c_List_Olist_ONil(_1697658))], (45561 ^ _784416) ^ [_1697755, _1697757] : [_1697757 = c_List_Olist_ONil(_1697755), -(hAPP(c_List_Oset(_1697755), _1697757) = c_Orderings_Obot__class_Obot(tc_fun(_1697755, tc_HOL_Obool)))], (45567 ^ _784416) ^ [_1697873, _1697875] : [c_Orderings_Obot__class_Obot(tc_fun(_1697873, tc_HOL_Obool)) = hAPP(c_List_Oset(_1697873), _1697875), -(_1697875 = c_List_Olist_ONil(_1697873))], (45573 ^ _784416) ^ [_1697970, _1697972] : [_1697972 = c_List_Olist_ONil(_1697970), -(c_Orderings_Obot__class_Obot(tc_fun(_1697970, tc_HOL_Obool)) = hAPP(c_List_Oset(_1697970), _1697972))], (45579 ^ _784416) ^ [_1698073] : [-(hAPP(c_List_Oset(_1698073), c_List_Olist_ONil(_1698073)) = c_Orderings_Obot__class_Obot(tc_fun(_1698073, tc_HOL_Obool)))], (45581 ^ _784416) ^ [_1698108, _1698110] : [-(c_List_Osublist(_1698108, c_List_Olist_ONil(_1698108), _1698110) = c_List_Olist_ONil(_1698108))], (45583 ^ _784416) ^ [_1698141] : [class_Groups_Omonoid__add(_1698141), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1698141), c_List_Olist_ONil(_1698141)) = c_Groups_Ozero__class_Ozero(_1698141))], (45589 ^ _784416) ^ [_1698232, _1698234, _1698236, _1698238] : [-(c_List_Ofoldr(_1698232, _1698234, _1698236, c_List_Olist_ONil(_1698232), _1698238) = _1698238)], (45591 ^ _784416) ^ [_1698269, _1698271, _1698273] : [-(hAPP(hAPP(c_Map_Omap__of(_1698269, _1698271), c_List_Olist_ONil(tc_prod(_1698269, _1698271))), _1698273) = c_Option_Ooption_ONone(_1698271))], (45593 ^ _784416) ^ [_1698312, _1698314, _1698316] : [-(c_Enum_Oproduct(_1698312, _1698314, c_List_Olist_ONil(_1698312), _1698316) = c_List_Olist_ONil(tc_prod(_1698312, _1698314)))], (45595 ^ _784416) ^ [_1698351, _1698353] : [-(c_List_Olist_Olist__size(_1698351, _1698353, c_List_Olist_ONil(_1698351)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45597 ^ _784416) ^ [_1698382, _1698384] : [-(c_List_Olistrelp(_1698382, _1698384, c_List_Olist_ONil(_1698382), c_List_Olist_ONil(_1698382)))], (45599 ^ _784416) ^ [_1698413, _1698415] : [-(c_List_Olistrelp(_1698413, _1698415, c_List_Olist_ONil(_1698413), c_List_Olist_ONil(_1698413)))], (45601 ^ _784416) ^ [_1698444] : [-(hBOOL(hAPP(c_List_Odistinct(_1698444), c_List_Olist_ONil(_1698444))))], (45603 ^ _784416) ^ [_1698473] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698473)), c_List_Olist_ONil(_1698473)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45605 ^ _784416) ^ [_1698520, _1698522] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698520)), _1698522) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1698522 = c_List_Olist_ONil(_1698520))], (45611 ^ _784416) ^ [_1698611, _1698613] : [_1698613 = c_List_Olist_ONil(_1698611), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698611)), _1698613) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45617 ^ _784416) ^ [_1698729, _1698731, _1698733, _1698735] : [hAPP(hAPP(c_List_Omap(_1698729, _1698731), _1698733), _1698735) = c_List_Olist_ONil(_1698731), -(_1698735 = c_List_Olist_ONil(_1698729))], (45623 ^ _784416) ^ [_1698832, _1698834, _1698836, _1698838] : [_1698838 = c_List_Olist_ONil(_1698832), -(hAPP(hAPP(c_List_Omap(_1698832, _1698834), _1698836), _1698838) = c_List_Olist_ONil(_1698834))], (45629 ^ _784416) ^ [_1698941, _1698943, _1698945] : [-(hAPP(hAPP(c_List_Omap(_1698941, _1698943), _1698945), c_List_Olist_ONil(_1698941)) = c_List_Olist_ONil(_1698943))], (45631 ^ _784416) ^ [_1699002, _1699004, _1699006, _1699008] : [c_List_Olist_ONil(_1699002) = hAPP(hAPP(c_List_Omap(_1699004, _1699002), _1699006), _1699008), -(_1699008 = c_List_Olist_ONil(_1699004))], (45637 ^ _784416) ^ [_1699105, _1699107, _1699109, _1699111] : [_1699111 = c_List_Olist_ONil(_1699107), -(c_List_Olist_ONil(_1699105) = hAPP(hAPP(c_List_Omap(_1699107, _1699105), _1699109), _1699111))], (45643 ^ _784416) ^ [_1699214, _1699216, _1699218] : [-(hAPP(hAPP(c_Map_Omap__of(_1699214, _1699216), c_List_Olist_ONil(tc_prod(_1699214, _1699216))), _1699218) = c_Option_Ooption_ONone(_1699216))], (45645 ^ _784416) ^ [_1699257, _1699259, _1699261, _1699263] : [-(c_Map_Omap__upds(_1699257, _1699259, _1699261, c_List_Olist_ONil(_1699257), _1699263) = _1699261)], (45647 ^ _784416) ^ [_1699294, _1699296, _1699298, _1699300] : [-(c_Map_Omap__upds(_1699294, _1699296, _1699298, _1699300, c_List_Olist_ONil(_1699296)) = _1699298)], (45649 ^ _784416) ^ [_1699331, _1699333, _1699335] : [-(hAPP(hAPP(c_List_Olist__update(_1699331, c_List_Olist_ONil(_1699331)), _1699333), _1699335) = c_List_Olist_ONil(_1699331))], (45651 ^ _784416) ^ [_1699371, _1699373, _1699375] : [-(hAPP(hAPP(c_List_Olist__update(_1699371, c_List_Olist_ONil(_1699371)), _1699373), _1699375) = c_List_Olist_ONil(_1699371))], (45653 ^ _784416) ^ [_1699432, _1699434, _1699436, _1699438] : [hAPP(hAPP(c_List_Olist__update(_1699432, _1699434), _1699436), _1699438) = c_List_Olist_ONil(_1699432), -(_1699434 = c_List_Olist_ONil(_1699432))], (45659 ^ _784416) ^ [_1699535, _1699537, _1699539, _1699541] : [_1699537 = c_List_Olist_ONil(_1699535), -(hAPP(hAPP(c_List_Olist__update(_1699535, _1699537), _1699539), _1699541) = c_List_Olist_ONil(_1699535))], (45665 ^ _784416) ^ [_1699659, _1699661] : [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(_1699659)), _1699661))), _1699661 = c_List_Olist_ONil(_1699659)], (45671 ^ _784416) ^ [_1699753, _1699755] : [-(_1699755 = c_List_Olist_ONil(_1699753)), -(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(_1699753)), _1699755))))], (45677 ^ _784416) ^ [_1699802, _1699804, _1699806] : [-(hAPP(hAPP(c_List_Otake(_1699802), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1699802), _1699804), _1699806)) = hAPP(hAPP(c_List_Olist_OCons(_1699802), _1699804), c_List_Olist_ONil(_1699802)))], (45679 ^ _784416) ^ [_1699870, _1699872, _1699874] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1699870), tc_List_Olist(_1699870))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1699870), tc_List_Olist(_1699870)), _1699872), c_List_Olist_ONil(_1699870))), c_List_Olistrel1(_1699870, _1699874)))], (45681 ^ _784416) ^ [_1699944, _1699946, _1699948] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1699944), tc_List_Olist(_1699944))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1699944), tc_List_Olist(_1699944)), c_List_Olist_ONil(_1699944)), _1699946)), c_List_Olistrel1(_1699944, _1699948)))], (45683 ^ _784416) ^ [_1700003, _1700005] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1700003), tc_List_Olist(_1700003))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1700003), tc_List_Olist(_1700003)), c_List_Olist_ONil(_1700003)), c_List_Olist_ONil(_1700003))), c_List_Olistrel(_1700003, _1700005))))], (45685 ^ _784416) ^ [_1700077, _1700079, _1700081] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1700077), tc_List_Olist(_1700077))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1700077), tc_List_Olist(_1700077)), _1700079), c_List_Olist_ONil(_1700077))), c_List_Olexord(_1700077, _1700081)))], (45687 ^ _784416) ^ [_1700151, _1700153, _1700155] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1700151), tc_List_Olist(_1700151))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1700151), tc_List_Olist(_1700151)), _1700153), c_List_Olist_ONil(_1700151))), c_List_Olex(_1700151, _1700155)))], (45689 ^ _784416) ^ [_1700225, _1700227, _1700229] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1700225), tc_List_Olist(_1700225))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1700225), tc_List_Olist(_1700225)), c_List_Olist_ONil(_1700225)), _1700227)), c_List_Olex(_1700225, _1700229)))], (45691 ^ _784416) ^ [_1700284, _1700286, _1700288, _1700290] : [-(hAPP(hAPP(c_List_Otake(_1700284), _1700286), hAPP(hAPP(c_List_Olist_OCons(_1700284), _1700288), _1700290)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1700284), c_List_Olist_ONil(_1700284), hAPP(hAPP(c_COMBB(tc_List_Olist(_1700284), tc_List_Olist(_1700284), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1700284), _1700288)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1700284), tc_List_Olist(_1700284)), c_List_Otake(_1700284)), _1700290)), _1700286))], (45693 ^ _784416) ^ [_1700382, _1700384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1700382), _1700384)), -(c_List_Oupto(_1700382, _1700384) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1700382), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1700382), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1700384)))], (45699 ^ _784416) ^ [_1700499, _1700501] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1700499), _1700501))), -(c_List_Oupto(_1700499, _1700501) = c_List_Olist_ONil(tc_Int_Oint))], (45705 ^ _784416) ^ [_1700557, _1700559, _1700561] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1700557)), -(c_List_Osublist(_1700559, hAPP(hAPP(c_List_Olist_OCons(_1700559), _1700561), c_List_Olist_ONil(_1700559)), _1700557) = hAPP(hAPP(c_List_Olist_OCons(_1700559), _1700561), c_List_Olist_ONil(_1700559)))], (45711 ^ _784416) ^ [_1700682, _1700684, _1700686] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1700682))), -(c_List_Osublist(_1700684, hAPP(hAPP(c_List_Olist_OCons(_1700684), _1700686), c_List_Olist_ONil(_1700684)), _1700682) = c_List_Olist_ONil(_1700684))], (45717 ^ _784416) ^ [_1700740] : [-(c_List_Olists(_1700740, c_Orderings_Obot__class_Obot(tc_fun(_1700740, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1700740)), c_List_Olist_ONil(_1700740)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1700740), tc_HOL_Obool))))], (45719 ^ _784416) ^ [_1700805, _1700807, _1700809, _1700811] : [_1700805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1700807), _1700805), hAPP(hAPP(c_List_Olist_OCons(_1700807), _1700809), _1700811)) = c_List_Olist_ONil(_1700807))], (45725 ^ _784416) ^ [_1700916, _1700918, _1700920, _1700922] : [-(_1700916 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1700918), _1700916), hAPP(hAPP(c_List_Olist_OCons(_1700918), _1700920), _1700922)) = hAPP(hAPP(c_List_Olist_OCons(_1700918), _1700920), hAPP(hAPP(c_List_Otake(_1700918), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1700916), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1700922)))], (45731 ^ _784416) ^ [_1701005, _1701007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1701005)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1701007))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1701005), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1701007)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1701005)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1701005)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1701007))))], (45737 ^ _784416) ^ [_1701164, _1701166] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1701164)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1701166)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1701164), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1701166)) = c_List_Olist_ONil(tc_Int_Oint))], (45743 ^ _784416) ^ [_1701218, _1701220, _1701222] : [-(_1701218 = c_List_Olist_ONil(_1701220)), -(hBOOL(hAPP(hAPP(c_member(_1701220), hAPP(c_Product__Type_Ofst(_1701220, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1701220, _1701218), _1701222))), hAPP(c_List_Oset(_1701220), _1701218))))], (45749 ^ _784416) ^ [_1701282, _1701284] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1701282), tc_List_Olist(_1701282), c_List_Olistrel(_1701282, _1701284)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1701282)), c_List_Olist_ONil(_1701282)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1701282), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1701282)), c_List_Olist_ONil(_1701282)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1701282), tc_HOL_Obool))))], (45751 ^ _784416) ^ [_1701359, _1701361] : [-(c_List_Oset__Cons(_1701359, _1701361, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1701359)), c_List_Olist_ONil(_1701359)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1701359), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1701359, tc_List_Olist(_1701359), hAPP(hAPP(c_COMBC(_1701359, tc_List_Olist(_1701359), tc_List_Olist(_1701359)), c_List_Olist_OCons(_1701359)), c_List_Olist_ONil(_1701359))), _1701361))], (45753 ^ _784416) ^ [_1701449, _1701451, _1701453, _1701455] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1701449) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1701451), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1701449)), hAPP(hAPP(c_List_Olist_OCons(_1701451), _1701453), _1701455)) = c_List_Olist_ONil(_1701451))], (45759 ^ _784416) ^ [_1701572, _1701574, _1701576, _1701578] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1701572) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1701574), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1701572)), hAPP(hAPP(c_List_Olist_OCons(_1701574), _1701576), _1701578)) = hAPP(hAPP(c_List_Olist_OCons(_1701574), _1701576), hAPP(hAPP(c_List_Otake(_1701574), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1701572)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1701578)))], (45765 ^ _784416) ^ [_1701661, _1701663] : [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), _1701661), _1701663))), 45768 ^ _784416 : [(45769 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1701661), _1701663)), -(c_List_Oupto(_1701661, _1701663) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1701661), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1701661), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1701663)))], (45775 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1701661), _1701663))), -(c_List_Oupto(_1701661, _1701663) = c_List_Olist_ONil(tc_Int_Oint))]]], (45781 ^ _784416) ^ [_1701933, _1701935, _1701937, _1701939, _1701941] : [_1701933 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1701935, _1701937, _1701939), _1701933), _1701941) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1701937), _1701935), c_List_Olist_ONil(_1701937)), _1701941))], (45787 ^ _784416) ^ [_1702056, _1702058, _1702060, _1702062, _1702064] : [-(_1702056 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1702058, _1702060, _1702062), _1702056), _1702064) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1702060), _1702058), tc_prod(_1702060, _1702058), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1702060), _1702058), c_List_Olist_ONil(_1702060)), _1702064), hAPP(c_Product__Type_Oprod_Oprod__case(_1702060, _1702058, tc_prod(tc_List_Olist(_1702060), _1702058)), hAPP(hAPP(c_COMBC(_1702060, tc_fun(_1702058, tc_prod(tc_List_Olist(_1702060), _1702058)), tc_fun(_1702058, tc_prod(tc_List_Olist(_1702060), _1702058))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1702060), _1702058), tc_prod(tc_List_Olist(_1702060), _1702058)), tc_fun(tc_fun(_1702058, tc_prod(tc_List_Olist(_1702060), _1702058)), tc_fun(_1702058, tc_prod(tc_List_Olist(_1702060), _1702058))), _1702060), c_COMBB(tc_prod(tc_List_Olist(_1702060), _1702058), tc_prod(tc_List_Olist(_1702060), _1702058), _1702058)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1702060), tc_fun(_1702058, tc_prod(tc_List_Olist(_1702060), _1702058))), tc_fun(tc_prod(tc_List_Olist(_1702060), _1702058), tc_prod(tc_List_Olist(_1702060), _1702058)), _1702060), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1702060), _1702058, tc_prod(tc_List_Olist(_1702060), _1702058))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1702060), tc_List_Olist(_1702060)), tc_fun(tc_List_Olist(_1702060), tc_fun(_1702058, tc_prod(tc_List_Olist(_1702060), _1702058))), _1702060), hAPP(c_COMBB(tc_List_Olist(_1702060), tc_fun(_1702058, tc_prod(tc_List_Olist(_1702060), _1702058)), tc_List_Olist(_1702060)), c_Product__Type_OPair(tc_List_Olist(_1702060), _1702058))), c_List_Olist_OCons(_1702060))))), hAPP(c_Lazy__Sequence_Oanamorph(_1702058, _1702060, _1702062), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1702056), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), hAPP(_1702062, _1702064)))], (45793 ^ _784416) ^ [_1702352] : [-(c_List_Olistset(_1702352, c_List_Olist_ONil(tc_fun(_1702352, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1702352)), c_List_Olist_ONil(_1702352)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1702352), tc_HOL_Obool))))], (45795 ^ _784416) ^ [_1702402, _1702404, _1702406, _1702408, _1702410] : [-(hAPP(hAPP(c_List_Ozip(_1702402, _1702404), hAPP(hAPP(c_List_Olist_OCons(_1702402), _1702406), _1702408)), _1702410) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1702402, _1702404)), _1702404, c_List_Olist_ONil(tc_prod(_1702402, _1702404)), hAPP(hAPP(c_COMBC(_1702404, tc_fun(tc_List_Olist(_1702404), tc_List_Olist(tc_prod(_1702402, _1702404))), tc_fun(tc_List_Olist(_1702404), tc_List_Olist(tc_prod(_1702402, _1702404)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1702402, _1702404)), tc_List_Olist(tc_prod(_1702402, _1702404))), tc_fun(tc_fun(tc_List_Olist(_1702404), tc_List_Olist(tc_prod(_1702402, _1702404))), tc_fun(tc_List_Olist(_1702404), tc_List_Olist(tc_prod(_1702402, _1702404)))), _1702404), c_COMBB(tc_List_Olist(tc_prod(_1702402, _1702404)), tc_List_Olist(tc_prod(_1702402, _1702404)), tc_List_Olist(_1702404))), hAPP(hAPP(c_COMBB(tc_prod(_1702402, _1702404), tc_fun(tc_List_Olist(tc_prod(_1702402, _1702404)), tc_List_Olist(tc_prod(_1702402, _1702404))), _1702404), c_List_Olist_OCons(tc_prod(_1702402, _1702404))), hAPP(c_Product__Type_OPair(_1702402, _1702404), _1702406)))), hAPP(c_List_Ozip(_1702402, _1702404), _1702408))), _1702410))], (45797 ^ _784416) ^ [_1702603, _1702605, _1702607, _1702609, _1702611, _1702613] : [-(hAPP(c_List_Olist_Olist__case(_1702603, _1702605, _1702607, _1702609), hAPP(hAPP(c_List_Olist_OCons(_1702605), _1702611), _1702613)) = hAPP(hAPP(_1702609, _1702611), _1702613))], (45799 ^ _784416) ^ [_1702658, _1702660, _1702662, _1702664] : [-(hAPP(c_List_Olist_Olist__case(_1702658, _1702660, _1702662, _1702664), c_List_Olist_ONil(_1702660)) = _1702662)], (45801 ^ _784416) ^ [_1702697, _1702699, _1702701] : [-(c_List_Olistset(_1702697, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1702697, tc_HOL_Obool)), _1702699), _1702701)) = c_List_Oset__Cons(_1702697, _1702699, c_List_Olistset(_1702697, _1702701)))], (45803 ^ _784416) ^ [_1702745, _1702747, _1702749, _1702751, _1702753] : [-(hAPP(hAPP(c_List_Ozip(_1702745, _1702747), _1702749), hAPP(hAPP(c_List_Olist_OCons(_1702747), _1702751), _1702753)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1702745, _1702747)), _1702745, c_List_Olist_ONil(tc_prod(_1702745, _1702747)), hAPP(hAPP(c_COMBC(_1702745, tc_fun(tc_List_Olist(_1702745), tc_List_Olist(tc_prod(_1702745, _1702747))), tc_fun(tc_List_Olist(_1702745), tc_List_Olist(tc_prod(_1702745, _1702747)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1702745, _1702747)), tc_List_Olist(tc_prod(_1702745, _1702747))), tc_fun(tc_fun(tc_List_Olist(_1702745), tc_List_Olist(tc_prod(_1702745, _1702747))), tc_fun(tc_List_Olist(_1702745), tc_List_Olist(tc_prod(_1702745, _1702747)))), _1702745), c_COMBB(tc_List_Olist(tc_prod(_1702745, _1702747)), tc_List_Olist(tc_prod(_1702745, _1702747)), tc_List_Olist(_1702745))), hAPP(hAPP(c_COMBB(tc_prod(_1702745, _1702747), tc_fun(tc_List_Olist(tc_prod(_1702745, _1702747)), tc_List_Olist(tc_prod(_1702745, _1702747))), _1702745), c_List_Olist_OCons(tc_prod(_1702745, _1702747))), hAPP(hAPP(c_COMBC(_1702745, _1702747, tc_prod(_1702745, _1702747)), c_Product__Type_OPair(_1702745, _1702747)), _1702751)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1702745), tc_List_Olist(_1702747), tc_List_Olist(tc_prod(_1702745, _1702747))), c_List_Ozip(_1702745, _1702747)), _1702753))), _1702749))], (45805 ^ _784416) ^ [_1702972, _1702974, _1702976] : [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), _1702972), _1702974))), -(hBOOL(hAPP(hAPP(_1702976, _1702972), _1702974))), 45812 ^ _784416 : [(45813 ^ _784416) ^ [] : [-(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), 45810 ^ [_1702972, _1702974, _1702976]), 45811 ^ [_1702972, _1702974, _1702976]))))], (45821 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1702976, 45810 ^ [_1702972, _1702974, _1702976]), 45811 ^ [_1702972, _1702974, _1702976]))], (45815 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 45810 ^ [_1702972, _1702974, _1702976]), 45811 ^ [_1702972, _1702974, _1702976])), -(hBOOL(hAPP(hAPP(_1702976, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 45810 ^ [_1702972, _1702974, _1702976]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 45811 ^ [_1702972, _1702974, _1702976])))]]], (45825 ^ _784416) ^ [_1703463, _1703465, _1703467, _1703469, _1703471, _1703473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703463)), _1703465)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703467)), _1703469))), -(c_Map_Omap__upds(_1703463, _1703467, _1703471, hAPP(hAPP(c_List_Oappend(_1703463), _1703465), hAPP(hAPP(c_List_Olist_OCons(_1703463), _1703473), c_List_Olist_ONil(_1703463))), _1703469) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1703463, tc_Option_Ooption(_1703467)), c_Map_Omap__upds(_1703463, _1703467, _1703471, _1703465, _1703469)), _1703473), hAPP(c_Option_Ooption_OSome(_1703467), hAPP(hAPP(c_List_Onth(_1703467), _1703469), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703463)), _1703465)))))], (45831 ^ _784416) ^ [_1703738, _1703740, _1703742, _1703744, _1703746] : [hAPP(hAPP(c_List_Oappend(_1703738), _1703740), hAPP(hAPP(c_List_Olist_OCons(_1703738), _1703742), c_List_Olist_ONil(_1703738))) = hAPP(hAPP(c_List_Oappend(_1703738), _1703744), hAPP(hAPP(c_List_Olist_OCons(_1703738), _1703746), c_List_Olist_ONil(_1703738))), 45834 ^ _784416 : [(45835 ^ _784416) ^ [] : [-(_1703740 = _1703744)], (45837 ^ _784416) ^ [] : [-(_1703742 = _1703746)]]], (45839 ^ _784416) ^ [_1703915, _1703917, _1703919, _1703921, _1703923] : [-(hAPP(hAPP(c_List_Oappend(_1703915), _1703917), hAPP(hAPP(c_List_Olist_OCons(_1703915), _1703919), c_List_Olist_ONil(_1703915))) = hAPP(hAPP(c_List_Oappend(_1703915), _1703921), hAPP(hAPP(c_List_Olist_OCons(_1703915), _1703923), c_List_Olist_ONil(_1703915)))), _1703917 = _1703921, _1703919 = _1703923], (45849 ^ _784416) ^ [_1704154, _1704156, _1704158, _1704160, _1704162] : [hAPP(hAPP(c_List_Olist_OCons(_1704154), _1704156), _1704158) = hAPP(hAPP(c_List_Oappend(_1704154), _1704160), _1704162), 45854 ^ _784416 : [(45855 ^ _784416) ^ [] : [-(_1704160 = c_List_Olist_ONil(_1704154))], (45857 ^ _784416) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1704154), _1704156), _1704158) = _1704162)]], 45859 ^ _784416 : [(45860 ^ _784416) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1704154), _1704156), 45858 ^ [_1704154, _1704156, _1704158, _1704160, _1704162]) = _1704160)], (45862 ^ _784416) ^ [] : [-(_1704158 = hAPP(hAPP(c_List_Oappend(_1704154), 45858 ^ [_1704154, _1704156, _1704158, _1704160, _1704162]), _1704162))]]], (45864 ^ _784416) ^ [_1704447, _1704449, _1704451, _1704453, _1704455] : [-(hAPP(hAPP(c_List_Olist_OCons(_1704447), _1704449), _1704451) = hAPP(hAPP(c_List_Oappend(_1704447), _1704453), _1704455)), 45865 ^ _784416 : [(45866 ^ _784416) ^ [] : [_1704453 = c_List_Olist_ONil(_1704447), hAPP(hAPP(c_List_Olist_OCons(_1704447), _1704449), _1704451) = _1704455], (45872 ^ _784416) ^ [_1704630] : [hAPP(hAPP(c_List_Olist_OCons(_1704447), _1704449), _1704630) = _1704453, _1704451 = hAPP(hAPP(c_List_Oappend(_1704447), _1704630), _1704455)]]], (45880 ^ _784416) ^ [_1704818, _1704820, _1704822, _1704824, _1704826] : [hAPP(hAPP(c_List_Oappend(_1704818), _1704820), _1704822) = hAPP(hAPP(c_List_Olist_OCons(_1704818), _1704824), _1704826), 45885 ^ _784416 : [(45886 ^ _784416) ^ [] : [-(_1704820 = c_List_Olist_ONil(_1704818))], (45888 ^ _784416) ^ [] : [-(_1704822 = hAPP(hAPP(c_List_Olist_OCons(_1704818), _1704824), _1704826))]], 45890 ^ _784416 : [(45891 ^ _784416) ^ [] : [-(_1704820 = hAPP(hAPP(c_List_Olist_OCons(_1704818), _1704824), 45889 ^ [_1704818, _1704820, _1704822, _1704824, _1704826]))], (45893 ^ _784416) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1704818), 45889 ^ [_1704818, _1704820, _1704822, _1704824, _1704826]), _1704822) = _1704826)]]], (45895 ^ _784416) ^ [_1705111, _1705113, _1705115, _1705117, _1705119] : [-(hAPP(hAPP(c_List_Oappend(_1705111), _1705113), _1705115) = hAPP(hAPP(c_List_Olist_OCons(_1705111), _1705117), _1705119)), 45896 ^ _784416 : [(45897 ^ _784416) ^ [] : [_1705113 = c_List_Olist_ONil(_1705111), _1705115 = hAPP(hAPP(c_List_Olist_OCons(_1705111), _1705117), _1705119)], (45903 ^ _784416) ^ [_1705294] : [_1705113 = hAPP(hAPP(c_List_Olist_OCons(_1705111), _1705117), _1705294), hAPP(hAPP(c_List_Oappend(_1705111), _1705294), _1705115) = _1705119]]], (45911 ^ _784416) ^ [_1705458, _1705460, _1705462] : [_1705458 = _1705460, -(_1705458 = hAPP(hAPP(c_List_Oappend(_1705462), c_List_Olist_ONil(_1705462)), _1705460))], (45917 ^ _784416) ^ [_1705575, _1705577, _1705579] : [hAPP(hAPP(c_List_Oappend(_1705575), _1705577), _1705579) = _1705579, -(_1705577 = c_List_Olist_ONil(_1705575))], (45923 ^ _784416) ^ [_1705670, _1705672, _1705674] : [_1705672 = c_List_Olist_ONil(_1705670), -(hAPP(hAPP(c_List_Oappend(_1705670), _1705672), _1705674) = _1705674)], (45929 ^ _784416) ^ [_1705789, _1705791, _1705793] : [hAPP(hAPP(c_List_Oappend(_1705789), _1705791), _1705793) = _1705791, -(_1705793 = c_List_Olist_ONil(_1705789))], (45935 ^ _784416) ^ [_1705884, _1705886, _1705888] : [_1705888 = c_List_Olist_ONil(_1705884), -(hAPP(hAPP(c_List_Oappend(_1705884), _1705886), _1705888) = _1705886)], (45941 ^ _784416) ^ [_1706003, _1706005, _1706007] : [hAPP(hAPP(c_List_Oappend(_1706003), _1706005), _1706007) = c_List_Olist_ONil(_1706003), 45944 ^ _784416 : [(45945 ^ _784416) ^ [] : [-(_1706005 = c_List_Olist_ONil(_1706003))], (45947 ^ _784416) ^ [] : [-(_1706007 = c_List_Olist_ONil(_1706003))]]], (45949 ^ _784416) ^ [_1706132, _1706134, _1706136] : [-(hAPP(hAPP(c_List_Oappend(_1706132), _1706134), _1706136) = c_List_Olist_ONil(_1706132)), _1706134 = c_List_Olist_ONil(_1706132), _1706136 = c_List_Olist_ONil(_1706132)], (45959 ^ _784416) ^ [_1706313, _1706315, _1706317] : [_1706313 = hAPP(hAPP(c_List_Oappend(_1706315), _1706317), _1706313), -(_1706317 = c_List_Olist_ONil(_1706315))], (45965 ^ _784416) ^ [_1706408, _1706410, _1706412] : [_1706412 = c_List_Olist_ONil(_1706410), -(_1706408 = hAPP(hAPP(c_List_Oappend(_1706410), _1706412), _1706408))], (45971 ^ _784416) ^ [_1706527, _1706529, _1706531] : [_1706527 = hAPP(hAPP(c_List_Oappend(_1706529), _1706527), _1706531), -(_1706531 = c_List_Olist_ONil(_1706529))], (45977 ^ _784416) ^ [_1706622, _1706624, _1706626] : [_1706626 = c_List_Olist_ONil(_1706624), -(_1706622 = hAPP(hAPP(c_List_Oappend(_1706624), _1706622), _1706626))], (45983 ^ _784416) ^ [_1706723, _1706725] : [-(hAPP(hAPP(c_List_Oappend(_1706723), _1706725), c_List_Olist_ONil(_1706723)) = _1706725)], (45985 ^ _784416) ^ [_1706776, _1706778, _1706780] : [c_List_Olist_ONil(_1706776) = hAPP(hAPP(c_List_Oappend(_1706776), _1706778), _1706780), 45988 ^ _784416 : [(45989 ^ _784416) ^ [] : [-(_1706778 = c_List_Olist_ONil(_1706776))], (45991 ^ _784416) ^ [] : [-(_1706780 = c_List_Olist_ONil(_1706776))]]], (45993 ^ _784416) ^ [_1706905, _1706907, _1706909] : [-(c_List_Olist_ONil(_1706905) = hAPP(hAPP(c_List_Oappend(_1706905), _1706907), _1706909)), _1706907 = c_List_Olist_ONil(_1706905), _1706909 = c_List_Olist_ONil(_1706905)], (46003 ^ _784416) ^ [_1707068, _1707070] : [-(hAPP(hAPP(c_List_Oappend(_1707068), c_List_Olist_ONil(_1707068)), _1707070) = _1707070)], (46005 ^ _784416) ^ [_1707103, _1707105, _1707107, _1707109, _1707111, _1707113] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707103)), _1707105) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707107)), _1707109), -(c_Map_Omap__upds(_1707103, _1707107, _1707111, hAPP(hAPP(c_List_Oappend(_1707103), _1707105), _1707113), _1707109) = c_Map_Omap__upds(_1707103, _1707107, _1707111, _1707105, _1707109))], (46011 ^ _784416) ^ [_1707256, _1707258, _1707260, _1707262, _1707264, _1707266] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707256)), _1707258) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707260)), _1707262), -(c_Map_Omap__upds(_1707256, _1707260, _1707264, _1707258, hAPP(hAPP(c_List_Oappend(_1707260), _1707262), _1707266)) = c_Map_Omap__upds(_1707256, _1707260, _1707264, _1707258, _1707262))], (46017 ^ _784416) ^ [_1707409, _1707411, _1707413, _1707415, _1707417] : [-(hAPP(hAPP(c_List_Omap(_1707409, _1707411), _1707413), hAPP(hAPP(c_List_Oappend(_1707409), _1707415), _1707417)) = hAPP(hAPP(c_List_Oappend(_1707411), hAPP(hAPP(c_List_Omap(_1707409, _1707411), _1707413), _1707415)), hAPP(hAPP(c_List_Omap(_1707409, _1707411), _1707413), _1707417)))], (46019 ^ _784416) ^ [_1707483, _1707485, _1707487] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707483)), hAPP(hAPP(c_List_Oappend(_1707483), _1707485), _1707487)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707483)), _1707485)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707483)), _1707487)))], (46021 ^ _784416) ^ [_1707545, _1707547, _1707549, _1707551, _1707553, _1707555] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707545)), _1707547) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707549)), _1707551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707545)), _1707553) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707549)), _1707555), -(hAPP(hAPP(c_List_Ozip(_1707545, _1707549), hAPP(hAPP(c_List_Oappend(_1707545), _1707547), _1707553)), hAPP(hAPP(c_List_Oappend(_1707549), _1707551), _1707555)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1707545, _1707549)), hAPP(hAPP(c_List_Ozip(_1707545, _1707549), _1707547), _1707551)), hAPP(hAPP(c_List_Ozip(_1707545, _1707549), _1707553), _1707555)))], (46031 ^ _784416) ^ [_1707854, _1707856, _1707858, _1707860] : [-(hAPP(c_Map_Omap__of(_1707854, _1707856), hAPP(hAPP(c_List_Oappend(tc_prod(_1707854, _1707856)), _1707858), _1707860)) = c_Map_Omap__add(_1707854, _1707856, hAPP(c_Map_Omap__of(_1707854, _1707856), _1707860), hAPP(c_Map_Omap__of(_1707854, _1707856), _1707858)))], (46033 ^ _784416) ^ [_1707917, _1707919, _1707921, _1707923] : [-(hAPP(hAPP(c_List_Oappend(_1707917), hAPP(hAPP(c_List_Oappend(_1707917), _1707919), _1707921)), _1707923) = hAPP(hAPP(c_List_Oappend(_1707917), _1707919), hAPP(hAPP(c_List_Oappend(_1707917), _1707921), _1707923)))], (46035 ^ _784416) ^ [_1708002, _1708004, _1708006, _1708008, _1708010] : [hAPP(hAPP(c_List_Oappend(_1708002), _1708004), _1708006) = hAPP(hAPP(c_List_Oappend(_1708002), _1708008), _1708010), 46041 ^ _784416 : [(46042 ^ _784416) ^ [] : [-(_1708004 = hAPP(hAPP(c_List_Oappend(_1708002), _1708008), 46038 ^ [_1708002, _1708004, _1708006, _1708008, _1708010]))], (46044 ^ _784416) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1708002), 46038 ^ [_1708002, _1708004, _1708006, _1708008, _1708010]), _1708006) = _1708010)]], 46045 ^ _784416 : [(46046 ^ _784416) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1708002), _1708004), 46038 ^ [_1708002, _1708004, _1708006, _1708008, _1708010]) = _1708008)], (46048 ^ _784416) ^ [] : [-(_1708006 = hAPP(hAPP(c_List_Oappend(_1708002), 46038 ^ [_1708002, _1708004, _1708006, _1708008, _1708010]), _1708010))]]], (46050 ^ _784416) ^ [_1708333, _1708335, _1708337, _1708339, _1708341] : [-(hAPP(hAPP(c_List_Oappend(_1708333), _1708335), _1708337) = hAPP(hAPP(c_List_Oappend(_1708333), _1708339), _1708341)), 46051 ^ _784416 : [(46052 ^ _784416) ^ [_1708445] : [_1708335 = hAPP(hAPP(c_List_Oappend(_1708333), _1708339), _1708445), hAPP(hAPP(c_List_Oappend(_1708333), _1708445), _1708337) = _1708341], (46058 ^ _784416) ^ [_1708557] : [hAPP(hAPP(c_List_Oappend(_1708333), _1708335), _1708557) = _1708339, _1708337 = hAPP(hAPP(c_List_Oappend(_1708333), _1708557), _1708341)]]], (46066 ^ _784416) ^ [_1708742, _1708744, _1708746, _1708748] : [hAPP(hAPP(c_List_Oappend(_1708742), _1708744), _1708746) = hAPP(hAPP(c_List_Oappend(_1708742), _1708744), _1708748), -(_1708746 = _1708748)], (46072 ^ _784416) ^ [_1708851, _1708853, _1708855, _1708857] : [_1708855 = _1708857, -(hAPP(hAPP(c_List_Oappend(_1708851), _1708853), _1708855) = hAPP(hAPP(c_List_Oappend(_1708851), _1708853), _1708857))], (46078 ^ _784416) ^ [_1708987, _1708989, _1708991, _1708993] : [hAPP(hAPP(c_List_Oappend(_1708987), _1708989), _1708991) = hAPP(hAPP(c_List_Oappend(_1708987), _1708993), _1708991), -(_1708989 = _1708993)], (46084 ^ _784416) ^ [_1709096, _1709098, _1709100, _1709102] : [_1709098 = _1709102, -(hAPP(hAPP(c_List_Oappend(_1709096), _1709098), _1709100) = hAPP(hAPP(c_List_Oappend(_1709096), _1709102), _1709100))], (46090 ^ _784416) ^ [_1709211, _1709213, _1709215, _1709217, _1709219, _1709221] : [hAPP(hAPP(c_List_Oappend(_1709211), _1709213), _1709215) = _1709217, _1709219 = hAPP(hAPP(c_List_Oappend(_1709211), _1709215), _1709221), -(hAPP(hAPP(c_List_Oappend(_1709211), _1709213), _1709219) = hAPP(hAPP(c_List_Oappend(_1709211), _1709217), _1709221))], (46100 ^ _784416) ^ [_1709420, _1709422, _1709424, _1709426, _1709428, _1709430] : [-(c_List_Ofoldr(_1709420, _1709422, _1709424, hAPP(hAPP(c_List_Oappend(_1709420), _1709426), _1709428), _1709430) = c_List_Ofoldr(_1709420, _1709422, _1709424, _1709426, c_List_Ofoldr(_1709420, _1709422, _1709424, _1709428, _1709430)))], (46102 ^ _784416) ^ [_1709479, _1709481, _1709483] : [class_Groups_Omonoid__add(_1709479), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1709479), hAPP(hAPP(c_List_Oappend(_1709479), _1709481), _1709483)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1709479), hAPP(c_List_Omonoid__add__class_Olistsum(_1709479), _1709481)), hAPP(c_List_Omonoid__add__class_Olistsum(_1709479), _1709483)))], (46108 ^ _784416) ^ [_1709618, _1709620, _1709622] : [-(hAPP(c_List_Oset(_1709618), hAPP(hAPP(c_List_Oappend(_1709618), _1709620), _1709622)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1709618, tc_HOL_Obool)), hAPP(c_List_Oset(_1709618), _1709620)), hAPP(c_List_Oset(_1709618), _1709622)))], (46110 ^ _784416) ^ [_1709700, _1709702, _1709704, _1709706] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709700)), hAPP(hAPP(c_List_Oappend(_1709700), _1709702), _1709704)), c_List_Olists(_1709700, _1709706))), 46113 ^ _784416 : [(46114 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709700)), _1709702), c_List_Olists(_1709700, _1709706))))], (46116 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709700)), _1709704), c_List_Olists(_1709700, _1709706))))]]], (46118 ^ _784416) ^ [_1709891, _1709893, _1709895, _1709897] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709891)), hAPP(hAPP(c_List_Oappend(_1709891), _1709893), _1709895)), c_List_Olists(_1709891, _1709897)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709891)), _1709893), c_List_Olists(_1709891, _1709897))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709891)), _1709895), c_List_Olists(_1709891, _1709897)))], (46128 ^ _784416) ^ [_1710118, _1710120, _1710122, _1710124, _1710126, _1710128] : [hAPP(hAPP(c_List_Olist_OCons(_1710118), _1710120), _1710122) = _1710124, _1710126 = hAPP(hAPP(c_List_Oappend(_1710118), _1710122), _1710128), -(hAPP(hAPP(c_List_Olist_OCons(_1710118), _1710120), _1710126) = hAPP(hAPP(c_List_Oappend(_1710118), _1710124), _1710128))], (46138 ^ _784416) ^ [_1710327, _1710329, _1710331, _1710333] : [-(hAPP(hAPP(c_List_Oappend(_1710327), hAPP(hAPP(c_List_Olist_OCons(_1710327), _1710329), _1710331)), _1710333) = hAPP(hAPP(c_List_Olist_OCons(_1710327), _1710329), hAPP(hAPP(c_List_Oappend(_1710327), _1710331), _1710333)))], (46140 ^ _784416) ^ [_1710388, _1710390, _1710392] : [-(c_Enum_Osublists(_1710388, hAPP(hAPP(c_List_Olist_OCons(_1710388), _1710390), _1710392)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1710388)), tc_List_Olist(tc_List_Olist(_1710388))), c_Enum_Osublists(_1710388, _1710392)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1710388)), tc_List_Olist(tc_List_Olist(_1710388)), tc_List_Olist(tc_List_Olist(_1710388))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1710388)), tc_fun(tc_List_Olist(tc_List_Olist(_1710388)), tc_List_Olist(tc_List_Olist(_1710388))), tc_List_Olist(tc_List_Olist(_1710388))), c_List_Oappend(tc_List_Olist(_1710388))), hAPP(c_List_Omap(tc_List_Olist(_1710388), tc_List_Olist(_1710388)), hAPP(c_List_Olist_OCons(_1710388), _1710390)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1710388))))))], (46142 ^ _784416) ^ [_1710522, _1710524, _1710526, _1710528] : [-(hAPP(hAPP(c_List_Onth(_1710522), hAPP(hAPP(c_List_Oappend(_1710522), _1710524), hAPP(hAPP(c_List_Olist_OCons(_1710522), _1710526), _1710528))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710522)), _1710524)) = _1710526)], (46144 ^ _784416) ^ [_1710582, _1710584, _1710586, _1710588] : [-(hAPP(hAPP(c_List_Onth(_1710582), hAPP(hAPP(c_List_Oappend(_1710582), _1710584), _1710586)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710582)), _1710584)), _1710588)) = hAPP(hAPP(c_List_Onth(_1710582), _1710586), _1710588))], (46146 ^ _784416) ^ [_1710648, _1710650, _1710652, _1710654] : [-(hAPP(hAPP(c_List_Otake(_1710648), _1710650), hAPP(hAPP(c_List_Oappend(_1710648), _1710652), _1710654)) = hAPP(hAPP(c_List_Oappend(_1710648), hAPP(hAPP(c_List_Otake(_1710648), _1710650), _1710652)), hAPP(hAPP(c_List_Otake(_1710648), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1710650), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710648)), _1710652))), _1710654)))], (46148 ^ _784416) ^ [_1710730, _1710732, _1710734, _1710736, _1710738] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1710730), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710732)), _1710734))), -(hAPP(hAPP(c_List_Olist__update(_1710732, hAPP(hAPP(c_List_Oappend(_1710732), _1710734), _1710736)), _1710730), _1710738) = hAPP(hAPP(c_List_Oappend(_1710732), hAPP(hAPP(c_List_Olist__update(_1710732, _1710734), _1710730), _1710738)), _1710736))], (46154 ^ _784416) ^ [_1710905, _1710907, _1710909, _1710911, _1710913] : [-(hAPP(hAPP(c_List_Olist__update(_1710905, hAPP(hAPP(c_List_Oappend(_1710905), _1710907), hAPP(hAPP(c_List_Olist_OCons(_1710905), _1710909), _1710911))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710905)), _1710907)), _1710913) = hAPP(hAPP(c_List_Oappend(_1710905), _1710907), hAPP(hAPP(c_List_Olist_OCons(_1710905), _1710913), _1710911)))], (46156 ^ _784416) ^ [_1710984, _1710986, _1710988, _1710990, _1710992, _1710994] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1710984), tc_List_Olist(_1710984))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1710984), tc_List_Olist(_1710984)), hAPP(hAPP(c_List_Oappend(_1710984), _1710986), _1710992)), hAPP(hAPP(c_List_Oappend(_1710984), _1710988), _1710994))), c_List_Olistrel1(_1710984, _1710990)))), 46157 ^ _784416 : [(46158 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1710984), tc_List_Olist(_1710984))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1710984), tc_List_Olist(_1710984)), _1710986), _1710988)), c_List_Olistrel1(_1710984, _1710990))), _1710992 = _1710994], (46164 ^ _784416) ^ [] : [_1710986 = _1710988, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1710984), tc_List_Olist(_1710984))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1710984), tc_List_Olist(_1710984)), _1710992), _1710994)), c_List_Olistrel1(_1710984, _1710990)))]]], (46172 ^ _784416) ^ [_1711432, _1711434, _1711436, _1711438, _1711440] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711432), tc_List_Olist(_1711432))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711432), tc_List_Olist(_1711432)), _1711434), _1711436)), c_List_Olexord(_1711432, _1711438))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1711432), tc_List_Olist(_1711432))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1711432), tc_List_Olist(_1711432)), hAPP(hAPP(c_List_Oappend(_1711432), _1711440), _1711434)), hAPP(hAPP(c_List_Oappend(_1711432), _1711440), _1711436))), c_List_Olexord(_1711432, _1711438))))], (46178 ^ _784416) ^ [_1711685, _1711687, _1711689] : [hBOOL(hAPP(c_List_Odistinct(_1711685), hAPP(hAPP(c_List_Oappend(_1711685), _1711687), _1711689))), 46181 ^ _784416 : [(46182 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1711685), _1711687)))], (46184 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1711685), _1711689)))], (46186 ^ _784416) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1711685, tc_HOL_Obool)), hAPP(c_List_Oset(_1711685), _1711687)), hAPP(c_List_Oset(_1711685), _1711689)) = c_Orderings_Obot__class_Obot(tc_fun(_1711685, tc_HOL_Obool)))]]], (46188 ^ _784416) ^ [_1711902, _1711904, _1711906] : [-(hBOOL(hAPP(c_List_Odistinct(_1711902), hAPP(hAPP(c_List_Oappend(_1711902), _1711904), _1711906)))), hBOOL(hAPP(c_List_Odistinct(_1711902), _1711904)), hBOOL(hAPP(c_List_Odistinct(_1711902), _1711906)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1711902, tc_HOL_Obool)), hAPP(c_List_Oset(_1711902), _1711904)), hAPP(c_List_Oset(_1711902), _1711906)) = c_Orderings_Obot__class_Obot(tc_fun(_1711902, tc_HOL_Obool))], (46202 ^ _784416) ^ [_1712198, _1712200, _1712202, _1712204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712198), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712200)), _1712202))), -(hAPP(hAPP(c_List_Onth(_1712200), hAPP(hAPP(c_List_Oappend(_1712200), _1712202), _1712204)), _1712198) = hAPP(hAPP(c_List_Onth(_1712200), _1712202), _1712198))], (46208 ^ _784416) ^ [_1712345, _1712347, _1712349, _1712351] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712345), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712347)), _1712349)))), -(hAPP(hAPP(c_List_Onth(_1712347), hAPP(hAPP(c_List_Oappend(_1712347), _1712349), _1712351)), _1712345) = hAPP(hAPP(c_List_Onth(_1712347), _1712351), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1712345), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712347)), _1712349))))], (46214 ^ _784416) ^ [_1712454, _1712456, _1712458, _1712460, _1712462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712454), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712456)), _1712458))), -(hAPP(hAPP(c_List_Olist__update(_1712456, hAPP(hAPP(c_List_Oappend(_1712456), _1712458), _1712460)), _1712454), _1712462) = hAPP(hAPP(c_List_Oappend(_1712456), hAPP(hAPP(c_List_Olist__update(_1712456, _1712458), _1712454), _1712462)), _1712460))], (46220 ^ _784416) ^ [_1712623, _1712625, _1712627, _1712629, _1712631] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712623), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712625)), _1712627)))), -(hAPP(hAPP(c_List_Olist__update(_1712625, hAPP(hAPP(c_List_Oappend(_1712625), _1712627), _1712629)), _1712623), _1712631) = hAPP(hAPP(c_List_Oappend(_1712625), _1712627), hAPP(hAPP(c_List_Olist__update(_1712625, _1712629), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1712623), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712625)), _1712627))), _1712631)))], (46226 ^ _784416) ^ [_1712726, _1712728, _1712730, _1712732, _1712734] : [-(c_Enum_Oproduct(_1712726, _1712728, hAPP(hAPP(c_List_Olist_OCons(_1712726), _1712730), _1712732), _1712734) = hAPP(hAPP(c_List_Oappend(tc_prod(_1712726, _1712728)), hAPP(hAPP(c_List_Omap(_1712728, tc_prod(_1712726, _1712728)), hAPP(c_Product__Type_OPair(_1712726, _1712728), _1712730)), _1712734)), c_Enum_Oproduct(_1712726, _1712728, _1712732, _1712734)))], (46228 ^ _784416) ^ [_1712804, _1712806, _1712808, _1712810] : [-(c_List_Osublist(_1712804, hAPP(hAPP(c_List_Oappend(_1712804), _1712806), _1712808), _1712810) = hAPP(hAPP(c_List_Oappend(_1712804), c_List_Osublist(_1712804, _1712806, _1712810)), c_List_Osublist(_1712804, _1712808, 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(_1712804)), _1712806)))), _1712810)))))], (46230 ^ _784416) ^ [_1712883, _1712885, _1712887, _1712889, _1712891, _1712893, _1712895, _1712897] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1712883, _1712883)), hAPP(hAPP(c_Product__Type_OPair(_1712883, _1712883), _1712885), _1712887)), _1712889)), _1712891 = hAPP(hAPP(c_List_Oappend(_1712883), _1712893), hAPP(hAPP(c_List_Olist_OCons(_1712883), _1712885), _1712895)), _1712897 = hAPP(hAPP(c_List_Oappend(_1712883), _1712893), hAPP(hAPP(c_List_Olist_OCons(_1712883), _1712887), _1712895)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1712883), tc_List_Olist(_1712883))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1712883), tc_List_Olist(_1712883)), _1712891), _1712897)), c_List_Olistrel1(_1712883, _1712889))))], (46244 ^ _784416) ^ [_1713262, _1713264, _1713266, _1713268, _1713270, _1713272, _1713274] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1713262, _1713262)), hAPP(hAPP(c_Product__Type_OPair(_1713262, _1713262), _1713264), _1713266)), _1713268)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713262), tc_List_Olist(_1713262))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713262), tc_List_Olist(_1713262)), hAPP(hAPP(c_List_Oappend(_1713262), _1713270), hAPP(hAPP(c_List_Olist_OCons(_1713262), _1713264), _1713272))), hAPP(hAPP(c_List_Oappend(_1713262), _1713270), hAPP(hAPP(c_List_Olist_OCons(_1713262), _1713266), _1713274)))), c_List_Olexord(_1713262, _1713268))))], (46250 ^ _784416) ^ [_1713511, _1713513, _1713515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713511), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713513)), _1713515))), -(hAPP(hAPP(c_List_Otake(_1713513), hAPP(c_Nat_OSuc, _1713511)), _1713515) = hAPP(hAPP(c_List_Oappend(_1713513), hAPP(hAPP(c_List_Otake(_1713513), _1713511), _1713515)), hAPP(hAPP(c_List_Olist_OCons(_1713513), hAPP(hAPP(c_List_Onth(_1713513), _1713515), _1713511)), c_List_Olist_ONil(_1713513))))], (46256 ^ _784416) ^ [_1713731, _1713733, _1713735, _1713737, _1713739, _1713741] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713731), tc_List_Olist(_1713731))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713731), tc_List_Olist(_1713731)), hAPP(hAPP(c_List_Oappend(_1713731), _1713733), hAPP(hAPP(c_List_Olist_OCons(_1713731), _1713735), c_List_Olist_ONil(_1713731)))), hAPP(hAPP(c_List_Oappend(_1713731), _1713737), hAPP(hAPP(c_List_Olist_OCons(_1713731), _1713739), c_List_Olist_ONil(_1713731))))), c_List_Olistrel1(_1713731, _1713741))), 46261 ^ _784416 : [(46262 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1713731), tc_List_Olist(_1713731))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713731), tc_List_Olist(_1713731)), _1713733), _1713737)), c_List_Olistrel1(_1713731, _1713741))))], (46264 ^ _784416) ^ [] : [-(_1713735 = _1713739)]], 46265 ^ _784416 : [(46266 ^ _784416) ^ [] : [-(_1713733 = _1713737)], (46268 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1713731, _1713731)), hAPP(hAPP(c_Product__Type_OPair(_1713731, _1713731), _1713735), _1713739)), _1713741)))]]], (46270 ^ _784416) ^ [_1714141, _1714143, _1714145, _1714147, _1714149, _1714151] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714141), tc_List_Olist(_1714141))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714141), tc_List_Olist(_1714141)), hAPP(hAPP(c_List_Oappend(_1714141), _1714143), hAPP(hAPP(c_List_Olist_OCons(_1714141), _1714145), c_List_Olist_ONil(_1714141)))), hAPP(hAPP(c_List_Oappend(_1714141), _1714147), hAPP(hAPP(c_List_Olist_OCons(_1714141), _1714149), c_List_Olist_ONil(_1714141))))), c_List_Olistrel1(_1714141, _1714151)))), 46271 ^ _784416 : [(46272 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714141), tc_List_Olist(_1714141))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714141), tc_List_Olist(_1714141)), _1714143), _1714147)), c_List_Olistrel1(_1714141, _1714151))), _1714145 = _1714149], (46278 ^ _784416) ^ [] : [_1714143 = _1714147, hBOOL(hAPP(hAPP(c_member(tc_prod(_1714141, _1714141)), hAPP(hAPP(c_Product__Type_OPair(_1714141, _1714141), _1714145), _1714149)), _1714151))]]], (46286 ^ _784416) ^ [_1714609, _1714611, _1714613, _1714615] : [-(c_List_Osublist(_1714609, hAPP(hAPP(c_List_Olist_OCons(_1714609), _1714611), _1714613), _1714615) = hAPP(hAPP(c_List_Oappend(_1714609), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1714609)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1714615)), hAPP(hAPP(c_List_Olist_OCons(_1714609), _1714611), c_List_Olist_ONil(_1714609))), c_List_Olist_ONil(_1714609))), c_List_Osublist(_1714609, _1714613, 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)), _1714615)))))], (46288 ^ _784416) ^ [_1714696, _1714698, _1714700, _1714702] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1714696), tc_List_Olist(_1714696))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714696), tc_List_Olist(_1714696)), _1714698), _1714700)), c_List_Olistrel1(_1714696, _1714702))), 46293 ^ _784416 : [(46294 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1714696, _1714696)), hAPP(hAPP(c_Product__Type_OPair(_1714696, _1714696), 46291 ^ [_1714696, _1714698, _1714700, _1714702]), 46292 ^ [_1714696, _1714698, _1714700, _1714702])), _1714702)))], (46298 ^ _784416) ^ [] : [-(_1714698 = hAPP(hAPP(c_List_Oappend(_1714696), 46295 ^ [_1714696, _1714698, _1714700, _1714702]), hAPP(hAPP(c_List_Olist_OCons(_1714696), 46291 ^ [_1714696, _1714698, _1714700, _1714702]), 46296 ^ [_1714696, _1714698, _1714700, _1714702])))], (46300 ^ _784416) ^ [] : [-(_1714700 = hAPP(hAPP(c_List_Oappend(_1714696), 46295 ^ [_1714696, _1714698, _1714700, _1714702]), hAPP(hAPP(c_List_Olist_OCons(_1714696), 46292 ^ [_1714696, _1714698, _1714700, _1714702]), 46296 ^ [_1714696, _1714698, _1714700, _1714702])))]]], (46302 ^ _784416) ^ [_1715101, _1715103, _1715105, _1715107, _1715109] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1715101), tc_List_Olist(_1715101))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1715101), tc_List_Olist(_1715101)), hAPP(hAPP(c_List_Oappend(_1715101), _1715103), _1715105)), hAPP(hAPP(c_List_Oappend(_1715101), _1715103), _1715107))), c_List_Olexord(_1715101, _1715109))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1715101, _1715101)), hAPP(hAPP(c_Product__Type_OPair(_1715101, _1715101), 46307 ^ [_1715101, _1715103, _1715105, _1715107, _1715109]), 46307 ^ [_1715101, _1715103, _1715105, _1715107, _1715109])), _1715109))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1715101), tc_List_Olist(_1715101))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1715101), tc_List_Olist(_1715101)), _1715105), _1715107)), c_List_Olexord(_1715101, _1715109))))], (46313 ^ _784416) ^ [_1715420, _1715422] : [-(hAPP(c_List_Orotate1(_1715420), _1715422) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1715420), _1715420, c_List_Olist_ONil(_1715420), hAPP(hAPP(c_COMBB(tc_List_Olist(_1715420), tc_fun(tc_List_Olist(_1715420), tc_List_Olist(_1715420)), _1715420), hAPP(c_COMBC(tc_List_Olist(_1715420), tc_List_Olist(_1715420), tc_List_Olist(_1715420)), c_List_Oappend(_1715420))), hAPP(hAPP(c_COMBC(_1715420, tc_List_Olist(_1715420), tc_List_Olist(_1715420)), c_List_Olist_OCons(_1715420)), c_List_Olist_ONil(_1715420)))), _1715422))], (46315 ^ _784416) ^ [_1715514, _1715516, _1715518, _1715520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1715514), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715516)), _1715518))), -(hAPP(hAPP(c_List_Olist__update(_1715516, _1715518), _1715514), _1715520) = hAPP(hAPP(c_List_Oappend(_1715516), hAPP(hAPP(c_List_Otake(_1715516), _1715514), _1715518)), hAPP(hAPP(c_List_Olist_OCons(_1715516), _1715520), hAPP(hAPP(c_List_Odrop(_1715516), hAPP(c_Nat_OSuc, _1715514)), _1715518))))], (46321 ^ _784416) ^ [_1715707, _1715709, _1715711] : [-(hAPP(hAPP(c_List_Oappend(_1715707), hAPP(hAPP(c_List_Otake(_1715707), _1715709), _1715711)), hAPP(hAPP(c_List_Odrop(_1715707), _1715709), _1715711)) = _1715711)], (46323 ^ _784416) ^ [_1715758, _1715760, _1715762, _1715764, _1715766] : [-(hAPP(hAPP(c_List_Odrop(_1715758), _1715760), hAPP(hAPP(c_List_Omap(_1715762, _1715758), _1715764), _1715766)) = hAPP(hAPP(c_List_Omap(_1715762, _1715758), _1715764), hAPP(hAPP(c_List_Odrop(_1715762), _1715760), _1715766)))], (46325 ^ _784416) ^ [_1715838, _1715840] : [hAPP(c_List_Orotate1(_1715838), _1715840) = c_List_Olist_ONil(_1715838), -(_1715840 = c_List_Olist_ONil(_1715838))], (46331 ^ _784416) ^ [_1715929, _1715931] : [_1715931 = c_List_Olist_ONil(_1715929), -(hAPP(c_List_Orotate1(_1715929), _1715931) = c_List_Olist_ONil(_1715929))], (46337 ^ _784416) ^ [_1716026, _1716028] : [-(hAPP(hAPP(c_List_Odrop(_1716026), _1716028), c_List_Olist_ONil(_1716026)) = c_List_Olist_ONil(_1716026))], (46339 ^ _784416) ^ [_1716063, _1716065, _1716067] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1716063, tc_HOL_Obool)), hAPP(c_List_Oset(_1716063), hAPP(hAPP(c_List_Odrop(_1716063), _1716065), _1716067))), hAPP(c_List_Oset(_1716063), _1716067))))], (46341 ^ _784416) ^ [_1716118, _1716120] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716118)), hAPP(c_List_Orotate1(_1716118), _1716120)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716118)), _1716120))], (46343 ^ _784416) ^ [_1716162, _1716164, _1716166] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716162)), hAPP(hAPP(c_List_Odrop(_1716162), _1716164), _1716166)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716162)), _1716166)), _1716164))], (46345 ^ _784416) ^ [_1716232, _1716234] : [hBOOL(hAPP(c_List_Odistinct(_1716232), hAPP(c_List_Orotate1(_1716232), _1716234))), -(hBOOL(hAPP(c_List_Odistinct(_1716232), _1716234)))], (46351 ^ _784416) ^ [_1716331, _1716333] : [hBOOL(hAPP(c_List_Odistinct(_1716331), _1716333)), -(hBOOL(hAPP(c_List_Odistinct(_1716331), hAPP(c_List_Orotate1(_1716331), _1716333))))], (46357 ^ _784416) ^ [_1716436, _1716438, _1716440] : [hBOOL(hAPP(c_List_Odistinct(_1716436), _1716438)), -(hBOOL(hAPP(c_List_Odistinct(_1716436), hAPP(hAPP(c_List_Odrop(_1716436), _1716440), _1716438))))], (46363 ^ _784416) ^ [_1716547, _1716549, _1716551, _1716553] : [-(hAPP(hAPP(c_List_Odrop(_1716547), _1716549), hAPP(hAPP(c_List_Odrop(_1716547), _1716551), _1716553)) = hAPP(hAPP(c_List_Odrop(_1716547), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1716549), _1716551)), _1716553))], (46365 ^ _784416) ^ [_1716606, _1716608] : [-(hAPP(hAPP(c_List_Odrop(_1716606), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1716608) = _1716608)], (46367 ^ _784416) ^ [_1716639, _1716641] : [-(hAPP(c_List_Oset(_1716639), hAPP(c_List_Orotate1(_1716639), _1716641)) = hAPP(c_List_Oset(_1716639), _1716641))], (46369 ^ _784416) ^ [_1716679, _1716681, _1716683, _1716685] : [hBOOL(hAPP(hAPP(c_member(_1716679), _1716681), hAPP(c_List_Oset(_1716679), hAPP(hAPP(c_List_Odrop(_1716679), _1716683), _1716685)))), -(hBOOL(hAPP(hAPP(c_member(_1716679), _1716681), hAPP(c_List_Oset(_1716679), _1716685))))], (46375 ^ _784416) ^ [_1716824, _1716826, _1716828, _1716830, _1716832] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1716824, _1716826)), _1716828), hAPP(hAPP(c_List_Ozip(_1716824, _1716826), _1716830), _1716832)) = hAPP(hAPP(c_List_Ozip(_1716824, _1716826), hAPP(hAPP(c_List_Odrop(_1716824), _1716828), _1716830)), hAPP(hAPP(c_List_Odrop(_1716826), _1716828), _1716832)))], (46377 ^ _784416) ^ [_1716900, _1716902, _1716904, _1716906] : [-(hAPP(hAPP(c_List_Otake(_1716900), _1716902), hAPP(hAPP(c_List_Odrop(_1716900), _1716904), _1716906)) = hAPP(hAPP(c_List_Odrop(_1716900), _1716904), hAPP(hAPP(c_List_Otake(_1716900), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1716902), _1716904)), _1716906)))], (46379 ^ _784416) ^ [_1716967, _1716969, _1716971, _1716973] : [-(hAPP(hAPP(c_List_Odrop(_1716967), _1716969), hAPP(hAPP(c_List_Otake(_1716967), _1716971), _1716973)) = hAPP(hAPP(c_List_Otake(_1716967), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1716971), _1716969)), hAPP(hAPP(c_List_Odrop(_1716967), _1716969), _1716973)))], (46381 ^ _784416) ^ [_1717034, _1717036, _1717038, _1717040, _1717042] : [hAPP(hAPP(c_List_Odrop(_1717034), _1717036), _1717038) = hAPP(hAPP(c_List_Olist_OCons(_1717034), _1717040), _1717042), -(hAPP(hAPP(c_List_Onth(_1717034), _1717038), _1717036) = _1717040)], (46387 ^ _784416) ^ [_1717165, _1717167, _1717169] : [-(hAPP(hAPP(c_List_Odrop(_1717165), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1717165), _1717167), _1717169)) = _1717169)], (46389 ^ _784416) ^ [_1717208, _1717210, _1717212, _1717214] : [-(hAPP(hAPP(c_List_Odrop(_1717208), hAPP(c_Nat_OSuc, _1717210)), hAPP(hAPP(c_List_Olist_OCons(_1717208), _1717212), _1717214)) = hAPP(hAPP(c_List_Odrop(_1717208), _1717210), _1717214))], (46391 ^ _784416) ^ [_1717264, _1717266, _1717268, _1717270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1717264), _1717266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1717268, tc_HOL_Obool)), hAPP(c_List_Oset(_1717268), hAPP(hAPP(c_List_Odrop(_1717268), _1717266), _1717270))), hAPP(c_List_Oset(_1717268), hAPP(hAPP(c_List_Odrop(_1717268), _1717264), _1717270)))))], (46397 ^ _784416) ^ [_1717427, _1717429, _1717431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717427)), _1717429)), _1717431)), -(hAPP(hAPP(c_List_Odrop(_1717427), _1717431), _1717429) = c_List_Olist_ONil(_1717427))], (46403 ^ _784416) ^ [_1717568, _1717570, _1717572] : [hAPP(hAPP(c_List_Odrop(_1717568), _1717570), _1717572) = c_List_Olist_ONil(_1717568), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717568)), _1717572)), _1717570)))], (46409 ^ _784416) ^ [_1717687, _1717689, _1717691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717687)), _1717691)), _1717689)), -(hAPP(hAPP(c_List_Odrop(_1717687), _1717689), _1717691) = c_List_Olist_ONil(_1717687))], (46415 ^ _784416) ^ [_1717812, _1717814, _1717816, _1717818] : [-(hAPP(hAPP(c_List_Odrop(_1717812), _1717814), hAPP(hAPP(c_List_Oappend(_1717812), _1717816), _1717818)) = hAPP(hAPP(c_List_Oappend(_1717812), hAPP(hAPP(c_List_Odrop(_1717812), _1717814), _1717816)), hAPP(hAPP(c_List_Odrop(_1717812), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1717814), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717812)), _1717816))), _1717818)))], (46417 ^ _784416) ^ [_1717915, _1717917, _1717919, _1717921] : [hAPP(hAPP(c_List_Oappend(_1717915), _1717917), _1717919) = _1717921, 46420 ^ _784416 : [(46421 ^ _784416) ^ [] : [-(_1717917 = hAPP(hAPP(c_List_Otake(_1717915), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717915)), _1717917)), _1717921))], (46423 ^ _784416) ^ [] : [-(_1717919 = hAPP(hAPP(c_List_Odrop(_1717915), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717915)), _1717917)), _1717921))]]], (46425 ^ _784416) ^ [_1718094, _1718096, _1718098, _1718100] : [-(hAPP(hAPP(c_List_Oappend(_1718094), _1718096), _1718098) = _1718100), _1718096 = hAPP(hAPP(c_List_Otake(_1718094), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718094)), _1718096)), _1718100), _1718098 = hAPP(hAPP(c_List_Odrop(_1718094), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718094)), _1718096)), _1718100)], (46435 ^ _784416) ^ [_1718309, _1718311, _1718313, _1718315] : [-(hAPP(hAPP(c_List_Odrop(_1718309), _1718311), hAPP(hAPP(c_List_Olist_OCons(_1718309), _1718313), _1718315)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1718309), hAPP(hAPP(c_List_Olist_OCons(_1718309), _1718313), _1718315), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1718309), tc_List_Olist(_1718309)), c_List_Odrop(_1718309)), _1718315), _1718311))], (46437 ^ _784416) ^ [_1718400, _1718402, _1718404, _1718406] : [_1718400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1718402), _1718400), hAPP(hAPP(c_List_Olist_OCons(_1718402), _1718404), _1718406)) = hAPP(hAPP(c_List_Olist_OCons(_1718402), _1718404), _1718406))], (46443 ^ _784416) ^ [_1718523, _1718525, _1718527, _1718529] : [-(_1718523 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1718525), _1718523), hAPP(hAPP(c_List_Olist_OCons(_1718525), _1718527), _1718529)) = hAPP(hAPP(c_List_Odrop(_1718525), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1718523), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1718529))], (46449 ^ _784416) ^ [_1718595, _1718597, _1718599, _1718601] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1718595), _1718597)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718599)), _1718601))), -(hAPP(hAPP(c_List_Onth(_1718599), hAPP(hAPP(c_List_Odrop(_1718599), _1718595), _1718601)), _1718597) = hAPP(hAPP(c_List_Onth(_1718599), _1718601), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1718595), _1718597)))], (46455 ^ _784416) ^ [_1718796, _1718798, _1718800, _1718802, _1718804] : [hAPP(hAPP(c_List_Oappend(_1718796), _1718798), _1718800) = hAPP(hAPP(c_List_Oappend(_1718796), _1718802), _1718804), 46458 ^ _784416 : [(46459 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718796)), _1718798)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718796)), _1718802))), 46462 ^ _784416 : [(46463 ^ _784416) ^ [] : [-(_1718798 = hAPP(hAPP(c_List_Otake(_1718796), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718796)), _1718798)), _1718802))], (46465 ^ _784416) ^ [] : [-(_1718800 = hAPP(hAPP(c_List_Oappend(_1718796), hAPP(hAPP(c_List_Odrop(_1718796), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718796)), _1718798)), _1718802)), _1718804))]]], (46467 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718796)), _1718798)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718796)), _1718802)))), 46470 ^ _784416 : [(46471 ^ _784416) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1718796), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718796)), _1718802)), _1718798) = _1718802)], (46473 ^ _784416) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1718796), hAPP(hAPP(c_List_Odrop(_1718796), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718796)), _1718802)), _1718798)), _1718800) = _1718804)]]]]], (46475 ^ _784416) ^ [_1719309, _1719311, _1719313, _1719315, _1719317] : [-(hAPP(hAPP(c_List_Oappend(_1719309), _1719311), _1719313) = hAPP(hAPP(c_List_Oappend(_1719309), _1719315), _1719317)), 46478 ^ _784416 : [(46479 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719309)), _1719311)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719309)), _1719315))))], (46481 ^ _784416) ^ [] : [_1719311 = hAPP(hAPP(c_List_Otake(_1719309), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719309)), _1719311)), _1719315), _1719313 = hAPP(hAPP(c_List_Oappend(_1719309), hAPP(hAPP(c_List_Odrop(_1719309), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719309)), _1719311)), _1719315)), _1719317)]], 46486 ^ _784416 : [(46487 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719309)), _1719311)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719309)), _1719315)))], (46489 ^ _784416) ^ [] : [hAPP(hAPP(c_List_Otake(_1719309), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719309)), _1719315)), _1719311) = _1719315, hAPP(hAPP(c_List_Oappend(_1719309), hAPP(hAPP(c_List_Odrop(_1719309), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719309)), _1719315)), _1719311)), _1719313) = _1719317]]], (46497 ^ _784416) ^ [_1719897, _1719899, _1719901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719897), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719899)), _1719901))), -(hAPP(hAPP(c_List_Olist_OCons(_1719899), hAPP(hAPP(c_List_Onth(_1719899), _1719901), _1719897)), hAPP(hAPP(c_List_Odrop(_1719899), hAPP(c_Nat_OSuc, _1719897)), _1719901)) = hAPP(hAPP(c_List_Odrop(_1719899), _1719897), _1719901))], (46503 ^ _784416) ^ [_1720068, _1720070, _1720072, _1720074] : [-(hAPP(c_List_Orotate1(_1720068), c_List_Olist_ONil(_1720068)) = c_List_Olist_ONil(_1720068))], (46505 ^ _784416) ^ [_1720103, _1720105, _1720107, _1720109] : [-(hAPP(c_List_Orotate1(_1720105), hAPP(hAPP(c_List_Olist_OCons(_1720105), _1720107), _1720109)) = hAPP(hAPP(c_List_Oappend(_1720105), _1720109), hAPP(hAPP(c_List_Olist_OCons(_1720105), _1720107), c_List_Olist_ONil(_1720105))))], (46507 ^ _784416) ^ [_1720180, _1720182, _1720184, _1720186] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1720180) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1720182), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1720180)), hAPP(hAPP(c_List_Olist_OCons(_1720182), _1720184), _1720186)) = hAPP(hAPP(c_List_Olist_OCons(_1720182), _1720184), _1720186))], (46513 ^ _784416) ^ [_1720315, _1720317, _1720319, _1720321] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1720315) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1720317), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1720315)), hAPP(hAPP(c_List_Olist_OCons(_1720317), _1720319), _1720321)) = hAPP(hAPP(c_List_Odrop(_1720317), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1720315)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1720321))], (46519 ^ _784416) ^ [_1720396, _1720398, _1720400, _1720402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1720396), _1720398)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720400)), _1720402))), -(hAPP(hAPP(c_List_Otake(_1720400), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1720396), _1720398)), _1720402) = hAPP(hAPP(c_List_Oappend(_1720400), hAPP(hAPP(c_List_Otake(_1720400), _1720396), _1720402)), hAPP(hAPP(c_List_Otake(_1720400), _1720398), hAPP(hAPP(c_List_Odrop(_1720400), _1720396), _1720402))))], (46525 ^ _784416) ^ [_1720605, _1720607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720605)), _1720607)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1720605), _1720607) = _1720607)], (46531 ^ _784416) ^ [_1720716, _1720718, _1720720, _1720722, _1720724] : [-(hAPP(hAPP(c_List_Ozip(_1720716, _1720718), _1720720), hAPP(hAPP(c_List_Oappend(_1720718), _1720722), _1720724)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1720716, _1720718)), hAPP(hAPP(c_List_Ozip(_1720716, _1720718), hAPP(hAPP(c_List_Otake(_1720716), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720718)), _1720722)), _1720720)), _1720722)), hAPP(hAPP(c_List_Ozip(_1720716, _1720718), hAPP(hAPP(c_List_Odrop(_1720716), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720718)), _1720722)), _1720720)), _1720724)))], (46533 ^ _784416) ^ [_1720823, _1720825, _1720827, _1720829, _1720831] : [-(hAPP(hAPP(c_List_Ozip(_1720823, _1720825), hAPP(hAPP(c_List_Oappend(_1720823), _1720827), _1720829)), _1720831) = hAPP(hAPP(c_List_Oappend(tc_prod(_1720823, _1720825)), hAPP(hAPP(c_List_Ozip(_1720823, _1720825), _1720827), hAPP(hAPP(c_List_Otake(_1720825), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720823)), _1720827)), _1720831))), hAPP(hAPP(c_List_Ozip(_1720823, _1720825), _1720829), hAPP(hAPP(c_List_Odrop(_1720825), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720823)), _1720827)), _1720831))))], (46535 ^ _784416) ^ [_1720930, _1720932, _1720934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1720930), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720932)), _1720934))), -(_1720934 = hAPP(hAPP(c_List_Oappend(_1720932), hAPP(hAPP(c_List_Otake(_1720932), _1720930), _1720934)), hAPP(hAPP(c_List_Olist_OCons(_1720932), hAPP(hAPP(c_List_Onth(_1720932), _1720934), _1720930)), hAPP(hAPP(c_List_Odrop(_1720932), hAPP(c_Nat_OSuc, _1720930)), _1720934))))], (46541 ^ _784416) ^ [_1721119, _1721121, _1721123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721119), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721121)), _1721123))), -(hAPP(hAPP(c_List_Oappend(_1721121), hAPP(hAPP(c_List_Otake(_1721121), _1721119), _1721123)), hAPP(hAPP(c_List_Olist_OCons(_1721121), hAPP(c_List_Ohd(_1721121), hAPP(hAPP(c_List_Odrop(_1721121), _1721119), _1721123))), c_List_Olist_ONil(_1721121))) = hAPP(hAPP(c_List_Otake(_1721121), hAPP(c_Nat_OSuc, _1721119)), _1721123))], (46547 ^ _784416) ^ [_1721321, _1721323, _1721325] : [-(_1721321 = c_List_Olist_ONil(_1721323)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721325), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721323)), _1721321))), -(hAPP(c_List_Ohd(_1721323), hAPP(hAPP(c_List_Odrop(_1721323), _1721325), _1721321)) = hAPP(hAPP(c_List_Onth(_1721323), _1721321), _1721325))], (46557 ^ _784416) ^ [_1721520, _1721522, _1721524] : [-(hAPP(c_List_Ohd(_1721520), hAPP(hAPP(c_List_Olist_OCons(_1721520), _1721522), _1721524)) = _1721522)], (46559 ^ _784416) ^ [_1721556, _1721558, _1721560, _1721562] : [-(_1721556 = c_List_Olist_ONil(_1721558)), -(hAPP(c_List_Ohd(_1721560), hAPP(hAPP(c_List_Omap(_1721558, _1721560), _1721562), _1721556)) = hAPP(_1721562, hAPP(c_List_Ohd(_1721558), _1721556)))], (46565 ^ _784416) ^ [_1721632, _1721634, _1721636] : [_1721632 = c_List_Olist_ONil(_1721634), -(hAPP(c_List_Ohd(_1721634), hAPP(hAPP(c_List_Oappend(_1721634), _1721632), _1721636)) = hAPP(c_List_Ohd(_1721634), _1721636))], (46571 ^ _784416) ^ [_1721745, _1721747, _1721749] : [-(_1721745 = c_List_Olist_ONil(_1721747)), -(hAPP(c_List_Ohd(_1721747), hAPP(hAPP(c_List_Oappend(_1721747), _1721745), _1721749)) = hAPP(c_List_Ohd(_1721747), _1721745))], (46577 ^ _784416) ^ [_1721801, _1721803, _1721805] : [-(_1721801 = c_List_Olist_ONil(_1721803)), -(hAPP(c_List_Ohd(_1721803), hAPP(hAPP(c_List_Oappend(_1721803), _1721801), _1721805)) = hAPP(c_List_Ohd(_1721803), _1721801))], (46583 ^ _784416) ^ [_1721855, _1721857] : [-(_1721855 = c_List_Olist_ONil(_1721857)), -(hBOOL(hAPP(hAPP(c_member(_1721857), hAPP(c_List_Ohd(_1721857), _1721855)), hAPP(c_List_Oset(_1721857), _1721855))))], (46589 ^ _784416) ^ [_1721906, _1721908] : [-(_1721906 = c_List_Olist_ONil(_1721908)), -(hAPP(c_List_Ohd(_1721908), _1721906) = hAPP(hAPP(c_List_Onth(_1721908), _1721906), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (46595 ^ _784416) ^ [_1721953, _1721955] : [-(_1721953 = c_List_Olist_ONil(_1721955)), -(hAPP(c_List_Orotate1(_1721955), _1721953) = hAPP(hAPP(c_List_Oappend(_1721955), hAPP(c_List_Otl(_1721955), _1721953)), hAPP(hAPP(c_List_Olist_OCons(_1721955), hAPP(c_List_Ohd(_1721955), _1721953)), c_List_Olist_ONil(_1721955))))], (46601 ^ _784416) ^ [_1722020, _1722022, _1722024] : [-(_1722020 = c_List_Olist_ONil(_1722022)), -(hAPP(c_List_Ohd(_1722022), hAPP(c_List_Orotate(_1722022, _1722024), _1722020)) = hAPP(hAPP(c_List_Onth(_1722022), _1722020), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1722024, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722022)), _1722020))))], (46607 ^ _784416) ^ [_1722090, _1722092, _1722094] : [-(hAPP(c_List_Otl(_1722090), hAPP(hAPP(c_List_Odrop(_1722090), _1722092), _1722094)) = hAPP(hAPP(c_List_Odrop(_1722090), _1722092), hAPP(c_List_Otl(_1722090), _1722094)))], (46609 ^ _784416) ^ [_1722143, _1722145, _1722147] : [-(hAPP(hAPP(c_List_Odrop(_1722143), _1722145), hAPP(c_List_Otl(_1722143), _1722147)) = hAPP(c_List_Otl(_1722143), hAPP(hAPP(c_List_Odrop(_1722143), _1722145), _1722147)))], (46611 ^ _784416) ^ [_1722196, _1722198, _1722200] : [-(hAPP(c_List_Orotate(_1722196, _1722198), _1722200) = hAPP(c_List_Orotate(_1722196, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1722198, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722196)), _1722200))), _1722200))], (46613 ^ _784416) ^ [_1722246, _1722248, _1722250] : [-(hAPP(hAPP(c_List_Odrop(_1722246), hAPP(c_Nat_OSuc, _1722248)), _1722250) = hAPP(hAPP(c_List_Odrop(_1722246), _1722248), hAPP(c_List_Otl(_1722246), _1722250)))], (46615 ^ _784416) ^ [_1722293, _1722295, _1722297] : [-(_1722293 = c_List_Olist_ONil(_1722295)), -(hAPP(c_List_Otl(_1722295), hAPP(hAPP(c_List_Oappend(_1722295), _1722293), _1722297)) = hAPP(hAPP(c_List_Oappend(_1722295), hAPP(c_List_Otl(_1722295), _1722293)), _1722297))], (46621 ^ _784416) ^ [_1722359, _1722361, _1722363, _1722365, _1722367] : [-(hAPP(c_List_Orotate(_1722359, _1722361), hAPP(hAPP(c_List_Omap(_1722363, _1722359), _1722365), _1722367)) = hAPP(hAPP(c_List_Omap(_1722363, _1722359), _1722365), hAPP(c_List_Orotate(_1722363, _1722361), _1722367)))], (46623 ^ _784416) ^ [_1722420, _1722422, _1722424, _1722426] : [-(hAPP(hAPP(c_List_Omap(_1722420, _1722422), _1722424), hAPP(c_List_Otl(_1722420), _1722426)) = hAPP(c_List_Otl(_1722422), hAPP(hAPP(c_List_Omap(_1722420, _1722422), _1722424), _1722426)))], (46625 ^ _784416) ^ [_1722495, _1722497, _1722499] : [hAPP(c_List_Orotate(_1722495, _1722497), _1722499) = c_List_Olist_ONil(_1722495), -(_1722499 = c_List_Olist_ONil(_1722495))], (46631 ^ _784416) ^ [_1722590, _1722592, _1722594] : [_1722594 = c_List_Olist_ONil(_1722590), -(hAPP(c_List_Orotate(_1722590, _1722592), _1722594) = c_List_Olist_ONil(_1722590))], (46637 ^ _784416) ^ [_1722691] : [-(hAPP(c_List_Otl(_1722691), c_List_Olist_ONil(_1722691)) = c_List_Olist_ONil(_1722691))], (46639 ^ _784416) ^ [_1722723, _1722725, _1722727] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722723)), hAPP(c_List_Orotate(_1722723, _1722725), _1722727)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722723)), _1722727))], (46641 ^ _784416) ^ [_1722788, _1722790, _1722792] : [hBOOL(hAPP(c_List_Odistinct(_1722788), hAPP(c_List_Orotate(_1722788, _1722790), _1722792))), -(hBOOL(hAPP(c_List_Odistinct(_1722788), _1722792)))], (46647 ^ _784416) ^ [_1722891, _1722893, _1722895] : [hBOOL(hAPP(c_List_Odistinct(_1722891), _1722895)), -(hBOOL(hAPP(c_List_Odistinct(_1722891), hAPP(c_List_Orotate(_1722891, _1722893), _1722895))))], (46653 ^ _784416) ^ [_1723000, _1723002] : [hBOOL(hAPP(c_List_Odistinct(_1723000), _1723002)), -(hBOOL(hAPP(c_List_Odistinct(_1723000), hAPP(c_List_Otl(_1723000), _1723002))))], (46659 ^ _784416) ^ [_1723103, _1723105, _1723107, _1723109] : [-(hAPP(c_List_Orotate(_1723103, _1723105), hAPP(c_List_Orotate(_1723103, _1723107), _1723109)) = hAPP(c_List_Orotate(_1723103, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1723105), _1723107)), _1723109))], (46661 ^ _784416) ^ [_1723156, _1723158, _1723160] : [-(hAPP(c_List_Oset(_1723156), hAPP(c_List_Orotate(_1723156, _1723158), _1723160)) = hAPP(c_List_Oset(_1723156), _1723160))], (46663 ^ _784416) ^ [_1723199, _1723201, _1723203] : [-(hAPP(c_List_Otl(_1723199), hAPP(hAPP(c_List_Olist_OCons(_1723199), _1723201), _1723203)) = _1723203)], (46665 ^ _784416) ^ [_1723239, _1723241, _1723243] : [-(hAPP(hAPP(c_List_Otake(_1723239), _1723241), hAPP(c_List_Otl(_1723239), _1723243)) = hAPP(c_List_Otl(_1723239), hAPP(hAPP(c_List_Otake(_1723239), hAPP(c_Nat_OSuc, _1723241)), _1723243)))], (46667 ^ _784416) ^ [_1723295, _1723297, _1723299] : [-(hAPP(c_List_Orotate1(_1723295), hAPP(c_List_Orotate(_1723295, _1723297), _1723299)) = hAPP(c_List_Orotate(_1723295, _1723297), hAPP(c_List_Orotate1(_1723295), _1723299)))], (46669 ^ _784416) ^ [_1723344, _1723346] : [-(c_List_Orotate(_1723344, _1723346) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1723344), tc_List_Olist(_1723344)), _1723346), c_List_Orotate1(_1723344)))], (46671 ^ _784416) ^ [_1723387, _1723389, _1723391] : [-(hAPP(c_List_Orotate(_1723387, hAPP(c_Nat_OSuc, _1723389)), _1723391) = hAPP(c_List_Orotate1(_1723387), hAPP(c_List_Orotate(_1723387, _1723389), _1723391)))], (46673 ^ _784416) ^ [_1723434, _1723436, _1723438] : [-(hAPP(c_List_Otl(_1723434), hAPP(hAPP(c_List_Oappend(_1723434), _1723436), _1723438)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1723434), _1723434, hAPP(c_List_Otl(_1723434), _1723438), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1723434), tc_List_Olist(_1723434)), _1723434), hAPP(hAPP(c_COMBC(tc_List_Olist(_1723434), tc_List_Olist(_1723434), tc_List_Olist(_1723434)), c_List_Oappend(_1723434)), _1723438))), _1723436))], (46675 ^ _784416) ^ [_1723520] : [-(c_List_Orotate(_1723520, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1723520)))], (46677 ^ _784416) ^ [_1723550, _1723552, _1723554] : [-(c_List_Orotate(_1723550, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1723552), _1723554)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1723550), tc_List_Olist(_1723550), tc_List_Olist(_1723550), c_List_Orotate(_1723550, _1723552)), c_List_Orotate(_1723550, _1723554)))], (46679 ^ _784416) ^ [_1723606, _1723608, _1723610] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1723606, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723608)), _1723610)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1723608, _1723606), _1723610) = _1723610)], (46685 ^ _784416) ^ [_1723719, _1723721, _1723723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723719)), _1723721)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1723719, _1723723), _1723721) = _1723721)], (46691 ^ _784416) ^ [_1723834, _1723836] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723834)), hAPP(c_List_Otl(_1723834), _1723836)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723834)), _1723836)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (46693 ^ _784416) ^ [_1723884, _1723886, _1723888] : [-(hAPP(c_List_Otl(_1723884), hAPP(hAPP(c_List_Otake(_1723884), _1723886), _1723888)) = hAPP(hAPP(c_List_Otake(_1723884), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1723886), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1723884), _1723888)))], (46695 ^ _784416) ^ [_1723939, _1723941, _1723943] : [-(_1723939 = c_List_Olist_ONil(_1723941)), -(hAPP(hAPP(c_List_Otake(_1723941), hAPP(c_Nat_OSuc, _1723943)), _1723939) = hAPP(hAPP(c_List_Olist_OCons(_1723941), hAPP(c_List_Ohd(_1723941), _1723939)), hAPP(hAPP(c_List_Otake(_1723941), _1723943), hAPP(c_List_Otl(_1723941), _1723939))))], (46701 ^ _784416) ^ [_1724016, _1724018, _1724020] : [-(hAPP(c_List_Orotate(_1724016, _1724018), _1724020) = hAPP(hAPP(c_List_Oappend(_1724016), hAPP(hAPP(c_List_Odrop(_1724016), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1724018, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724016)), _1724020))), _1724020)), hAPP(hAPP(c_List_Otake(_1724016), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1724018, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724016)), _1724020))), _1724020)))], (46703 ^ _784416) ^ [_1724095, _1724097] : [class_Lattices_Oab__semigroup__idem__mult(_1724095), -(_1724097 = c_List_Olist_ONil(_1724095)), -(hAPP(c_Finite__Set_Ofold1(_1724095, c_Groups_Otimes__class_Otimes(_1724095)), hAPP(c_List_Oset(_1724095), _1724097)) = hAPP(c_List_Ofoldl(_1724095, _1724095, c_Groups_Otimes__class_Otimes(_1724095), hAPP(c_List_Ohd(_1724095), _1724097)), hAPP(c_List_Otl(_1724095), _1724097)))], (46713 ^ _784416) ^ [_1724255, _1724257, _1724259, _1724261] : [46714 ^ _784416 : [(46715 ^ _784416) ^ [_1724352, _1724354] : [_1724255 = hAPP(hAPP(c_List_Olist_OCons(_1724257), _1724354), _1724352)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1724257), tc_List_Olist(_1724257))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1724257), tc_List_Olist(_1724257)), _1724259), hAPP(hAPP(c_List_Oappend(_1724257), _1724259), _1724255))), c_List_Olexord(_1724257, _1724261))))], (46719 ^ _784416) ^ [_1724451, _1724453, _1724455, _1724457, _1724459, _1724461] : [-(hAPP(c_List_Ofoldl(_1724451, _1724453, _1724455, _1724457), hAPP(hAPP(c_List_Olist_OCons(_1724453), _1724459), _1724461)) = hAPP(c_List_Ofoldl(_1724451, _1724453, _1724455, hAPP(hAPP(_1724455, _1724457), _1724459)), _1724461))], (46721 ^ _784416) ^ [_1724514, _1724516, _1724518, _1724520] : [class_Groups_Osemigroup__add(_1724514), -(hAPP(c_List_Ofoldl(_1724514, _1724514, c_Groups_Oplus__class_Oplus(_1724514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1724514), _1724516), _1724518)), _1724520) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1724514), _1724516), hAPP(c_List_Ofoldl(_1724514, _1724514, c_Groups_Oplus__class_Oplus(_1724514), _1724518), _1724520)))], (46727 ^ _784416) ^ [_1724665, _1724667, _1724669] : [class_Groups_Omonoid__add(_1724665), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1724665), _1724667), hAPP(c_List_Ofoldl(_1724665, _1724665, c_Groups_Oplus__class_Oplus(_1724665), c_Groups_Ozero__class_Ozero(_1724665)), _1724669)) = hAPP(c_List_Ofoldl(_1724665, _1724665, c_Groups_Oplus__class_Oplus(_1724665), _1724667), _1724669))], (46733 ^ _784416) ^ [_1724802, _1724804, _1724806] : [class_Groups_Oab__semigroup__add(_1724802), -(c_List_Ofoldr(_1724802, _1724802, c_Groups_Oplus__class_Oplus(_1724802), _1724804, _1724806) = hAPP(c_List_Ofoldl(_1724802, _1724802, c_Groups_Oplus__class_Oplus(_1724802), _1724806), _1724804))], (46739 ^ _784416) ^ [_1724915, _1724917, _1724919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1724915), _1724917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1724915), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1724917), _1724919))))], (46745 ^ _784416) ^ [_1725030, _1725032, _1725034, _1725036] : [-(hAPP(c_List_Ofoldl(_1725030, _1725032, _1725034, _1725036), c_List_Olist_ONil(_1725032)) = _1725036)], (46747 ^ _784416) ^ [_1725069, _1725071, _1725073, _1725075, _1725077, _1725079, _1725081] : [-(hAPP(c_List_Ofoldl(_1725069, _1725071, _1725073, _1725075), hAPP(hAPP(c_List_Omap(_1725077, _1725071), _1725079), _1725081)) = hAPP(c_List_Ofoldl(_1725069, _1725077, hAPP(hAPP(c_COMBC(_1725069, tc_fun(_1725077, _1725071), tc_fun(_1725077, _1725069)), hAPP(hAPP(c_COMBB(tc_fun(_1725071, _1725069), tc_fun(tc_fun(_1725077, _1725071), tc_fun(_1725077, _1725069)), _1725069), c_COMBB(_1725071, _1725069, _1725077)), _1725073)), _1725079), _1725075), _1725081))], (46749 ^ _784416) ^ [_1725171, _1725173, _1725175, _1725177, _1725179, _1725181] : [-(hAPP(c_List_Ofoldl(_1725171, _1725173, _1725175, _1725177), hAPP(hAPP(c_List_Oappend(_1725173), _1725179), _1725181)) = hAPP(c_List_Ofoldl(_1725171, _1725173, _1725175, hAPP(c_List_Ofoldl(_1725171, _1725173, _1725175, _1725177), _1725179)), _1725181))], (46751 ^ _784416) ^ [_1725236] : [class_Groups_Omonoid__add(_1725236), -(c_List_Omonoid__add__class_Olistsum(_1725236) = c_List_Ofoldl(_1725236, _1725236, c_Groups_Oplus__class_Oplus(_1725236), c_Groups_Ozero__class_Ozero(_1725236)))], (46757 ^ _784416) ^ [_1725331, _1725333] : [class_Groups_Omonoid__add(_1725331), -(hAPP(c_List_Ofoldl(_1725331, _1725331, c_Groups_Oplus__class_Oplus(_1725331), c_Groups_Ozero__class_Ozero(_1725331)), _1725333) = c_List_Ofoldr(_1725331, _1725331, c_Groups_Oplus__class_Oplus(_1725331), _1725333, c_Groups_Ozero__class_Ozero(_1725331)))], (46763 ^ _784416) ^ [_1725450, _1725452, _1725454] : [class_Groups_Omonoid__add(_1725450), -(hAPP(c_List_Ofoldl(_1725450, _1725450, c_Groups_Oplus__class_Oplus(_1725450), _1725452), _1725454) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1725450), _1725452), c_List_Ofoldr(_1725450, _1725450, c_Groups_Oplus__class_Oplus(_1725450), _1725454, c_Groups_Ozero__class_Ozero(_1725450))))], (46769 ^ _784416) ^ [_1725598, _1725600] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1725598), _1725600) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 46772 ^ _784416 : [(46773 ^ _784416) ^ [] : [-(_1725598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46775 ^ _784416) ^ [_1725712] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1725712), hAPP(c_List_Oset(tc_Nat_Onat), _1725600))), -(_1725712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (46781 ^ _784416) ^ [_1725809, _1725811] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1725809), _1725811) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1725809 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 46787 ^ _784416 : [(46788 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 46786 ^ [_1725809, _1725811]), hAPP(c_List_Oset(tc_Nat_Onat), _1725811))))], (46790 ^ _784416) ^ [] : [46786 ^ [_1725809, _1725811] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (46794 ^ _784416) ^ [_1726035, _1726037, _1726039, _1726041, _1726043] : [c_Finite__Set_Ofun__left__comm__idem(_1726035, _1726037, _1726039), -(hAPP(hAPP(c_Finite__Set_Ofold(_1726035, _1726037, _1726039), _1726041), hAPP(c_List_Oset(_1726035), _1726043)) = hAPP(c_List_Ofoldl(_1726037, _1726035, hAPP(c_COMBC(_1726035, _1726037, _1726037), _1726039), _1726041), _1726043))], (46800 ^ _784416) ^ [_1726180, _1726182] : [class_Complete__Lattice_Ocomplete__lattice(_1726180), -(c_Complete__Lattice_OSup__class_OSup(_1726180, hAPP(c_List_Oset(_1726180), _1726182)) = hAPP(c_List_Ofoldl(_1726180, _1726180, c_Lattices_Osemilattice__sup__class_Osup(_1726180), c_Orderings_Obot__class_Obot(_1726180)), _1726182))], (46806 ^ _784416) ^ [_1726295, _1726297] : [class_Complete__Lattice_Ocomplete__lattice(_1726295), -(c_Complete__Lattice_OInf__class_OInf(_1726295, hAPP(c_List_Oset(_1726295), _1726297)) = hAPP(c_List_Ofoldl(_1726295, _1726295, c_Lattices_Osemilattice__inf__class_Oinf(_1726295), c_Orderings_Otop__class_Otop(_1726295)), _1726297))], (46812 ^ _784416) ^ [_1726410, _1726412, _1726414] : [class_Lattices_Olattice(_1726410), -(c_Big__Operators_Olattice__class_OSup__fin(_1726410, hAPP(c_List_Oset(_1726410), hAPP(hAPP(c_List_Olist_OCons(_1726410), _1726412), _1726414))) = hAPP(c_List_Ofoldl(_1726410, _1726410, c_Lattices_Osemilattice__sup__class_Osup(_1726410), _1726412), _1726414))], (46818 ^ _784416) ^ [_1726539, _1726541, _1726543] : [class_Lattices_Olattice(_1726539), -(c_Big__Operators_Olattice__class_OInf__fin(_1726539, hAPP(c_List_Oset(_1726539), hAPP(hAPP(c_List_Olist_OCons(_1726539), _1726541), _1726543))) = hAPP(c_List_Ofoldl(_1726539, _1726539, c_Lattices_Osemilattice__inf__class_Oinf(_1726539), _1726541), _1726543))], (46824 ^ _784416) ^ [_1726668, _1726670, _1726672] : [class_Orderings_Olinorder(_1726668), -(c_Big__Operators_Olinorder__class_OMin(_1726668, hAPP(c_List_Oset(_1726668), hAPP(hAPP(c_List_Olist_OCons(_1726668), _1726670), _1726672))) = hAPP(c_List_Ofoldl(_1726668, _1726668, c_Orderings_Oord__class_Omin(_1726668), _1726670), _1726672))], (46830 ^ _784416) ^ [_1726797, _1726799, _1726801] : [class_Orderings_Olinorder(_1726797), -(c_Big__Operators_Olinorder__class_OMax(_1726797, hAPP(c_List_Oset(_1726797), hAPP(hAPP(c_List_Olist_OCons(_1726797), _1726799), _1726801))) = hAPP(c_List_Ofoldl(_1726797, _1726797, c_Orderings_Oord__class_Omax(_1726797), _1726799), _1726801))], (46836 ^ _784416) ^ [_1726926, _1726928, _1726930] : [class_Orderings_Olinorder(_1726926), -(c_Big__Operators_Olattice_OInf__fin(_1726926, c_Orderings_Oord__class_Omin(_1726926), hAPP(c_List_Oset(_1726926), hAPP(hAPP(c_List_Olist_OCons(_1726926), _1726928), _1726930))) = hAPP(c_List_Ofoldl(_1726926, _1726926, c_Orderings_Oord__class_Omin(_1726926), _1726928), _1726930))], (46842 ^ _784416) ^ [_1727061, _1727063, _1727065] : [class_Orderings_Olinorder(_1727061), -(c_Big__Operators_Olattice_OSup__fin(_1727061, c_Orderings_Oord__class_Omax(_1727061), hAPP(c_List_Oset(_1727061), hAPP(hAPP(c_List_Olist_OCons(_1727061), _1727063), _1727065))) = hAPP(c_List_Ofoldl(_1727061, _1727061, c_Orderings_Oord__class_Omax(_1727061), _1727063), _1727065))], (46848 ^ _784416) ^ [_1727196, _1727198, _1727200, _1727202] : [class_Complete__Lattice_Ocomplete__lattice(_1727196), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1727198, _1727196), hAPP(c_List_Oset(_1727198), _1727200)), _1727202) = hAPP(c_List_Ofoldl(_1727196, _1727198, hAPP(c_COMBC(_1727198, _1727196, _1727196), hAPP(hAPP(c_COMBB(_1727196, tc_fun(_1727196, _1727196), _1727198), c_Lattices_Osemilattice__sup__class_Osup(_1727196)), _1727202)), c_Orderings_Obot__class_Obot(_1727196)), _1727200))], (46854 ^ _784416) ^ [_1727367, _1727369, _1727371, _1727373] : [class_Complete__Lattice_Ocomplete__lattice(_1727367), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1727369, _1727367), hAPP(c_List_Oset(_1727369), _1727371)), _1727373) = hAPP(c_List_Ofoldl(_1727367, _1727369, hAPP(c_COMBC(_1727369, _1727367, _1727367), hAPP(hAPP(c_COMBB(_1727367, tc_fun(_1727367, _1727367), _1727369), c_Lattices_Osemilattice__inf__class_Oinf(_1727367)), _1727373)), c_Orderings_Otop__class_Otop(_1727367)), _1727371))], (46860 ^ _784416) ^ [_1727538, _1727540, _1727542, _1727544, _1727546] : [-(c_Map_Omap__upds(_1727538, _1727540, _1727542, _1727544, _1727546) = hAPP(c_List_Ofoldl(tc_fun(_1727538, tc_Option_Ooption(_1727540)), tc_prod(_1727538, _1727540), hAPP(hAPP(c_COMBB(tc_fun(_1727538, tc_fun(_1727540, tc_fun(_1727538, tc_Option_Ooption(_1727540)))), tc_fun(tc_prod(_1727538, _1727540), tc_fun(_1727538, tc_Option_Ooption(_1727540))), tc_fun(_1727538, tc_Option_Ooption(_1727540))), c_Product__Type_Oprod_Oprod__case(_1727538, _1727540, tc_fun(_1727538, tc_Option_Ooption(_1727540)))), hAPP(hAPP(c_COMBC(tc_fun(_1727538, tc_Option_Ooption(_1727540)), tc_fun(_1727540, tc_Option_Ooption(_1727540)), tc_fun(_1727538, tc_fun(_1727540, tc_fun(_1727538, tc_Option_Ooption(_1727540))))), hAPP(hAPP(c_COMBB(tc_fun(_1727538, tc_fun(tc_fun(_1727540, tc_Option_Ooption(_1727540)), tc_fun(_1727540, tc_fun(_1727538, tc_Option_Ooption(_1727540))))), tc_fun(tc_fun(_1727540, tc_Option_Ooption(_1727540)), tc_fun(_1727538, tc_fun(_1727540, tc_fun(_1727538, tc_Option_Ooption(_1727540))))), tc_fun(_1727538, tc_Option_Ooption(_1727540))), c_COMBC(_1727538, tc_fun(_1727540, tc_Option_Ooption(_1727540)), tc_fun(_1727540, tc_fun(_1727538, tc_Option_Ooption(_1727540))))), hAPP(hAPP(c_COMBB(tc_fun(_1727538, tc_fun(tc_Option_Ooption(_1727540), tc_fun(_1727538, tc_Option_Ooption(_1727540)))), tc_fun(_1727538, tc_fun(tc_fun(_1727540, tc_Option_Ooption(_1727540)), tc_fun(_1727540, tc_fun(_1727538, tc_Option_Ooption(_1727540))))), tc_fun(_1727538, tc_Option_Ooption(_1727540))), hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1727540), tc_fun(_1727538, tc_Option_Ooption(_1727540))), tc_fun(tc_fun(_1727540, tc_Option_Ooption(_1727540)), tc_fun(_1727540, tc_fun(_1727538, tc_Option_Ooption(_1727540)))), _1727538), c_COMBB(tc_Option_Ooption(_1727540), tc_fun(_1727538, tc_Option_Ooption(_1727540)), _1727540))), c_Fun_Ofun__upd(_1727538, tc_Option_Ooption(_1727540))))), c_Option_Ooption_OSome(_1727540))), _1727542), hAPP(hAPP(c_List_Ozip(_1727538, _1727540), _1727544), _1727546)))], (46862 ^ _784416) ^ [_1727845, _1727847] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1727845), hAPP(c_List_Oset(tc_Nat_Onat), _1727847))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1727845), 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)), _1727847))))], (46868 ^ _784416) ^ [_1727972, _1727974, _1727976] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1727972), tc_List_Olist(_1727972))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1727972), tc_List_Olist(_1727972)), c_List_Olist_ONil(_1727972)), _1727974)), c_List_Olexord(_1727972, _1727976))), -(_1727974 = hAPP(hAPP(c_List_Olist_OCons(_1727972), 46871 ^ [_1727972, _1727974, _1727976]), 46872 ^ [_1727972, _1727974, _1727976]))], (46876 ^ _784416) ^ [_1728155, _1728157, _1728159] : [46877 ^ _784416 : [(46878 ^ _784416) ^ [_1728244, _1728246] : [_1728157 = hAPP(hAPP(c_List_Olist_OCons(_1728155), _1728246), _1728244)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1728155), tc_List_Olist(_1728155))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1728155), tc_List_Olist(_1728155)), c_List_Olist_ONil(_1728155)), _1728157)), c_List_Olexord(_1728155, _1728159))))], (46882 ^ _784416) ^ [_1728338, _1728340, _1728342, _1728344] : [-(_1728338 = c_List_Olist_ONil(_1728340)), 46885 ^ _784416 : [(46886 ^ _784416) ^ [] : [_1728342 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728340)), _1728338)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1728340, hAPP(hAPP(c_List_Olist__update(_1728340, _1728338), _1728342), _1728344)) = _1728344)], (46892 ^ _784416) ^ [] : [-(_1728342 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728340)), _1728338)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1728340, hAPP(hAPP(c_List_Olist__update(_1728340, _1728338), _1728342), _1728344)) = c_List_Olast(_1728340, _1728338))]]], (46898 ^ _784416) ^ [_1728628, _1728630, _1728632] : [_1728628 = c_List_Olist_ONil(_1728630), -(c_List_Olast(_1728630, hAPP(hAPP(c_List_Oappend(_1728630), _1728632), _1728628)) = c_List_Olast(_1728630, _1728632))], (46904 ^ _784416) ^ [_1728735, _1728737, _1728739] : [-(_1728735 = c_List_Olist_ONil(_1728737)), -(c_List_Olast(_1728737, hAPP(hAPP(c_List_Oappend(_1728737), _1728739), _1728735)) = c_List_Olast(_1728737, _1728735))], (46910 ^ _784416) ^ [_1728801, _1728803, _1728805] : [_1728801 = c_List_Olist_ONil(_1728803), -(c_List_Olast(_1728803, hAPP(hAPP(c_List_Oappend(_1728803), _1728805), _1728801)) = c_List_Olast(_1728803, _1728805))], (46916 ^ _784416) ^ [_1728906, _1728908, _1728910] : [-(_1728906 = c_List_Olist_ONil(_1728908)), -(c_List_Olast(_1728908, hAPP(hAPP(c_List_Oappend(_1728908), _1728910), _1728906)) = c_List_Olast(_1728908, _1728906))], (46922 ^ _784416) ^ [_1728958, _1728960, _1728962, _1728964] : [-(_1728958 = c_List_Olist_ONil(_1728960)), -(c_List_Olast(_1728962, hAPP(hAPP(c_List_Omap(_1728960, _1728962), _1728964), _1728958)) = hAPP(_1728964, c_List_Olast(_1728960, _1728958)))], (46928 ^ _784416) ^ [_1729030, _1729032, _1729034] : [_1729030 = c_List_Olist_ONil(_1729032), -(c_List_Olast(_1729032, hAPP(hAPP(c_List_Olist_OCons(_1729032), _1729034), _1729030)) = _1729034)], (46934 ^ _784416) ^ [_1729129, _1729131, _1729133] : [-(_1729129 = c_List_Olist_ONil(_1729131)), -(c_List_Olast(_1729131, hAPP(hAPP(c_List_Olist_OCons(_1729131), _1729133), _1729129)) = c_List_Olast(_1729131, _1729129))], (46940 ^ _784416) ^ [_1729181, _1729183, _1729185] : [-(_1729181 = c_List_Olist_ONil(_1729183)), -(c_List_Olast(_1729183, hAPP(hAPP(c_List_Olist_OCons(_1729183), _1729185), _1729181)) = c_List_Olast(_1729183, _1729181))], (46946 ^ _784416) ^ [_1729235, _1729237, _1729239] : [_1729235 = c_List_Olist_ONil(_1729237), -(c_List_Olast(_1729237, hAPP(hAPP(c_List_Olist_OCons(_1729237), _1729239), _1729235)) = _1729239)], (46952 ^ _784416) ^ [_1729336, _1729338] : [-(_1729336 = c_List_Olist_ONil(_1729338)), -(hBOOL(hAPP(hAPP(c_member(_1729338), c_List_Olast(_1729338, _1729336)), hAPP(c_List_Oset(_1729338), _1729336))))], (46958 ^ _784416) ^ [_1729389, _1729391, _1729393] : [-(c_List_Olast(_1729389, hAPP(hAPP(c_List_Oappend(_1729389), _1729391), hAPP(hAPP(c_List_Olist_OCons(_1729389), _1729393), c_List_Olist_ONil(_1729389)))) = _1729393)], (46960 ^ _784416) ^ [_1729437, _1729439, _1729441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729437), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729439)), _1729441))), -(c_List_Olast(_1729439, hAPP(hAPP(c_List_Odrop(_1729439), _1729437), _1729441)) = c_List_Olast(_1729439, _1729441))], (46966 ^ _784416) ^ [_1729564, _1729566] : [-(_1729564 = c_List_Olist_ONil(_1729566)), -(c_List_Olast(_1729566, _1729564) = hAPP(hAPP(c_List_Onth(_1729566), _1729564), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729566)), _1729564)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (46972 ^ _784416) ^ [_1729626, _1729628, _1729630, _1729632] : [class_Enum_Oenum(_1729626), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729628)), _1729630) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729626)), c_Enum_Oenum__class_Oenum(_1729626)), -(hAPP(hAPP(c_Map_Omap__of(_1729626, _1729628), hAPP(hAPP(c_List_Ozip(_1729626, _1729628), c_Enum_Oenum__class_Oenum(_1729626)), _1729630)), _1729632) = hAPP(c_Option_Ooption_OSome(_1729628), 46979 ^ [_1729626, _1729628, _1729630, _1729632]))], (46983 ^ _784416) ^ [_1729859, _1729861] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1729859), _1729861) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1729859, 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)))), _1729861))))], (46985 ^ _784416) ^ [_1729896, _1729898, _1729900] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729896, _1729896)), hAPP(hAPP(c_Product__Type_OPair(_1729896, _1729896), 46986 ^ [_1729896, _1729898, _1729900]), 46986 ^ [_1729896, _1729898, _1729900])), _1729898))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1729896), tc_List_Olist(_1729896))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1729896), tc_List_Olist(_1729896)), _1729900), _1729900)), c_List_Olexord(_1729896, _1729898)))], (46992 ^ _784416) ^ [_1730071, _1730073, _1730075, _1730077] : [46995 ^ _784416 : [(46996 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1730071, _1730071)), hAPP(hAPP(c_Product__Type_OPair(_1730071, _1730071), 46993 ^ [_1730071, _1730073, _1730075, _1730077]), 46994 ^ [_1730071, _1730073, _1730075, _1730077])), _1730073))], (46998 ^ _784416) ^ [] : [46993 ^ [_1730071, _1730073, _1730075, _1730077] = 46994 ^ [_1730071, _1730073, _1730075, _1730077]], (47000 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1730071, _1730071)), hAPP(hAPP(c_Product__Type_OPair(_1730071, _1730071), 46994 ^ [_1730071, _1730073, _1730075, _1730077]), 46993 ^ [_1730071, _1730073, _1730075, _1730077])), _1730073))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1730071), tc_List_Olist(_1730071))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1730071), tc_List_Olist(_1730071)), _1730075), _1730077)), c_List_Olexord(_1730071, _1730073)))), -(_1730075 = _1730077), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1730071), tc_List_Olist(_1730071))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1730071), tc_List_Olist(_1730071)), _1730077), _1730075)), c_List_Olexord(_1730071, _1730073))))], (47012 ^ _784416) ^ [_1730636, _1730638, _1730640] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1730636)), _1730638), c_List_Olists(_1730636, _1730640))), -(_1730638 = c_List_Olist_ONil(_1730636)), 47021 ^ _784416 : [(47022 ^ _784416) ^ [] : [-(_1730638 = hAPP(hAPP(c_List_Olist_OCons(_1730636), 47019 ^ [_1730636, _1730638, _1730640]), 47020 ^ [_1730636, _1730638, _1730640]))], (47024 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730636), 47019 ^ [_1730636, _1730638, _1730640]), _1730640)))], (47026 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1730636)), 47020 ^ [_1730636, _1730638, _1730640]), c_List_Olists(_1730636, _1730640))))]]], (47028 ^ _784416) ^ [_1730919, _1730921, _1730923] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1730919)), _1730921), c_List_Olists(_1730919, _1730923)))), 47029 ^ _784416 : [(47030 ^ _784416) ^ [] : [_1730921 = c_List_Olist_ONil(_1730919)], (47032 ^ _784416) ^ [_1731047, _1731049] : [_1730921 = hAPP(hAPP(c_List_Olist_OCons(_1730919), _1731049), _1731047), hBOOL(hAPP(hAPP(c_member(_1730919), _1731049), _1730923)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1730919)), _1731047), c_List_Olists(_1730919, _1730923)))]]], (47044 ^ _784416) ^ [_1731285, _1731287, _1731289, _1731291, _1731293] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1731285, _1731287)), hAPP(hAPP(c_Product__Type_OPair(_1731285, _1731287), _1731289), _1731291)), hAPP(c_List_Oset(tc_prod(_1731285, _1731287)), _1731293))), -(hAPP(hAPP(c_Map_Omap__of(_1731285, _1731287), _1731293), _1731289) = hAPP(c_Option_Ooption_OSome(_1731287), 47047 ^ [_1731285, _1731287, _1731289, _1731291, _1731293]))], (47051 ^ _784416) ^ [_1731468, _1731470, _1731472, _1731474] : [47053 ^ _784416 : [(47054 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1731468), 47052 ^ [_1731468, _1731470, _1731472, _1731474]), hAPP(c_List_Oset(_1731468), _1731470))))], (47056 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1731472, 47052 ^ [_1731468, _1731470, _1731472, _1731474])), hAPP(_1731474, 47052 ^ [_1731468, _1731470, _1731472, _1731474])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1731468, _1731472, _1731470)), c_List_Olist_Olist__size(_1731468, _1731474, _1731470))))], (47060 ^ _784416) ^ [_1731718, _1731720, _1731722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1731718), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731720)), _1731722))), -(c_List_Obutlast(_1731720, hAPP(hAPP(c_List_Otake(_1731720), _1731718), _1731722)) = hAPP(hAPP(c_List_Otake(_1731720), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1731718), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1731722))], (47066 ^ _784416) ^ [_1731871, _1731873, _1731875] : [-(c_List_Obutlast(_1731871, hAPP(hAPP(c_List_Odrop(_1731871), _1731873), _1731875)) = hAPP(hAPP(c_List_Odrop(_1731871), _1731873), c_List_Obutlast(_1731871, _1731875)))], (47068 ^ _784416) ^ [_1731920, _1731922, _1731924] : [-(hAPP(hAPP(c_List_Odrop(_1731920), _1731922), c_List_Obutlast(_1731920, _1731924)) = c_List_Obutlast(_1731920, hAPP(hAPP(c_List_Odrop(_1731920), _1731922), _1731924)))], (47070 ^ _784416) ^ [_1731981, _1731983, _1731985] : [_1731981 = c_List_Olist_ONil(_1731983), -(c_List_Obutlast(_1731983, hAPP(hAPP(c_List_Oappend(_1731983), _1731985), _1731981)) = c_List_Obutlast(_1731983, _1731985))], (47076 ^ _784416) ^ [_1732086, _1732088, _1732090] : [-(_1732086 = c_List_Olist_ONil(_1732088)), -(c_List_Obutlast(_1732088, hAPP(hAPP(c_List_Oappend(_1732088), _1732090), _1732086)) = hAPP(hAPP(c_List_Oappend(_1732088), _1732090), c_List_Obutlast(_1732088, _1732086)))], (47082 ^ _784416) ^ [_1732150, _1732152, _1732154, _1732156] : [-(hAPP(hAPP(c_List_Omap(_1732150, _1732152), _1732154), c_List_Obutlast(_1732150, _1732156)) = c_List_Obutlast(_1732152, hAPP(hAPP(c_List_Omap(_1732150, _1732152), _1732154), _1732156)))], (47084 ^ _784416) ^ [_1732203] : [-(c_List_Obutlast(_1732203, c_List_Olist_ONil(_1732203)) = c_List_Olist_ONil(_1732203))], (47086 ^ _784416) ^ [_1732232, _1732234] : [-(_1732232 = c_List_Olist_ONil(_1732234)), hBOOL(hAPP(c_List_Odistinct(_1732234), _1732232)), -(hBOOL(hAPP(c_List_Odistinct(_1732234), c_List_Obutlast(_1732234, _1732232))))], (47096 ^ _784416) ^ [_1732383, _1732385, _1732387] : [hBOOL(hAPP(hAPP(c_member(_1732383), _1732385), hAPP(c_List_Oset(_1732383), c_List_Obutlast(_1732383, _1732387)))), -(hBOOL(hAPP(hAPP(c_member(_1732383), _1732385), hAPP(c_List_Oset(_1732383), _1732387))))], (47102 ^ _784416) ^ [_1732528, _1732530, _1732532] : [_1732528 = c_List_Olist_ONil(_1732530), -(c_List_Obutlast(_1732530, hAPP(hAPP(c_List_Olist_OCons(_1732530), _1732532), _1732528)) = c_List_Olist_ONil(_1732530))], (47108 ^ _784416) ^ [_1732631, _1732633, _1732635] : [-(_1732631 = c_List_Olist_ONil(_1732633)), -(c_List_Obutlast(_1732633, hAPP(hAPP(c_List_Olist_OCons(_1732633), _1732635), _1732631)) = hAPP(hAPP(c_List_Olist_OCons(_1732633), _1732635), c_List_Obutlast(_1732633, _1732631)))], (47114 ^ _784416) ^ [_1732695, _1732697, _1732699, _1732701] : [47115 ^ _784416 : [(47116 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1732695), _1732697), hAPP(c_List_Oset(_1732695), c_List_Obutlast(_1732695, _1732699))))], (47118 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1732695), _1732697), hAPP(c_List_Oset(_1732695), c_List_Obutlast(_1732695, _1732701))))]], -(hBOOL(hAPP(hAPP(c_member(_1732695), _1732697), hAPP(c_List_Oset(_1732695), c_List_Obutlast(_1732695, hAPP(hAPP(c_List_Oappend(_1732695), _1732699), _1732701))))))], (47122 ^ _784416) ^ [_1732920, _1732922, _1732924] : [-(c_List_Obutlast(_1732920, hAPP(hAPP(c_List_Oappend(_1732920), _1732922), hAPP(hAPP(c_List_Olist_OCons(_1732920), _1732924), c_List_Olist_ONil(_1732920)))) = _1732922)], (47124 ^ _784416) ^ [_1732968, _1732970, _1732972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1732968), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732970)), _1732972))), -(hAPP(hAPP(c_List_Otake(_1732970), _1732968), c_List_Obutlast(_1732970, _1732972)) = hAPP(hAPP(c_List_Otake(_1732970), _1732968), _1732972))], (47130 ^ _784416) ^ [_1733109, _1733111] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733109)), c_List_Obutlast(_1733109, _1733111)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733109)), _1733111)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (47132 ^ _784416) ^ [_1733157, _1733159] : [-(c_List_Obutlast(_1733157, _1733159) = hAPP(hAPP(c_List_Otake(_1733157), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733157)), _1733159)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1733159))], (47134 ^ _784416) ^ [_1733221, _1733223, _1733225, _1733227] : [_1733221 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733223)), _1733225)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1733223, hAPP(hAPP(c_List_Olist__update(_1733223, _1733225), _1733221), _1733227)) = c_List_Obutlast(_1733223, _1733225))], (47140 ^ _784416) ^ [_1733352, _1733354, _1733356, _1733358] : [-(_1733352 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733354)), _1733356)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1733354, hAPP(hAPP(c_List_Olist__update(_1733354, _1733356), _1733352), _1733358)) = hAPP(hAPP(c_List_Olist__update(_1733354, c_List_Obutlast(_1733354, _1733356)), _1733352), _1733358))], (47146 ^ _784416) ^ [_1733427, _1733429] : [-(_1733427 = c_List_Olist_ONil(_1733429)), -(hAPP(hAPP(c_List_Oappend(_1733429), c_List_Obutlast(_1733429, _1733427)), hAPP(hAPP(c_List_Olist_OCons(_1733429), c_List_Olast(_1733429, _1733427)), c_List_Olist_ONil(_1733429))) = _1733427)], (47152 ^ _784416) ^ [_1733510, _1733512, _1733514, _1733516] : [hAPP(hAPP(c_List_Oappend(_1733510), _1733512), hAPP(hAPP(c_List_Olist_OCons(_1733510), _1733514), c_List_Olist_ONil(_1733510))) = _1733516, 47155 ^ _784416 : [(47156 ^ _784416) ^ [] : [_1733516 = c_List_Olist_ONil(_1733510)], (47158 ^ _784416) ^ [] : [-(c_List_Obutlast(_1733510, _1733516) = _1733512)], (47160 ^ _784416) ^ [] : [-(c_List_Olast(_1733510, _1733516) = _1733514)]]], (47162 ^ _784416) ^ [_1733699, _1733701, _1733703, _1733705] : [-(hAPP(hAPP(c_List_Oappend(_1733699), _1733701), hAPP(hAPP(c_List_Olist_OCons(_1733699), _1733703), c_List_Olist_ONil(_1733699))) = _1733705), -(_1733705 = c_List_Olist_ONil(_1733699)), c_List_Obutlast(_1733699, _1733705) = _1733701, c_List_Olast(_1733699, _1733705) = _1733703], (47176 ^ _784416) ^ [_1733949, _1733951, _1733953, _1733955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1733949), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733951)), _1733953))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1733949), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733951)), _1733955))), 47186 ^ _784416 : [(47187 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47185 ^ [_1733949, _1733951, _1733953, _1733955]), _1733949)))], (47189 ^ _784416) ^ [] : [hAPP(hAPP(c_List_Onth(_1733951), _1733953), 47185 ^ [_1733949, _1733951, _1733953, _1733955]) = hAPP(hAPP(c_List_Onth(_1733951), _1733955), 47185 ^ [_1733949, _1733951, _1733953, _1733955])]], -(hAPP(hAPP(c_List_Otake(_1733951), _1733949), _1733953) = hAPP(hAPP(c_List_Otake(_1733951), _1733949), _1733955))], (47193 ^ _784416) ^ [_1734366, _1734368] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1734366))), c_List_Otranspose(_1734366, _1734368)) = c_List_Ofoldr(tc_List_Olist(_1734366), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1734366)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1734366))), _1734368, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (47195 ^ _784416) ^ [_1734427] : [-(c_List_Otranspose(_1734427, c_List_Olist_ONil(tc_List_Olist(_1734427))) = c_List_Olist_ONil(tc_List_Olist(_1734427)))], (47197 ^ _784416) ^ [_1734461, _1734463] : [-(c_List_Otranspose(_1734461, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1734461)), c_List_Olist_ONil(_1734461)), _1734463)) = c_List_Otranspose(_1734461, _1734463))], (47199 ^ _784416) ^ [_1734504, _1734506, _1734508, _1734510] : [-(c_List_Otranspose(_1734504, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1734506), tc_List_Olist(_1734504)), hAPP(c_List_Omap(_1734506, _1734504), _1734508)), _1734510)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1734506), tc_List_Olist(_1734504)), hAPP(c_List_Omap(_1734506, _1734504), _1734508)), c_List_Otranspose(_1734506, _1734510)))], (47211 ^ _784416) ^ [_1734802, _1734804] : [47213 ^ _784416 : [(47214 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1734802)), 47212 ^ [_1734802, _1734804]), hAPP(c_List_Oset(tc_List_Olist(_1734802)), _1734804))))], (47216 ^ _784416) ^ [] : [47212 ^ [_1734802, _1734804] = c_List_Olist_ONil(_1734802)]], -(c_List_Otranspose(_1734802, _1734804) = c_List_Olist_ONil(tc_List_Olist(_1734802)))], (47201 ^ _784416) ^ [_1734592, _1734594] : [c_List_Otranspose(_1734592, _1734594) = c_List_Olist_ONil(tc_List_Olist(_1734592)), 47204 ^ _784416 : [(47205 ^ _784416) ^ [_1734687] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1734592)), _1734687), hAPP(c_List_Oset(tc_List_Olist(_1734592)), _1734594))), -(_1734687 = c_List_Olist_ONil(_1734592))]]], (47220 ^ _784416) ^ [_1734997, _1734999] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1734997)), c_List_Otranspose__rel(_1734997)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1734997)), c_List_Olist_ONil(_1734997)), _1734999))), -(c_List_Otranspose(_1734997, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1734997)), c_List_Olist_ONil(_1734997)), _1734999)) = c_List_Otranspose(_1734997, _1734999))], (47226 ^ _784416) ^ [_1735156, _1735158] : [-(c_List_Ofoldr(tc_List_Olist(_1735156), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1735156)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1735156))), c_List_Otranspose(_1735156, _1735158), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1735156))), hAPP(c_List_Ofilter(tc_List_Olist(_1735156), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1735156)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1735156), tc_List_Olist(_1735156), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1735156)))), _1735158)))], (47228 ^ _784416) ^ [_1735253, _1735255, _1735257, _1735259] : [-(hAPP(c_List_Ofilter(_1735253, _1735255), hAPP(hAPP(c_List_Oappend(_1735253), _1735257), _1735259)) = hAPP(hAPP(c_List_Oappend(_1735253), hAPP(c_List_Ofilter(_1735253, _1735255), _1735257)), hAPP(c_List_Ofilter(_1735253, _1735255), _1735259)))], (47230 ^ _784416) ^ [_1735316, _1735318, _1735320, _1735322, _1735324] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735316)), hAPP(c_List_Ofilter(_1735316, _1735318), hAPP(hAPP(c_List_Omap(_1735320, _1735316), _1735322), _1735324))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735320)), hAPP(c_List_Ofilter(_1735320, hAPP(c_Fun_Ocomp(_1735316, tc_HOL_Obool, _1735320, _1735318), _1735322)), _1735324)))], (47232 ^ _784416) ^ [_1735390, _1735392, _1735394, _1735396, _1735398] : [-(hAPP(c_List_Ofilter(_1735390, _1735392), hAPP(hAPP(c_List_Omap(_1735394, _1735390), _1735396), _1735398)) = hAPP(hAPP(c_List_Omap(_1735394, _1735390), _1735396), hAPP(c_List_Ofilter(_1735394, hAPP(c_Fun_Ocomp(_1735390, tc_HOL_Obool, _1735394, _1735392), _1735396)), _1735398)))], (47244 ^ _784416) ^ [_1735682, _1735684, _1735686] : [47246 ^ _784416 : [(47247 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1735682), 47245 ^ [_1735682, _1735684, _1735686]), hAPP(c_List_Oset(_1735682), _1735686))))], (47249 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1735684, 47245 ^ [_1735682, _1735684, _1735686])))]], -(hAPP(c_List_Ofilter(_1735682, _1735684), _1735686) = c_List_Olist_ONil(_1735682))], (47234 ^ _784416) ^ [_1735477, _1735479, _1735481] : [hAPP(c_List_Ofilter(_1735477, _1735479), _1735481) = c_List_Olist_ONil(_1735477), 47237 ^ _784416 : [(47238 ^ _784416) ^ [_1735574] : [hBOOL(hAPP(hAPP(c_member(_1735477), _1735574), hAPP(c_List_Oset(_1735477), _1735481))), hBOOL(hAPP(_1735479, _1735574))]]], (47253 ^ _784416) ^ [_1735799, _1735801] : [-(hAPP(c_List_Ofilter(_1735799, _1735801), c_List_Olist_ONil(_1735799)) = c_List_Olist_ONil(_1735799))], (47255 ^ _784416) ^ [_1735834, _1735836, _1735838] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1735834, tc_HOL_Obool)), hAPP(c_List_Oset(_1735834), hAPP(c_List_Ofilter(_1735834, _1735836), _1735838))), hAPP(c_List_Oset(_1735834), _1735838))))], (47257 ^ _784416) ^ [_1735887, _1735889, _1735891] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735887)), hAPP(c_List_Ofilter(_1735887, _1735889), _1735891))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735887)), hAPP(c_List_Ofilter(_1735887, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1735887), c_fNot), _1735889)), _1735891))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735887)), _1735891))], (47259 ^ _784416) ^ [_1735963, _1735965, _1735967] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735963)), hAPP(c_List_Ofilter(_1735963, _1735965), _1735967))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735963)), _1735967))))], (47261 ^ _784416) ^ [_1736015, _1736017, _1736019] : [hBOOL(hAPP(c_List_Odistinct(_1736015), _1736017)), -(hBOOL(hAPP(c_List_Odistinct(_1736015), hAPP(c_List_Ofilter(_1736015, _1736019), _1736017))))], (47267 ^ _784416) ^ [_1736122, _1736124, _1736126, _1736128] : [-(hAPP(c_List_Ofilter(_1736122, _1736124), hAPP(c_List_Ofilter(_1736122, _1736126), _1736128)) = hAPP(c_List_Ofilter(_1736122, hAPP(hAPP(c_COMBS(_1736122, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1736122), c_fconj), _1736126)), _1736124)), _1736128))], (47279 ^ _784416) ^ [_1736407, _1736409, _1736411] : [47281 ^ _784416 : [(47282 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1736407), 47280 ^ [_1736407, _1736409, _1736411]), hAPP(c_List_Oset(_1736407), _1736411))))], (47284 ^ _784416) ^ [] : [hBOOL(hAPP(_1736409, 47280 ^ [_1736407, _1736409, _1736411]))]], -(hAPP(c_List_Ofilter(_1736407, _1736409), _1736411) = _1736411)], (47269 ^ _784416) ^ [_1736207, _1736209, _1736211] : [hAPP(c_List_Ofilter(_1736207, _1736209), _1736211) = _1736211, 47272 ^ _784416 : [(47273 ^ _784416) ^ [_1736298] : [hBOOL(hAPP(hAPP(c_member(_1736207), _1736298), hAPP(c_List_Oset(_1736207), _1736211))), -(hBOOL(hAPP(_1736209, _1736298)))]]], (47288 ^ _784416) ^ [_1736614, _1736616, _1736618, _1736620] : [hBOOL(hAPP(_1736614, _1736616)), -(hAPP(c_List_Ofilter(_1736618, _1736614), hAPP(hAPP(c_List_Olist_OCons(_1736618), _1736616), _1736620)) = hAPP(hAPP(c_List_Olist_OCons(_1736618), _1736616), hAPP(c_List_Ofilter(_1736618, _1736614), _1736620)))], (47294 ^ _784416) ^ [_1736749, _1736751, _1736753, _1736755] : [-(hBOOL(hAPP(_1736749, _1736751))), -(hAPP(c_List_Ofilter(_1736753, _1736749), hAPP(hAPP(c_List_Olist_OCons(_1736753), _1736751), _1736755)) = hAPP(c_List_Ofilter(_1736753, _1736749), _1736755))], (47300 ^ _784416) ^ [_1736813, _1736815, _1736817] : [-(hAPP(c_List_Oset(_1736813), hAPP(c_List_Ofilter(_1736813, _1736815), _1736817)) = hAPP(c_Set_OCollect(_1736813), hAPP(hAPP(c_COMBS(_1736813, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1736813), c_fconj), hAPP(hAPP(c_COMBC(_1736813, tc_fun(_1736813, tc_HOL_Obool), tc_HOL_Obool), c_member(_1736813)), hAPP(c_List_Oset(_1736813), _1736817)))), _1736815)))], (47302 ^ _784416) ^ [_1736896, _1736898, _1736900, _1736902] : [hBOOL(hAPP(hAPP(c_member(_1736896), _1736898), hAPP(c_List_Oset(_1736896), _1736900))), -(hBOOL(hAPP(_1736902, _1736898))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736896)), hAPP(c_List_Ofilter(_1736896, _1736902), _1736900))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736896)), _1736900))))], (47312 ^ _784416) ^ [_1737070, _1737072, _1737074] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1737070, tc_HOL_Obool)), hAPP(c_List_Oset(_1737070), _1737072)), hAPP(hAPP(c_Set_Oinsert(_1737070), _1737074), c_Orderings_Obot__class_Obot(tc_fun(_1737070, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1737070), hAPP(c_List_Ofilter(_1737070, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1737070), c_fNot), hAPP(hAPP(c_COMBC(_1737070, _1737070, tc_HOL_Obool), c_fequal), _1737074))), _1737072)))], (47314 ^ _784416) ^ [_1737157, _1737159, _1737161] : [hBOOL(hAPP(c_List_Odistinct(_1737157), _1737159)), -(hAPP(c_List_Ofilter(_1737157, hAPP(hAPP(c_COMBC(_1737157, tc_fun(_1737157, tc_HOL_Obool), tc_HOL_Obool), c_member(_1737157)), hAPP(c_List_Oset(_1737157), c_List_Osublist(_1737157, _1737159, _1737161)))), _1737159) = c_List_Osublist(_1737157, _1737159, _1737161))], (47320 ^ _784416) ^ [_1737312, _1737314, _1737316] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737312)), hAPP(c_List_Ofilter(_1737312, _1737314), _1737316)) = 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(_1737312)), _1737316)))), hAPP(hAPP(c_COMBB(_1737312, tc_HOL_Obool, tc_Nat_Onat), _1737314), hAPP(c_List_Onth(_1737312), _1737316))))))], (47322 ^ _784416) ^ [_1737392, _1737394, _1737396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737392), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1737394))), c_List_Otranspose(_1737394, _1737396)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1737394)), c_List_Otranspose(_1737394, _1737396)), _1737392) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1737394), _1737394), hAPP(hAPP(c_COMBC(tc_List_Olist(_1737394), tc_Nat_Onat, _1737394), c_List_Onth(_1737394)), _1737392)), hAPP(c_List_Ofilter(tc_List_Olist(_1737394), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1737394)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737392)), c_Nat_Osize__class_Osize(tc_List_Olist(_1737394)))), _1737396)))], (47328 ^ _784416) ^ [_1737635, _1737637, _1737639, _1737641] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737635)), _1737637))), c_List_Ofoldr(tc_List_Olist(_1737639), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1737639)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1737639))), _1737641, 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(_1737635)), _1737637)), c_List_Ofoldr(tc_List_Olist(_1737639), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1737639)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1737639), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1737639)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1737639)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1737639), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1737639)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1737639), tc_List_Olist(_1737639), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1737639)))), _1737641), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (47330 ^ _784416) ^ [_1737804] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1737804)), c_List_Otranspose__rel(_1737804)), c_List_Olist_ONil(tc_List_Olist(_1737804)))), -(c_List_Otranspose(_1737804, c_List_Olist_ONil(tc_List_Olist(_1737804))) = c_List_Olist_ONil(tc_List_Olist(_1737804)))], (47336 ^ _784416) ^ [_1737931, _1737933, _1737935, _1737937] : [-(c_List_Omap__filter(_1737931, _1737933, _1737935, _1737937) = hAPP(hAPP(c_List_Omap(_1737931, _1737933), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1737933), _1737933, _1737931, c_Option_Othe(_1737933)), _1737935)), hAPP(c_List_Ofilter(_1737931, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1737931), c_fNot), hAPP(hAPP(c_COMBC(_1737931, tc_Option_Ooption(_1737933), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1737933), tc_fun(tc_Option_Ooption(_1737933), tc_HOL_Obool), _1737931), c_fequal), _1737935)), c_Option_Ooption_ONone(_1737933)))), _1737937)))], (47338 ^ _784416) ^ [_1738033, _1738035] : [-(c_List_Oconcat(_1738033, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1738033), tc_List_Olist(_1738033)), c_List_Olist_Olist__case(tc_List_Olist(_1738033), _1738033, c_List_Olist_ONil(_1738033), hAPP(hAPP(c_COMBB(tc_List_Olist(_1738033), tc_fun(tc_List_Olist(_1738033), tc_List_Olist(_1738033)), _1738033), c_COMBK(tc_List_Olist(_1738033), tc_List_Olist(_1738033))), hAPP(hAPP(c_COMBC(_1738033, tc_List_Olist(_1738033), tc_List_Olist(_1738033)), c_List_Olist_OCons(_1738033)), c_List_Olist_ONil(_1738033))))), _1738035)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1738033), _1738033), c_List_Ohd(_1738033)), hAPP(c_List_Ofilter(tc_List_Olist(_1738033), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1738033)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1738033), tc_List_Olist(_1738033), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1738033)))), _1738035)))], (47340 ^ _784416) ^ [_1738176, _1738178, _1738180, _1738182] : [-(hAPP(hAPP(c_List_Omap(_1738176, _1738178), _1738180), c_List_Oconcat(_1738176, _1738182)) = c_List_Oconcat(_1738178, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1738176), tc_List_Olist(_1738178)), hAPP(c_List_Omap(_1738176, _1738178), _1738180)), _1738182)))], (47342 ^ _784416) ^ [_1738239, _1738241, _1738243] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1738239), tc_List_Olist(_1738239), c_List_Oappend(_1738239), _1738241), _1738243) = hAPP(hAPP(c_List_Oappend(_1738239), _1738241), c_List_Oconcat(_1738239, _1738243)))], (47344 ^ _784416) ^ [_1738291, _1738293] : [-(c_List_Oconcat(_1738291, _1738293) = hAPP(c_List_Ofoldl(tc_List_Olist(_1738291), tc_List_Olist(_1738291), c_List_Oappend(_1738291), c_List_Olist_ONil(_1738291)), _1738293))], (47346 ^ _784416) ^ [_1738335, _1738337, _1738339] : [-(c_List_Omap__filter(_1738335, _1738337, _1738339, c_List_Olist_ONil(_1738335)) = c_List_Olist_ONil(_1738337))], (47348 ^ _784416) ^ [_1738371] : [-(c_List_Oconcat(_1738371, c_List_Olist_ONil(tc_List_Olist(_1738371))) = c_List_Olist_ONil(_1738371))], (47350 ^ _784416) ^ [_1738403, _1738405, _1738407] : [-(c_List_Oconcat(_1738403, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1738403)), _1738405), _1738407)) = hAPP(hAPP(c_List_Oappend(_1738403), _1738405), c_List_Oconcat(_1738403, _1738407)))], (47362 ^ _784416) ^ [_1738675, _1738677] : [47364 ^ _784416 : [(47365 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1738675)), 47363 ^ [_1738675, _1738677]), hAPP(c_List_Oset(tc_List_Olist(_1738675)), _1738677))))], (47367 ^ _784416) ^ [] : [47363 ^ [_1738675, _1738677] = c_List_Olist_ONil(_1738675)]], -(c_List_Oconcat(_1738675, _1738677) = c_List_Olist_ONil(_1738675))], (47352 ^ _784416) ^ [_1738469, _1738471] : [c_List_Oconcat(_1738469, _1738471) = c_List_Olist_ONil(_1738469), 47355 ^ _784416 : [(47356 ^ _784416) ^ [_1738560] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1738469)), _1738560), hAPP(c_List_Oset(tc_List_Olist(_1738469)), _1738471))), -(_1738560 = c_List_Olist_ONil(_1738469))]]], (47381 ^ _784416) ^ [_1739087, _1739089] : [47383 ^ _784416 : [(47384 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1739087)), 47382 ^ [_1739087, _1739089]), hAPP(c_List_Oset(tc_List_Olist(_1739087)), _1739089))))], (47386 ^ _784416) ^ [] : [47382 ^ [_1739087, _1739089] = c_List_Olist_ONil(_1739087)]], -(c_List_Olist_ONil(_1739087) = c_List_Oconcat(_1739087, _1739089))], (47371 ^ _784416) ^ [_1738881, _1738883] : [c_List_Olist_ONil(_1738881) = c_List_Oconcat(_1738881, _1738883), 47374 ^ _784416 : [(47375 ^ _784416) ^ [_1738972] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1738881)), _1738972), hAPP(c_List_Oset(tc_List_Olist(_1738881)), _1738883))), -(_1738972 = c_List_Olist_ONil(_1738881))]]], (47390 ^ _784416) ^ [_1739278, _1739280, _1739282] : [-(hAPP(c_List_Ofilter(_1739278, _1739280), c_List_Oconcat(_1739278, _1739282)) = c_List_Oconcat(_1739278, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1739278), tc_List_Olist(_1739278)), c_List_Ofilter(_1739278, _1739280)), _1739282)))], (47392 ^ _784416) ^ [_1739333, _1739335] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739333)), c_List_Oconcat(_1739333, _1739335)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1739333), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1739333))), _1739335)))], (47394 ^ _784416) ^ [_1739386, _1739388, _1739390, _1739392, _1739394, _1739396] : [hAPP(hAPP(c_Map_Omap__of(_1739386, _1739388), _1739390), _1739392) = hAPP(c_Option_Ooption_OSome(_1739388), _1739394), hBOOL(hAPP(hAPP(_1739396, _1739392), _1739394)), -(hAPP(hAPP(c_Map_Omap__of(_1739386, _1739388), hAPP(c_List_Ofilter(tc_prod(_1739386, _1739388), hAPP(c_Product__Type_Oprod_Oprod__case(_1739386, _1739388, tc_HOL_Obool), _1739396)), _1739390)), _1739392) = hAPP(c_Option_Ooption_OSome(_1739388), _1739394))], (47404 ^ _784416) ^ [_1739629, _1739631, _1739633, _1739635, _1739637] : [-(c_List_Omap__filter(_1739629, _1739631, _1739633, hAPP(hAPP(c_List_Olist_OCons(_1739629), _1739635), _1739637)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(_1739631), _1739631, c_List_Omap__filter(_1739629, _1739631, _1739633, _1739637), hAPP(hAPP(c_COMBC(_1739631, tc_List_Olist(_1739631), tc_List_Olist(_1739631)), c_List_Olist_OCons(_1739631)), c_List_Omap__filter(_1739629, _1739631, _1739633, _1739637))), hAPP(_1739633, _1739635)))], (47406 ^ _784416) ^ [_1739712, _1739714] : [-(hAPP(c_List_Oset(_1739712), c_List_Oconcat(_1739712, _1739714)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1739712), tc_fun(_1739712, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1739712)), _1739714)), c_List_Oset(_1739712)))], (47408 ^ _784416) ^ [_1739768, _1739770, _1739772] : [-(c_List_Oconcat(_1739768, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1739768)), _1739770), _1739772)) = hAPP(hAPP(c_List_Oappend(_1739768), c_List_Oconcat(_1739768, _1739770)), c_List_Oconcat(_1739768, _1739772)))], (47410 ^ _784416) ^ [_1739822, _1739824, _1739826, _1739828] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1739822, tc_Nat_Onat), _1739822), c_Product__Type_Ofst(_1739822, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1739822, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1739822, tc_Nat_Onat)), _1739824), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1739822, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1739822, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1739822, tc_Nat_Onat), _1739826), _1739828))) = hAPP(hAPP(c_List_Omap(tc_prod(_1739822, tc_Nat_Onat), _1739822), c_Product__Type_Ofst(_1739822, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1739822, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1739822, tc_Nat_Onat)), _1739824), c_Product__Type_Osnd(_1739822, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1739822, tc_Nat_Onat), _1739826), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1739828)))))], (47412 ^ _784416) ^ [_1739965, _1739967] : [-(c_Random_Opick(_1739965, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1739965), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1739965, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1739965, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1739965)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1739967)) = c_Random_Opick(_1739965, _1739967))], (47414 ^ _784416) ^ [_1740028, _1740030] : [-(c_Random_Oselect__weight(_1740028, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1740028), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1740028, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1740028, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1740028)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1740030)) = c_Random_Oselect__weight(_1740028, _1740030))], (47416 ^ _784416) ^ [_1740091, _1740093, _1740095, _1740097] : [-(c_List_Otranspose(_1740091, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1740091)), hAPP(hAPP(c_List_Olist_OCons(_1740091), _1740093), _1740095)), _1740097)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1740091)), hAPP(hAPP(c_List_Olist_OCons(_1740091), _1740093), c_List_Oconcat(_1740091, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1740091), tc_List_Olist(_1740091)), c_List_Olist_Olist__case(tc_List_Olist(_1740091), _1740091, c_List_Olist_ONil(_1740091), hAPP(hAPP(c_COMBB(tc_List_Olist(_1740091), tc_fun(tc_List_Olist(_1740091), tc_List_Olist(_1740091)), _1740091), c_COMBK(tc_List_Olist(_1740091), tc_List_Olist(_1740091))), hAPP(hAPP(c_COMBC(_1740091, tc_List_Olist(_1740091), tc_List_Olist(_1740091)), c_List_Olist_OCons(_1740091)), c_List_Olist_ONil(_1740091))))), _1740097)))), c_List_Otranspose(_1740091, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1740091)), _1740095), c_List_Oconcat(tc_List_Olist(_1740091), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1740091), tc_List_Olist(tc_List_Olist(_1740091))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1740091)), _1740091, c_List_Olist_ONil(tc_List_Olist(_1740091)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1740091), tc_List_Olist(tc_List_Olist(_1740091))), _1740091), hAPP(hAPP(c_COMBC(tc_List_Olist(_1740091), tc_List_Olist(tc_List_Olist(_1740091)), tc_List_Olist(tc_List_Olist(_1740091))), c_List_Olist_OCons(tc_List_Olist(_1740091))), c_List_Olist_ONil(tc_List_Olist(_1740091)))))), _1740097))))))], (47418 ^ _784416) ^ [_1740317, _1740319, _1740321] : [c_List_Oconcat(_1740317, _1740319) = c_List_Oconcat(_1740317, _1740321), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1740317))), _1740319) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1740317))), _1740321), 47428 ^ _784416 : [(47429 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1740317), tc_List_Olist(_1740317))), 47427 ^ [_1740317, _1740319, _1740321]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1740317), tc_List_Olist(_1740317))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1740317), tc_List_Olist(_1740317)), _1740319), _1740321)))))], (47431 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1740317), tc_List_Olist(_1740317), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1740317), tc_fun(tc_List_Olist(_1740317), tc_Nat_Onat), tc_fun(tc_List_Olist(_1740317), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1740317), tc_Nat_Onat), tc_fun(tc_List_Olist(_1740317), tc_HOL_Obool)), tc_List_Olist(_1740317)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1740317))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1740317)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1740317))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1740317)))), 47427 ^ [_1740317, _1740319, _1740321]))]], -(_1740319 = _1740321)], (47435 ^ _784416) ^ [_1740958, _1740960, _1740962] : [47437 ^ _784416 : [(47438 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1740958), tc_List_Olist(_1740958))), 47436 ^ [_1740958, _1740960, _1740962]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1740958), tc_List_Olist(_1740958))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1740958), tc_List_Olist(_1740958)), _1740960), _1740962)))))], (47440 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1740958), tc_List_Olist(_1740958), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1740958), tc_fun(tc_List_Olist(_1740958), tc_Nat_Onat), tc_fun(tc_List_Olist(_1740958), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1740958), tc_Nat_Onat), tc_fun(tc_List_Olist(_1740958), tc_HOL_Obool)), tc_List_Olist(_1740958)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1740958))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1740958)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1740958))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1740958)))), 47436 ^ [_1740958, _1740960, _1740962]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1740958))), _1740960) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1740958))), _1740962), 47445 ^ _784416 : [(47446 ^ _784416) ^ [] : [c_List_Oconcat(_1740958, _1740960) = c_List_Oconcat(_1740958, _1740962), -(_1740960 = _1740962)], (47452 ^ _784416) ^ [] : [_1740960 = _1740962, -(c_List_Oconcat(_1740958, _1740960) = c_List_Oconcat(_1740958, _1740962))]]], (47458 ^ _784416) ^ [_1741685, _1741687, _1741689, _1741691] : [-(c_List_Oconcat(_1741685, hAPP(hAPP(c_List_Omap(_1741687, tc_List_Olist(_1741685)), hAPP(hAPP(c_COMBC(_1741687, tc_List_Olist(_1741685), tc_List_Olist(_1741685)), hAPP(hAPP(c_COMBB(_1741685, tc_fun(tc_List_Olist(_1741685), tc_List_Olist(_1741685)), _1741687), c_List_Olist_OCons(_1741685)), _1741689)), c_List_Olist_ONil(_1741685))), _1741691)) = hAPP(hAPP(c_List_Omap(_1741687, _1741685), _1741689), _1741691))], (47460 ^ _784416) ^ [_1741772, _1741774, _1741776] : [-(c_Enum_On__lists(_1741772, hAPP(c_Nat_OSuc, _1741774), _1741776) = c_List_Oconcat(tc_List_Olist(_1741772), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1741772), tc_List_Olist(tc_List_Olist(_1741772))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1741772), tc_List_Olist(_1741772), tc_List_Olist(tc_List_Olist(_1741772))), hAPP(hAPP(c_COMBB(tc_fun(_1741772, tc_List_Olist(_1741772)), tc_fun(tc_List_Olist(_1741772), tc_List_Olist(tc_List_Olist(_1741772))), tc_List_Olist(_1741772)), c_List_Omap(_1741772, tc_List_Olist(_1741772))), hAPP(c_COMBC(_1741772, tc_List_Olist(_1741772), tc_List_Olist(_1741772)), c_List_Olist_OCons(_1741772)))), _1741776)), c_Enum_On__lists(_1741772, _1741774, _1741776))))], (47462 ^ _784416) ^ [_1741892, _1741894, _1741896, _1741898] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1741892)), c_List_Otranspose__rel(_1741892)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1741892)), hAPP(hAPP(c_List_Olist_OCons(_1741892), _1741894), _1741896)), _1741898))), -(c_List_Otranspose(_1741892, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1741892)), hAPP(hAPP(c_List_Olist_OCons(_1741892), _1741894), _1741896)), _1741898)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1741892)), hAPP(hAPP(c_List_Olist_OCons(_1741892), _1741894), c_List_Oconcat(_1741892, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1741892), tc_List_Olist(_1741892)), c_List_Olist_Olist__case(tc_List_Olist(_1741892), _1741892, c_List_Olist_ONil(_1741892), hAPP(hAPP(c_COMBB(tc_List_Olist(_1741892), tc_fun(tc_List_Olist(_1741892), tc_List_Olist(_1741892)), _1741892), c_COMBK(tc_List_Olist(_1741892), tc_List_Olist(_1741892))), hAPP(hAPP(c_COMBC(_1741892, tc_List_Olist(_1741892), tc_List_Olist(_1741892)), c_List_Olist_OCons(_1741892)), c_List_Olist_ONil(_1741892))))), _1741898)))), c_List_Otranspose(_1741892, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1741892)), _1741896), c_List_Oconcat(tc_List_Olist(_1741892), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1741892), tc_List_Olist(tc_List_Olist(_1741892))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1741892)), _1741892, c_List_Olist_ONil(tc_List_Olist(_1741892)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1741892), tc_List_Olist(tc_List_Olist(_1741892))), _1741892), hAPP(hAPP(c_COMBC(tc_List_Olist(_1741892), tc_List_Olist(tc_List_Olist(_1741892)), tc_List_Olist(tc_List_Olist(_1741892))), c_List_Olist_OCons(tc_List_Olist(_1741892))), c_List_Olist_ONil(tc_List_Olist(_1741892)))))), _1741898))))))], (47468 ^ _784416) ^ [_1742425, _1742427] : [-(c_List_Oconcat(tc_List_Olist(_1742425), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1742425), tc_List_Olist(tc_List_Olist(_1742425))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1742425)), _1742425, c_List_Olist_ONil(tc_List_Olist(_1742425)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1742425), tc_List_Olist(tc_List_Olist(_1742425))), _1742425), hAPP(hAPP(c_COMBC(tc_List_Olist(_1742425), tc_List_Olist(tc_List_Olist(_1742425)), tc_List_Olist(tc_List_Olist(_1742425))), c_List_Olist_OCons(tc_List_Olist(_1742425))), c_List_Olist_ONil(tc_List_Olist(_1742425)))))), _1742427)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1742425), tc_List_Olist(_1742425)), c_List_Otl(_1742425)), hAPP(c_List_Ofilter(tc_List_Olist(_1742425), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1742425)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1742425), tc_List_Olist(_1742425), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1742425)))), _1742427)))], (47470 ^ _784416) ^ [_1742577, _1742579, _1742581, _1742583, _1742585] : [-(hAPP(hAPP(c_List_Omap(_1742577, _1742579), _1742581), hAPP(c_List_Ofilter(_1742577, _1742583), _1742585)) = c_List_Omap__filter(_1742577, _1742579, hAPP(hAPP(c_COMBC(_1742577, tc_Option_Ooption(_1742579), tc_Option_Ooption(_1742579)), hAPP(hAPP(c_COMBS(_1742577, tc_Option_Ooption(_1742579), tc_fun(tc_Option_Ooption(_1742579), tc_Option_Ooption(_1742579))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1742579), tc_fun(tc_Option_Ooption(_1742579), tc_Option_Ooption(_1742579))), _1742577), c_If(tc_Option_Ooption(_1742579))), _1742583)), hAPP(hAPP(c_COMBB(_1742579, tc_Option_Ooption(_1742579), _1742577), c_Option_Ooption_OSome(_1742579)), _1742581))), c_Option_Ooption_ONone(_1742579)), _1742585))], (47472 ^ _784416) ^ [_1742703, _1742705, _1742707] : [-(c_List_Osublist(_1742703, _1742705, _1742707) = hAPP(hAPP(c_List_Omap(tc_prod(_1742703, tc_Nat_Onat), _1742703), c_Product__Type_Ofst(_1742703, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1742703, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1742703, 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(_1742703, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1742703, tc_Nat_Onat))), _1742707)), hAPP(hAPP(c_List_Ozip(_1742703, tc_Nat_Onat), _1742705), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742703)), _1742705))))))], (47474 ^ _784416) ^ [_1742806, _1742808, _1742810, _1742812] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1742806, tc_Nat_Onat), _1742806), c_Product__Type_Ofst(_1742806, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1742806, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1742806, 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(_1742806, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1742806, tc_Nat_Onat))), _1742808)), hAPP(hAPP(c_List_Ozip(_1742806, tc_Nat_Onat), _1742810), c_List_Oupt(_1742812, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1742812), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742806)), _1742810)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1742806, tc_Nat_Onat), _1742806), c_Product__Type_Ofst(_1742806, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1742806, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1742806, 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(_1742806, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1742806, 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(_1742806, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1742806, tc_Nat_Onat))), _1742812))), _1742808)), hAPP(hAPP(c_List_Ozip(_1742806, tc_Nat_Onat), _1742810), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742806)), _1742810))))))], (47476 ^ _784416) ^ [_1743011, _1743013] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1743011, _1743013)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1743011), hAPP(c_Nat_OSuc, _1743013)))], (47478 ^ _784416) ^ [_1743051, _1743053, _1743055] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1743051), c_List_Oupt(_1743053, _1743055)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1743053), _1743051), _1743055))], (47480 ^ _784416) ^ [_1743096, _1743098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1743096), _1743098)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1743096, _1743098)) = _1743096)], (47486 ^ _784416) ^ [_1743204, _1743206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1743204), _1743206)), -(c_List_Oupt(_1743204, hAPP(c_Nat_OSuc, _1743206)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1743204, _1743206)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1743206), c_List_Olist_ONil(tc_Nat_Onat))))], (47492 ^ _784416) ^ [_1743327, _1743329] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1743327), _1743329))), -(c_List_Oupt(_1743327, hAPP(c_Nat_OSuc, _1743329)) = c_List_Olist_ONil(tc_Nat_Onat))], (47498 ^ _784416) ^ [_1743376, _1743378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1743376), _1743378)), -(c_List_Oupt(_1743376, hAPP(c_Nat_OSuc, _1743378)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1743376, _1743378)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1743378), c_List_Olist_ONil(tc_Nat_Onat))))], (47504 ^ _784416) ^ [_1743505, _1743507, _1743509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1743505), _1743507)), -(c_List_Oupt(_1743505, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1743507), _1743509)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1743505, _1743507)), c_List_Oupt(_1743507, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1743507), _1743509))))], (47510 ^ _784416) ^ [_1743648] : [-(c_List_Oupt(_1743648, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (47512 ^ _784416) ^ [_1743674, _1743676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1743674), _1743676)), -(c_List_Oupt(_1743676, _1743674) = c_List_Olist_ONil(tc_Nat_Onat))], (47528 ^ _784416) ^ [_1743884, _1743886] : [47529 ^ _784416 : [(47530 ^ _784416) ^ [] : [_1743886 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47532 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1743886), _1743884))]], -(c_List_Oupt(_1743884, _1743886) = c_List_Olist_ONil(tc_Nat_Onat))], (47518 ^ _784416) ^ [_1743782, _1743784] : [c_List_Oupt(_1743782, _1743784) = c_List_Olist_ONil(tc_Nat_Onat), -(_1743784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1743784), _1743782)))], (47536 ^ _784416) ^ [_1744017, _1744019] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1744017, _1744019)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1744017), _1744019))], (47538 ^ _784416) ^ [_1744054, _1744056] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1744054), _1744056) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1744054, _1744056)))], (47540 ^ _784416) ^ [_1744091, _1744093] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1744091, _1744093))))], (47542 ^ _784416) ^ [_1744121, _1744123, _1744125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1744121), _1744123)), _1744125)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1744123), c_List_Oupt(_1744121, _1744125)) = c_List_Oupt(_1744121, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1744121), _1744123)))], (47548 ^ _784416) ^ [_1744258, _1744260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744258), _1744260)), -(c_List_Oupt(_1744258, _1744260) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1744258), c_List_Oupt(hAPP(c_Nat_OSuc, _1744258), _1744260)))], (47554 ^ _784416) ^ [_1744384, _1744386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744384), _1744386)), -(c_List_Oupt(_1744384, _1744386) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1744384), c_List_Oupt(hAPP(c_Nat_OSuc, _1744384), _1744386)))], (47560 ^ _784416) ^ [_1744495, _1744497] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744495), _1744497))), -(c_List_Oupt(_1744495, _1744497) = c_List_Olist_ONil(tc_Nat_Onat))], (47566 ^ _784416) ^ [_1744541, _1744543] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1744541, _1744543)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1744543), _1744541))], (47568 ^ _784416) ^ [_1744587, _1744589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1744587)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1744589))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1744587), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1744589)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1744587)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1744587)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1744589))))], (47574 ^ _784416) ^ [_1744740, _1744742] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1744740)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1744742)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1744740), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1744742)) = c_List_Olist_ONil(tc_Nat_Onat))], (47580 ^ _784416) ^ [_1744819, _1744821, _1744823, _1744825] : [c_List_Oupt(_1744819, _1744821) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1744823), _1744825), 47583 ^ _784416 : [(47584 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744819), _1744821)))], (47586 ^ _784416) ^ [] : [-(_1744819 = _1744823)], (47588 ^ _784416) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1744819), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1744821) = _1744825)]]], (47590 ^ _784416) ^ [_1744992, _1744994, _1744996, _1744998] : [-(c_List_Oupt(_1744992, _1744994) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1744996), _1744998)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1744992), _1744994)), _1744992 = _1744996, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1744992), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1744994) = _1744998], (47604 ^ _784416) ^ [_1745233, _1745235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1745233), _1745235)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1745233, _1745235)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1745235), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (47610 ^ _784416) ^ [_1745344, _1745346] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1745344), hAPP(c_List_Onth(_1745344), _1745346)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745344)), _1745346))) = _1745346)], (47612 ^ _784416) ^ [_1745393, _1745395] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1745393, _1745395) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1745393, hAPP(c_Nat_OSuc, _1745395))))], (47614 ^ _784416) ^ [_1745431] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1745431) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1745431)))], (47616 ^ _784416) ^ [_1745463, _1745465, _1745467, _1745469] : [class_Groups_Ocomm__monoid__add(_1745463), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1745463), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1745463), _1745465), c_List_Oupt(_1745467, _1745469))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1745463), _1745465), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1745467, _1745469))))], (47622 ^ _784416) ^ [_1745606, _1745608, _1745610, _1745612] : [class_Groups_Ocomm__monoid__add(_1745606), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1745606), _1745608), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1745610, _1745612))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1745606), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1745606), _1745608), c_List_Oupt(_1745610, _1745612))))], (47628 ^ _784416) ^ [_1745749, _1745751, _1745753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1745749), _1745751)), _1745753)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1745749, _1745753)), _1745751) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1745749), _1745751))], (47634 ^ _784416) ^ [_1745880, _1745882] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1745880, _1745882) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1745880), hAPP(c_Nat_OSuc, _1745882))))], (47636 ^ _784416) ^ [_1745921, _1745923] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1745921, _1745923) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1745921), _1745923)))], (47638 ^ _784416) ^ [_1745959, _1745961, _1745963, _1745965, _1745967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1745959), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1745961), _1745963))), -(hAPP(hAPP(c_List_Onth(_1745965), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1745965), _1745967), c_List_Oupt(_1745963, _1745961))), _1745959) = hAPP(_1745967, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1745963), _1745959)))], (47644 ^ _784416) ^ [_1746122] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1746122) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1746122))))], (47646 ^ _784416) ^ [_1746157, _1746159, _1746161] : [47647 ^ _784416 : [(47648 ^ _784416) ^ [] : [-(_1746157 = c_List_Olist_ONil(tc_List_Olist(_1746159)))], (47650 ^ _784416) ^ [] : [_1746161 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 47654 ^ _784416 : [(47655 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47653 ^ [_1746157, _1746159, _1746161]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1746159))), _1746157))))], (47657 ^ _784416) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746159)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1746159)), _1746157), 47653 ^ [_1746157, _1746159, _1746161])) = _1746161]], -(c_List_Otranspose(_1746159, _1746157) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1746159)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1746159)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1746159), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1746159)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1746159)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1746159), hAPP(hAPP(c_COMBB(tc_List_Olist(_1746159), tc_fun(tc_Nat_Onat, _1746159), tc_Nat_Onat), c_List_Onth(_1746159)), hAPP(c_List_Onth(tc_List_Olist(_1746159)), _1746157))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1746159))), _1746157)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1746161)))], (47661 ^ _784416) ^ [_1746667, _1746669] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746667)), c_List_Oremdups(_1746667, c_List_Oconcat(_1746667, _1746669))) = hAPP(c_Finite__Set_Ocard(_1746667), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1746667), tc_fun(_1746667, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1746667)), _1746669)), c_List_Oset(_1746667))))], (47663 ^ _784416) ^ [_1746733, _1746735] : [-(hBOOL(hAPP(c_List_Odistinct(_1746733), c_List_Oremdups(_1746733, _1746735))))], (47665 ^ _784416) ^ [_1746765, _1746767] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746765)), c_List_Oremdups(_1746765, _1746767))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746765)), _1746767))))], (47667 ^ _784416) ^ [_1746812, _1746814, _1746816] : [-(c_List_Oremdups(_1746812, hAPP(c_List_Ofilter(_1746812, _1746814), _1746816)) = hAPP(c_List_Ofilter(_1746812, _1746814), c_List_Oremdups(_1746812, _1746816)))], (47669 ^ _784416) ^ [_1746857, _1746859, _1746861, _1746863] : [-(c_List_Oremdups(_1746857, hAPP(hAPP(c_List_Omap(_1746859, _1746857), _1746861), c_List_Oremdups(_1746859, _1746863))) = c_List_Oremdups(_1746857, hAPP(hAPP(c_List_Omap(_1746859, _1746857), _1746861), _1746863)))], (47671 ^ _784416) ^ [_1746913, _1746915] : [-(hAPP(c_List_Oset(_1746913), c_List_Oremdups(_1746913, _1746915)) = hAPP(c_List_Oset(_1746913), _1746915))], (47673 ^ _784416) ^ [_1746951, _1746953] : [-(c_List_Oremdups(_1746951, c_List_Oremdups(_1746951, _1746953)) = c_List_Oremdups(_1746951, _1746953))], (47675 ^ _784416) ^ [_1746985, _1746987] : [hBOOL(hAPP(c_List_Odistinct(_1746985), _1746987)), -(c_List_Oremdups(_1746985, _1746987) = _1746987)], (47681 ^ _784416) ^ [_1747091, _1747093] : [c_List_Oremdups(_1747091, _1747093) = _1747093, -(hBOOL(hAPP(c_List_Odistinct(_1747091), _1747093)))], (47687 ^ _784416) ^ [_1747178, _1747180] : [hBOOL(hAPP(c_List_Odistinct(_1747178), _1747180)), -(c_List_Oremdups(_1747178, _1747180) = _1747180)], (47693 ^ _784416) ^ [_1747286, _1747288] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747286)), c_List_Oremdups(_1747286, _1747288)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747286)), _1747288), -(c_List_Oremdups(_1747286, _1747288) = _1747288)], (47699 ^ _784416) ^ [_1747399, _1747401] : [c_List_Oremdups(_1747399, _1747401) = _1747401, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747399)), c_List_Oremdups(_1747399, _1747401)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747399)), _1747401))], (47705 ^ _784416) ^ [_1747518] : [-(c_List_Oremdups(_1747518, c_List_Olist_ONil(_1747518)) = c_List_Olist_ONil(_1747518))], (47707 ^ _784416) ^ [_1747563, _1747565] : [c_List_Olist_ONil(_1747563) = c_List_Oremdups(_1747563, _1747565), -(_1747565 = c_List_Olist_ONil(_1747563))], (47713 ^ _784416) ^ [_1747650, _1747652] : [_1747652 = c_List_Olist_ONil(_1747650), -(c_List_Olist_ONil(_1747650) = c_List_Oremdups(_1747650, _1747652))], (47719 ^ _784416) ^ [_1747758, _1747760] : [c_List_Oremdups(_1747758, _1747760) = c_List_Olist_ONil(_1747758), -(_1747760 = c_List_Olist_ONil(_1747758))], (47725 ^ _784416) ^ [_1747845, _1747847] : [_1747847 = c_List_Olist_ONil(_1747845), -(c_List_Oremdups(_1747845, _1747847) = c_List_Olist_ONil(_1747845))], (47731 ^ _784416) ^ [_1747950, _1747952, _1747954] : [hBOOL(hAPP(hAPP(c_member(_1747950), _1747952), hAPP(c_List_Oset(_1747950), _1747954))), -(c_List_Oremdups(_1747950, hAPP(hAPP(c_List_Olist_OCons(_1747950), _1747952), _1747954)) = c_List_Oremdups(_1747950, _1747954))], (47737 ^ _784416) ^ [_1748075, _1748077, _1748079] : [-(hBOOL(hAPP(hAPP(c_member(_1748075), _1748077), hAPP(c_List_Oset(_1748075), _1748079)))), -(c_List_Oremdups(_1748075, hAPP(hAPP(c_List_Olist_OCons(_1748075), _1748077), _1748079)) = hAPP(hAPP(c_List_Olist_OCons(_1748075), _1748077), c_List_Oremdups(_1748075, _1748079)))], (47743 ^ _784416) ^ [_1748149, _1748151] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748149)), c_List_Oremdups(_1748149, _1748151)) = hAPP(c_Finite__Set_Ocard(_1748149), hAPP(c_List_Oset(_1748149), _1748151)))], (47745 ^ _784416) ^ [_1748194, _1748196, _1748198, _1748200, _1748202] : [c_Finite__Set_Ofun__left__comm(_1748194, _1748196, _1748198), -(hAPP(hAPP(c_Finite__Set_Ofold(_1748194, _1748196, _1748198), _1748200), hAPP(c_List_Oset(_1748194), _1748202)) = hAPP(c_List_Ofoldl(_1748196, _1748194, hAPP(c_COMBC(_1748194, _1748196, _1748196), _1748198), _1748200), c_List_Oremdups(_1748194, _1748202)))], (47751 ^ _784416) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (47753 ^ _784416) ^ [_1748363, _1748365, _1748367, _1748369, _1748371] : [class_Groups_Omonoid__add(_1748363), 47759 ^ _784416 : [(47760 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1748365), 47758 ^ [_1748363, _1748365, _1748367, _1748369, _1748371]), hAPP(c_List_Oset(_1748365), _1748367))))], (47762 ^ _784416) ^ [] : [hBOOL(hAPP(_1748369, 47758 ^ [_1748363, _1748365, _1748367, _1748369, _1748371]))], (47764 ^ _784416) ^ [] : [hAPP(_1748371, 47758 ^ [_1748363, _1748365, _1748367, _1748369, _1748371]) = c_Groups_Ozero__class_Ozero(_1748363)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1748363), hAPP(hAPP(c_List_Omap(_1748365, _1748363), _1748371), hAPP(c_List_Ofilter(_1748365, _1748369), _1748367))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1748363), hAPP(hAPP(c_List_Omap(_1748365, _1748363), _1748371), _1748367)))], (47768 ^ _784416) ^ [_1748754] : [-(c_List_Oreturn__list(_1748754) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1748754))], (47770 ^ _784416) ^ [_1748782] : [c_List_Onat__list(_1748782), -(c_List_Oembed__list(c_List_Oreturn__list(_1748782)) = _1748782)], (47776 ^ _784416) ^ [_1748863, _1748865] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1748863), _1748865) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1748863)), c_List_Oembed__list(_1748865))))], (47778 ^ _784416) ^ [_1748906] : [-(c_List_Oembed__list(_1748906) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1748906))], (47780 ^ _784416) ^ [_1748934, _1748936, _1748938, _1748940, _1748942] : [class_Groups_Ocomm__monoid__add(_1748934), hBOOL(hAPP(hAPP(c_member(_1748936), _1748938), hAPP(c_List_Oset(_1748936), _1748940))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1748934), hAPP(hAPP(c_List_Omap(_1748936, _1748934), _1748942), _1748940)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1748934), hAPP(_1748942, _1748938)), hAPP(c_List_Omonoid__add__class_Olistsum(_1748934), hAPP(hAPP(c_List_Omap(_1748936, _1748934), _1748942), c_List_Oremove1(_1748936, _1748938, _1748940)))))], (47790 ^ _784416) ^ [_1749183, _1749185, _1749187] : [hBOOL(hAPP(c_List_Odistinct(_1749183), _1749185)), -(hAPP(c_List_Oset(_1749183), c_List_Oremove1(_1749183, _1749187, _1749185)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1749183, tc_HOL_Obool)), hAPP(c_List_Oset(_1749183), _1749185)), hAPP(hAPP(c_Set_Oinsert(_1749183), _1749187), c_Orderings_Obot__class_Obot(tc_fun(_1749183, tc_HOL_Obool)))))], (47796 ^ _784416) ^ [_1749361, _1749363, _1749365, _1749367] : [_1749361 = _1749363, -(c_List_Oremove1(_1749365, _1749361, hAPP(hAPP(c_List_Olist_OCons(_1749365), _1749363), _1749367)) = _1749367)], (47802 ^ _784416) ^ [_1749460, _1749462, _1749464, _1749466] : [-(_1749460 = _1749462), -(c_List_Oremove1(_1749464, _1749460, hAPP(hAPP(c_List_Olist_OCons(_1749464), _1749462), _1749466)) = hAPP(hAPP(c_List_Olist_OCons(_1749464), _1749462), c_List_Oremove1(_1749464, _1749460, _1749466)))], (47808 ^ _784416) ^ [_1749526, _1749528, _1749530] : [hBOOL(hAPP(c_List_Odistinct(_1749526), _1749528)), -(c_List_Oremove1(_1749526, _1749530, c_List_Oremdups(_1749526, _1749528)) = c_List_Oremdups(_1749526, c_List_Oremove1(_1749526, _1749530, _1749528)))], (47814 ^ _784416) ^ [_1749641, _1749643, _1749645] : [hBOOL(hAPP(c_List_Odistinct(_1749641), _1749643)), -(hBOOL(hAPP(c_List_Odistinct(_1749641), c_List_Oremove1(_1749641, _1749645, _1749643))))], (47820 ^ _784416) ^ [_1749744, _1749746] : [-(c_List_Oremove1(_1749744, _1749746, c_List_Olist_ONil(_1749744)) = c_List_Olist_ONil(_1749744))], (47822 ^ _784416) ^ [_1749777, _1749779, _1749781, _1749783] : [-(c_List_Oremove1(_1749777, _1749779, c_List_Oremove1(_1749777, _1749781, _1749783)) = c_List_Oremove1(_1749777, _1749781, c_List_Oremove1(_1749777, _1749779, _1749783)))], (47824 ^ _784416) ^ [_1749818, _1749820, _1749822] : [-(hBOOL(hAPP(hAPP(c_member(_1749818), _1749820), hAPP(c_List_Oset(_1749818), _1749822)))), -(c_List_Oremove1(_1749818, _1749820, _1749822) = _1749822)], (47830 ^ _784416) ^ [_1749871, _1749873, _1749875, _1749877] : [-(hBOOL(hAPP(hAPP(c_member(_1749871), _1749873), hAPP(c_List_Oset(_1749871), _1749875)))), hBOOL(hAPP(hAPP(c_member(_1749871), _1749873), hAPP(c_List_Oset(_1749871), c_List_Oremove1(_1749871, _1749877, _1749875))))], (47836 ^ _784416) ^ [_1749994, _1749996, _1749998, _1750000] : [-(_1749994 = _1749996), 47839 ^ _784416 : [(47840 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1749998), _1749994), hAPP(c_List_Oset(_1749998), c_List_Oremove1(_1749998, _1749996, _1750000)))), -(hBOOL(hAPP(hAPP(c_member(_1749998), _1749994), hAPP(c_List_Oset(_1749998), _1750000))))], (47846 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1749998), _1749994), hAPP(c_List_Oset(_1749998), _1750000))), -(hBOOL(hAPP(hAPP(c_member(_1749998), _1749994), hAPP(c_List_Oset(_1749998), c_List_Oremove1(_1749998, _1749996, _1750000)))))]]], (47852 ^ _784416) ^ [_1750295, _1750297, _1750299] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1750295, tc_HOL_Obool)), hAPP(c_List_Oset(_1750295), c_List_Oremove1(_1750295, _1750297, _1750299))), hAPP(c_List_Oset(_1750295), _1750299))))], (47854 ^ _784416) ^ [_1750342, _1750344, _1750346, _1750348] : [-(hBOOL(hAPP(_1750342, _1750344))), -(c_List_Oremove1(_1750346, _1750344, hAPP(c_List_Ofilter(_1750346, _1750342), _1750348)) = hAPP(c_List_Ofilter(_1750346, _1750342), _1750348))], (47860 ^ _784416) ^ [_1750400, _1750402, _1750404, _1750406] : [-(hAPP(c_List_Ofilter(_1750400, _1750402), c_List_Oremove1(_1750400, _1750404, _1750406)) = c_List_Oremove1(_1750400, _1750404, hAPP(c_List_Ofilter(_1750400, _1750402), _1750406)))], (47862 ^ _784416) ^ [_1750464, _1750466, _1750468, _1750470] : [hBOOL(hAPP(hAPP(c_member(_1750464), _1750466), hAPP(c_List_Oset(_1750464), _1750468))), -(c_List_Oremove1(_1750464, _1750466, hAPP(hAPP(c_List_Oappend(_1750464), _1750468), _1750470)) = hAPP(hAPP(c_List_Oappend(_1750464), c_List_Oremove1(_1750464, _1750466, _1750468)), _1750470))], (47868 ^ _784416) ^ [_1750611, _1750613, _1750615, _1750617] : [-(hBOOL(hAPP(hAPP(c_member(_1750611), _1750613), hAPP(c_List_Oset(_1750611), _1750615)))), -(c_List_Oremove1(_1750611, _1750613, hAPP(hAPP(c_List_Oappend(_1750611), _1750615), _1750617)) = hAPP(hAPP(c_List_Oappend(_1750611), _1750615), c_List_Oremove1(_1750611, _1750613, _1750617)))], (47874 ^ _784416) ^ [_1750701, _1750703, _1750705] : [hBOOL(hAPP(hAPP(c_member(_1750701), _1750703), hAPP(c_List_Oset(_1750701), _1750705))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750701)), c_List_Oremove1(_1750701, _1750703, _1750705)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750701)), _1750705)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (47880 ^ _784416) ^ [_1750846, _1750848, _1750850] : [-(hBOOL(hAPP(hAPP(c_member(_1750846), _1750848), hAPP(c_List_Oset(_1750846), _1750850)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750846)), c_List_Oremove1(_1750846, _1750848, _1750850)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750846)), _1750850))], (47886 ^ _784416) ^ [_1750916, _1750918, _1750920] : [class_Orderings_Olinorder(_1750916), hBOOL(hAPP(c_Finite__Set_Ofinite(_1750916), _1750918)), -(c_List_Olinorder__class_Osorted__list__of__set(_1750916, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1750916, tc_HOL_Obool)), _1750918), hAPP(hAPP(c_Set_Oinsert(_1750916), _1750920), c_Orderings_Obot__class_Obot(tc_fun(_1750916, tc_HOL_Obool))))) = c_List_Oremove1(_1750916, _1750920, c_List_Olinorder__class_Osorted__list__of__set(_1750916, _1750918)))], (47896 ^ _784416) ^ [_1751123, _1751125, _1751127, _1751129, _1751131] : [c_List_Opartition(_1751123, _1751125, _1751127) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751123), tc_List_Olist(_1751123)), _1751129), _1751131), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1751123, tc_HOL_Obool)), hAPP(c_List_Oset(_1751123), _1751129)), hAPP(c_List_Oset(_1751123), _1751131)) = hAPP(c_List_Oset(_1751123), _1751127))], (47902 ^ _784416) ^ [_1751292, _1751294, _1751296] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1751292), tc_List_Olist(_1751292)), c_List_Opartition(_1751292, _1751294, _1751296)) = hAPP(c_List_Ofilter(_1751292, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1751292, c_fNot), _1751294)), _1751296))], (47904 ^ _784416) ^ [_1751347, _1751349, _1751351] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1751347), tc_List_Olist(_1751347)), c_List_Opartition(_1751347, _1751349, _1751351)) = hAPP(c_List_Ofilter(_1751347, _1751349), _1751351))], (47906 ^ _784416) ^ [_1751394] : [class_Orderings_Olinorder(_1751394), -(c_List_Olinorder__class_Osorted__list__of__set(_1751394, c_Orderings_Obot__class_Obot(tc_fun(_1751394, tc_HOL_Obool))) = c_List_Olist_ONil(_1751394))], (47912 ^ _784416) ^ [_1751487, _1751489] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1751487), _1751489)) = c_List_Oupt(_1751487, _1751489))], (47914 ^ _784416) ^ [_1751524, _1751526, _1751528, _1751530, _1751532] : [c_List_Opartition(_1751524, _1751526, _1751528) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751524), tc_List_Olist(_1751524)), _1751530), _1751532), 47917 ^ _784416 : [(47918 ^ _784416) ^ [_1751677] : [hBOOL(hAPP(hAPP(c_member(_1751524), _1751677), hAPP(c_List_Oset(_1751524), _1751530))), -(hBOOL(hAPP(_1751526, _1751677)))], (47924 ^ _784416) ^ [_1751786] : [hBOOL(hAPP(hAPP(c_member(_1751524), _1751786), hAPP(c_List_Oset(_1751524), _1751532))), hBOOL(hAPP(_1751526, _1751786))]]], (47930 ^ _784416) ^ [_1751906, _1751908] : [-(c_List_Opartition(_1751906, _1751908, c_List_Olist_ONil(_1751906)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751906), tc_List_Olist(_1751906)), c_List_Olist_ONil(_1751906)), c_List_Olist_ONil(_1751906)))], (47932 ^ _784416) ^ [_1751954, _1751956, _1751958] : [-(c_List_Opartition(_1751954, _1751956, _1751958) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1751954), tc_List_Olist(_1751954)), hAPP(c_List_Ofilter(_1751954, _1751956), _1751958)), hAPP(c_List_Ofilter(_1751954, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1751954, c_fNot), _1751956)), _1751958)))], (47934 ^ _784416) ^ [_1752018, _1752020, _1752022, _1752024] : [-(c_List_Opartition(_1752018, _1752020, hAPP(hAPP(c_List_Olist_OCons(_1752018), _1752022), _1752024)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1752018), tc_List_Olist(_1752018), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1752018), tc_fun(tc_List_Olist(_1752018), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018))), tc_fun(tc_List_Olist(_1752018), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1752018), tc_fun(tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018)), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018)))), tc_fun(tc_fun(tc_List_Olist(_1752018), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018))), tc_fun(tc_List_Olist(_1752018), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018)))), tc_List_Olist(_1752018)), c_COMBS(tc_List_Olist(_1752018), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018)), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1752018), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018))), tc_fun(tc_List_Olist(_1752018), tc_fun(tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018)), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018)))), tc_List_Olist(_1752018)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018)), tc_fun(tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018)), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018))), tc_List_Olist(_1752018)), hAPP(c_If(tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018))), hAPP(_1752020, _1752022)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1752018), tc_fun(tc_List_Olist(_1752018), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018))), tc_List_Olist(_1752018)), c_Product__Type_OPair(tc_List_Olist(_1752018), tc_List_Olist(_1752018))), hAPP(c_List_Olist_OCons(_1752018), _1752022))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1752018), tc_fun(tc_List_Olist(_1752018), tc_List_Olist(_1752018)), tc_fun(tc_List_Olist(_1752018), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1752018), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018))), tc_fun(tc_fun(tc_List_Olist(_1752018), tc_List_Olist(_1752018)), tc_fun(tc_List_Olist(_1752018), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018)))), tc_List_Olist(_1752018)), c_COMBB(tc_List_Olist(_1752018), tc_prod(tc_List_Olist(_1752018), tc_List_Olist(_1752018)), tc_List_Olist(_1752018))), c_Product__Type_OPair(tc_List_Olist(_1752018), tc_List_Olist(_1752018)))), hAPP(c_List_Olist_OCons(_1752018), _1752022)))), c_List_Opartition(_1752018, _1752020, _1752024)))], (47936 ^ _784416) ^ [_1752437, _1752439, _1752441] : [class_Orderings_Olinorder(_1752437), hBOOL(hAPP(c_Finite__Set_Ofinite(_1752437), _1752439)), -(c_List_Olinorder__class_Osorted__list__of__set(_1752437, hAPP(hAPP(c_Set_Oinsert(_1752437), _1752441), _1752439)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1752437, _1752437, c_COMBI(_1752437)), _1752441), c_List_Olinorder__class_Osorted__list__of__set(_1752437, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1752437, tc_HOL_Obool)), _1752439), hAPP(hAPP(c_Set_Oinsert(_1752437), _1752441), c_Orderings_Obot__class_Obot(tc_fun(_1752437, tc_HOL_Obool)))))))], (47946 ^ _784416) ^ [_1752676, _1752678] : [class_Orderings_Olinorder(_1752676), -(c_List_Olinorder__class_Osorted__list__of__set(_1752676, hAPP(c_List_Oset(_1752676), _1752678)) = c_List_Olinorder__class_Osort__key(_1752676, _1752676, c_COMBI(_1752676), c_List_Oremdups(_1752676, _1752678)))], (47952 ^ _784416) ^ [_1752787, _1752789] : [class_Orderings_Olinorder(_1752787), -(c_List_Olinorder__class_Osort__key(_1752787, _1752787, c_COMBI(_1752787), _1752789) = hAPP(c_List_Ofoldl(tc_List_Olist(_1752787), _1752787, hAPP(c_COMBC(_1752787, tc_List_Olist(_1752787), tc_List_Olist(_1752787)), c_List_Olinorder__class_Oinsort__key(_1752787, _1752787, c_COMBI(_1752787))), c_List_Olist_ONil(_1752787)), _1752789))], (47958 ^ _784416) ^ [_1752934, _1752936, _1752938, _1752940] : [class_Orderings_Olinorder(_1752934), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1752936, _1752934, _1752938), _1752940), c_List_Olist_ONil(_1752936)) = hAPP(hAPP(c_List_Olist_OCons(_1752936), _1752940), c_List_Olist_ONil(_1752936)))], (47964 ^ _784416) ^ [_1753057, _1753059, _1753061, _1753063, _1753065] : [class_Orderings_Olinorder(_1753057), -(c_List_Olinorder__class_Osort__key(_1753059, _1753057, _1753061, hAPP(hAPP(c_List_Olist_OCons(_1753059), _1753063), _1753065)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1753059, _1753057, _1753061), _1753063), c_List_Olinorder__class_Osort__key(_1753059, _1753057, _1753061, _1753065)))], (47970 ^ _784416) ^ [_1753194, _1753196, _1753198, _1753200, _1753202, _1753204] : [class_Orderings_Olinorder(_1753194), 47973 ^ _784416 : [(47974 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1753194), hAPP(_1753196, _1753198)), hAPP(_1753196, _1753200))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1753202, _1753194, _1753196), _1753198), hAPP(hAPP(c_List_Olist_OCons(_1753202), _1753200), _1753204)) = hAPP(hAPP(c_List_Olist_OCons(_1753202), _1753198), hAPP(hAPP(c_List_Olist_OCons(_1753202), _1753200), _1753204)))], (47980 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1753194), hAPP(_1753196, _1753198)), hAPP(_1753196, _1753200)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1753202, _1753194, _1753196), _1753198), hAPP(hAPP(c_List_Olist_OCons(_1753202), _1753200), _1753204)) = hAPP(hAPP(c_List_Olist_OCons(_1753202), _1753200), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1753202, _1753194, _1753196), _1753198), _1753204)))]]], (47986 ^ _784416) ^ [_1753576, _1753578, _1753580, _1753582] : [class_Orderings_Olinorder(_1753576), 47989 ^ _784416 : [(47990 ^ _784416) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1753578), c_List_Olinorder__class_Osort__key(_1753578, _1753576, _1753580, _1753582))), -(hBOOL(hAPP(c_List_Odistinct(_1753578), _1753582)))], (47996 ^ _784416) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1753578), _1753582)), -(hBOOL(hAPP(c_List_Odistinct(_1753578), c_List_Olinorder__class_Osort__key(_1753578, _1753576, _1753580, _1753582))))]]], (48002 ^ _784416) ^ [_1753832, _1753834, _1753836, _1753838, _1753840] : [class_Orderings_Olinorder(_1753832), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1753834, _1753832, _1753836), _1753838), _1753840) = c_List_Olist_ONil(_1753834)], (48008 ^ _784416) ^ [_1753938, _1753940, _1753942] : [class_Orderings_Olinorder(_1753938), -(c_List_Olinorder__class_Osort__key(_1753940, _1753938, _1753942, c_List_Olist_ONil(_1753940)) = c_List_Olist_ONil(_1753940))], (48014 ^ _784416) ^ [_1754033, _1754035, _1754037, _1754039, _1754041] : [class_Orderings_Olinorder(_1754033), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754035)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1754035, _1754033, _1754037), _1754039), _1754041)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754035)), _1754041)))], (48020 ^ _784416) ^ [_1754168, _1754170, _1754172, _1754174] : [class_Orderings_Olinorder(_1754168), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754170)), c_List_Olinorder__class_Osort__key(_1754170, _1754168, _1754172, _1754174)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754170)), _1754174))], (48026 ^ _784416) ^ [_1754285, _1754287, _1754289, _1754291] : [class_Orderings_Olinorder(_1754285), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1754285, _1754285, c_COMBI(_1754285)), _1754287), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1754285, _1754285, c_COMBI(_1754285)), _1754289), _1754291)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1754285, _1754285, c_COMBI(_1754285)), _1754289), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1754285, _1754285, c_COMBI(_1754285)), _1754287), _1754291)))], (48032 ^ _784416) ^ [_1754460, _1754462, _1754464, _1754466, _1754468, _1754470] : [class_Orderings_Olinorder(_1754460), -(hAPP(_1754462, _1754464) = hAPP(_1754462, _1754466)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1754468, _1754460, _1754462), _1754466), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1754468, _1754460, _1754462), _1754464), _1754470)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1754468, _1754460, _1754462), _1754464), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1754468, _1754460, _1754462), _1754466), _1754470)))], (48042 ^ _784416) ^ [_1754650] : [class_Orderings_Olinorder(_1754650), -(c_Finite__Set_Ofun__left__comm(_1754650, tc_List_Olist(_1754650), c_List_Olinorder__class_Oinsort__key(_1754650, _1754650, c_COMBI(_1754650))))], (48048 ^ _784416) ^ [_1754741, _1754743, _1754745, _1754747, _1754749] : [class_Orderings_Olinorder(_1754741), -(hAPP(c_List_Oset(_1754743), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1754743, _1754741, _1754745), _1754747), _1754749)) = hAPP(hAPP(c_Set_Oinsert(_1754743), _1754747), hAPP(c_List_Oset(_1754743), _1754749)))], (48054 ^ _784416) ^ [_1754878, _1754880, _1754882, _1754884] : [class_Orderings_Olinorder(_1754878), -(hAPP(c_List_Oset(_1754880), c_List_Olinorder__class_Osort__key(_1754880, _1754878, _1754882, _1754884)) = hAPP(c_List_Oset(_1754880), _1754884))], (48060 ^ _784416) ^ [_1754987, _1754989, _1754991, _1754993, _1754995, _1754997] : [class_Orderings_Olinorder(_1754987), -(hBOOL(hAPP(_1754989, _1754991))), -(hAPP(c_List_Ofilter(_1754993, _1754989), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1754993, _1754987, _1754995), _1754991), _1754997)) = hAPP(c_List_Ofilter(_1754993, _1754989), _1754997))], (48070 ^ _784416) ^ [_1755133, _1755135, _1755137, _1755139, _1755141] : [class_Orderings_Olinorder(_1755133), -(hAPP(c_List_Ofilter(_1755135, _1755137), c_List_Olinorder__class_Osort__key(_1755135, _1755133, _1755139, _1755141)) = c_List_Olinorder__class_Osort__key(_1755135, _1755133, _1755139, hAPP(c_List_Ofilter(_1755135, _1755137), _1755141)))], (48076 ^ _784416) ^ [_1755258, _1755260, _1755262] : [class_Orderings_Olinorder(_1755258), -(c_List_Oremove1(_1755258, _1755260, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1755258, _1755258, c_COMBI(_1755258)), _1755260), _1755262)) = _1755262)], (48082 ^ _784416) ^ [_1755367, _1755369, _1755371, _1755373, _1755375] : [class_Orderings_Olinorder(_1755367), 48085 ^ _784416 : [(48086 ^ _784416) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1755369), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1755369, _1755367, _1755371), _1755373), _1755375))), 48089 ^ _784416 : [(48090 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1755369), _1755373), hAPP(c_List_Oset(_1755369), _1755375)))], (48092 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1755369), _1755375)))]]], (48094 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1755369), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1755369, _1755367, _1755371), _1755373), _1755375)))), -(hBOOL(hAPP(hAPP(c_member(_1755369), _1755373), hAPP(c_List_Oset(_1755369), _1755375)))), hBOOL(hAPP(c_List_Odistinct(_1755369), _1755375))]]], (48104 ^ _784416) ^ [_1755769, _1755771, _1755773, _1755775, _1755777] : [class_Orderings_Olinorder(_1755769), hBOOL(hAPP(hAPP(c_member(_1755771), _1755773), hAPP(c_List_Oset(_1755771), _1755775))), c_List_Olinorder__class_Osorted(_1755769, hAPP(hAPP(c_List_Omap(_1755771, _1755769), _1755777), _1755775)), hAPP(c_List_Ohd(_1755771), hAPP(c_List_Ofilter(_1755771, hAPP(hAPP(c_COMBB(_1755769, tc_HOL_Obool, _1755771), hAPP(c_fequal, hAPP(_1755777, _1755773))), _1755777)), _1755775)) = _1755773, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1755771, _1755769, _1755777), _1755773), c_List_Oremove1(_1755771, _1755773, _1755775)) = _1755775)], (48122 ^ _784416) ^ [_1756148, _1756150, _1756152, _1756154, _1756156] : [class_Orderings_Olinorder(_1756148), -(hBOOL(hAPP(hAPP(c_member(_1756148), hAPP(_1756150, _1756152)), hAPP(c_Set_Oimage(_1756154, _1756148, _1756150), hAPP(c_List_Oset(_1756154), _1756156))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1756154, _1756148, _1756150, _1756152, _1756156) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1756154, _1756148, _1756150), _1756152), _1756156))], (48132 ^ _784416) ^ [_1756320] : [class_Orderings_Olinorder(_1756320), -(c_List_Olinorder__class_Osorted(_1756320, c_List_Olist_ONil(_1756320)))], (48138 ^ _784416) ^ [_1756397, _1756399] : [class_Orderings_Olinorder(_1756397), -(c_List_Olinorder__class_Osorted(_1756397, hAPP(hAPP(c_List_Olist_OCons(_1756397), _1756399), c_List_Olist_ONil(_1756397))))], (48144 ^ _784416) ^ [_1756492, _1756494, _1756496] : [class_Orderings_Olinorder(_1756492), 48147 ^ _784416 : [(48148 ^ _784416) ^ [] : [c_List_Olinorder__class_Osorted(_1756492, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1756492, _1756492, c_COMBI(_1756492)), _1756494), _1756496)), -(c_List_Olinorder__class_Osorted(_1756492, _1756496))], (48154 ^ _784416) ^ [] : [c_List_Olinorder__class_Osorted(_1756492, _1756496), -(c_List_Olinorder__class_Osorted(_1756492, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1756492, _1756492, c_COMBI(_1756492)), _1756494), _1756496)))]]], (48160 ^ _784416) ^ [_1756739, _1756741] : [class_Orderings_Olinorder(_1756739), -(c_List_Olinorder__class_Osorted(_1756739, c_List_Olinorder__class_Osort__key(_1756739, _1756739, c_COMBI(_1756739), _1756741)))], (48166 ^ _784416) ^ [_1756828, _1756830, _1756832, _1756834] : [class_Orderings_Olinorder(_1756828), -(c_List_Olinorder__class_Osorted(_1756828, hAPP(hAPP(c_List_Omap(_1756830, _1756828), _1756832), c_List_Olinorder__class_Osort__key(_1756830, _1756828, _1756832, _1756834))))], (48172 ^ _784416) ^ [_1756935, _1756937, _1756939, _1756941, _1756943] : [class_Orderings_Olinorder(_1756935), 48175 ^ _784416 : [(48176 ^ _784416) ^ [] : [c_List_Olinorder__class_Osorted(_1756935, hAPP(hAPP(c_List_Omap(_1756937, _1756935), _1756939), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1756937, _1756935, _1756939), _1756941), _1756943))), -(c_List_Olinorder__class_Osorted(_1756935, hAPP(hAPP(c_List_Omap(_1756937, _1756935), _1756939), _1756943)))], (48182 ^ _784416) ^ [] : [c_List_Olinorder__class_Osorted(_1756935, hAPP(hAPP(c_List_Omap(_1756937, _1756935), _1756939), _1756943)), -(c_List_Olinorder__class_Osorted(_1756935, hAPP(hAPP(c_List_Omap(_1756937, _1756935), _1756939), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1756937, _1756935, _1756939), _1756941), _1756943))))]]], (48188 ^ _784416) ^ [_1757242, _1757244, _1757246, _1757248, _1757250] : [class_Orderings_Olinorder(_1757242), c_List_Olinorder__class_Osorted(_1757242, hAPP(hAPP(c_List_Omap(_1757244, _1757242), _1757246), _1757248)), -(c_List_Olinorder__class_Osorted(_1757242, hAPP(hAPP(c_List_Omap(_1757244, _1757242), _1757246), c_List_Olinorder__class_Oinsort__insert__key(_1757244, _1757242, _1757246, _1757250, _1757248))))], (48198 ^ _784416) ^ [_1757429, _1757431, _1757433, _1757435, _1757437] : [class_Orderings_Olinorder(_1757429), c_List_Olinorder__class_Osorted(_1757429, hAPP(hAPP(c_List_Omap(_1757431, _1757429), _1757433), _1757435)), -(c_List_Olinorder__class_Osorted(_1757429, hAPP(hAPP(c_List_Omap(_1757431, _1757429), _1757433), c_List_Oremove1(_1757431, _1757437, _1757435))))], (48208 ^ _784416) ^ [_1757612, _1757614, _1757616, _1757618, _1757620] : [class_Orderings_Olinorder(_1757612), -(c_List_Olinorder__class_Osorted(_1757612, hAPP(hAPP(c_List_Omap(_1757614, _1757612), _1757616), hAPP(c_List_Ofilter(_1757614, hAPP(hAPP(c_COMBC(_1757614, _1757612, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1757612, tc_fun(_1757612, tc_HOL_Obool), _1757614), c_fequal), _1757616)), hAPP(_1757618, _1757620))), _1757620))))], (48214 ^ _784416) ^ [_1757775, _1757777, _1757779, _1757781, _1757783] : [class_Orderings_Olinorder(_1757775), c_List_Olinorder__class_Osorted(_1757775, hAPP(hAPP(c_List_Omap(_1757777, _1757775), _1757779), _1757781)), -(c_List_Olinorder__class_Osorted(_1757775, hAPP(hAPP(c_List_Omap(_1757777, _1757775), _1757779), hAPP(c_List_Ofilter(_1757777, _1757783), _1757781))))], (48224 ^ _784416) ^ [_1757962, _1757964, _1757966] : [class_Orderings_Olinorder(_1757962), c_List_Olinorder__class_Osorted(_1757962, _1757964), -(c_List_Olinorder__class_Osorted(_1757962, c_List_Oremove1(_1757962, _1757966, _1757964)))], (48234 ^ _784416) ^ [_1758101, _1758103, _1758105] : [class_Orderings_Olinorder(_1758101), -(c_List_Olinorder__class_Osorted(_1758101, hAPP(c_List_Ofilter(_1758101, hAPP(hAPP(c_COMBC(_1758101, _1758101, tc_HOL_Obool), c_fequal), hAPP(_1758103, _1758105))), _1758105)))], (48240 ^ _784416) ^ [_1758216, _1758218] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1758216, _1758218)))], (48242 ^ _784416) ^ [_1758244, _1758246] : [class_Orderings_Olinorder(_1758244), c_List_Olinorder__class_Osorted(_1758244, _1758246), -(c_List_Olinorder__class_Osorted(_1758244, hAPP(c_List_Otl(_1758244), _1758246)))], (48252 ^ _784416) ^ [_1758381, _1758383] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1758381, _1758383)))], (48254 ^ _784416) ^ [_1758409, _1758411, _1758413] : [class_Orderings_Olinorder(_1758409), c_List_Olinorder__class_Osorted(_1758409, _1758411), -(c_List_Olinorder__class_Osorted(_1758409, c_List_Olinorder__class_Oinsort__insert__key(_1758409, _1758409, c_COMBI(_1758409), _1758413, _1758411)))], (48264 ^ _784416) ^ [_1758556, _1758558, _1758560] : [class_Orderings_Olinorder(_1758556), c_List_Olinorder__class_Osorted(_1758556, _1758558), -(c_List_Olinorder__class_Osorted(_1758556, hAPP(hAPP(c_List_Odrop(_1758556), _1758560), _1758558)))], (48274 ^ _784416) ^ [_1758703] : [class_Orderings_Olinorder(_1758703), -(c_List_Olinorder__class_Osorted(_1758703, c_List_Olist_ONil(_1758703)))], (48280 ^ _784416) ^ [_1758780, _1758782, _1758784, _1758786, _1758788] : [class_Orderings_Olinorder(_1758780), hBOOL(hAPP(c_List_Odistinct(_1758782), _1758784)), -(hBOOL(hAPP(c_List_Odistinct(_1758782), c_List_Olinorder__class_Oinsort__insert__key(_1758782, _1758780, _1758786, _1758788, _1758784))))], (48290 ^ _784416) ^ [_1758947, _1758949] : [class_Orderings_Olinorder(_1758947), c_List_Olinorder__class_Osorted(_1758947, _1758949), -(c_List_Olinorder__class_Osorted(_1758947, c_List_Oremdups(_1758947, _1758949)))], (48300 ^ _784416) ^ [_1759080, _1759082, _1759084] : [class_Orderings_Olinorder(_1759080), c_List_Olinorder__class_Osorted(_1759080, _1759082), -(c_List_Olinorder__class_Osorted(_1759080, hAPP(hAPP(c_List_Otake(_1759080), _1759084), _1759082)))], (48310 ^ _784416) ^ [_1759227, _1759229, _1759231, _1759233] : [class_Orderings_Olinorder(_1759227), 48313 ^ _784416 : [(48314 ^ _784416) ^ [] : [c_List_Olinorder__class_Osorted(_1759227, hAPP(hAPP(c_List_Olist_OCons(_1759227), _1759229), hAPP(hAPP(c_List_Olist_OCons(_1759227), _1759231), _1759233))), 48317 ^ _784416 : [(48318 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1759227), _1759229), _1759231)))], (48320 ^ _784416) ^ [] : [-(c_List_Olinorder__class_Osorted(_1759227, hAPP(hAPP(c_List_Olist_OCons(_1759227), _1759231), _1759233)))]]], (48322 ^ _784416) ^ [] : [-(c_List_Olinorder__class_Osorted(_1759227, hAPP(hAPP(c_List_Olist_OCons(_1759227), _1759229), hAPP(hAPP(c_List_Olist_OCons(_1759227), _1759231), _1759233)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1759227), _1759229), _1759231)), c_List_Olinorder__class_Osorted(_1759227, hAPP(hAPP(c_List_Olist_OCons(_1759227), _1759231), _1759233))]]], (48332 ^ _784416) ^ [_1759613, _1759615, _1759617, _1759619] : [class_Orderings_Olinorder(_1759613), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1759613), _1759615), _1759617)), c_List_Olinorder__class_Osorted(_1759613, hAPP(hAPP(c_List_Olist_OCons(_1759613), _1759617), _1759619)), -(c_List_Olinorder__class_Osorted(_1759613, hAPP(hAPP(c_List_Olist_OCons(_1759613), _1759615), hAPP(hAPP(c_List_Olist_OCons(_1759613), _1759617), _1759619))))], (48346 ^ _784416) ^ [_1759866, _1759868] : [class_Orderings_Olinorder(_1759866), -(_1759868 = c_List_Olist_ONil(_1759866)), c_List_Olinorder__class_Osorted(_1759866, _1759868), -(c_List_Olinorder__class_Osorted(_1759866, c_List_Obutlast(_1759866, _1759868)))], (48360 ^ _784416) ^ [_1760058, _1760060, _1760062] : [class_Orderings_Olinorder(_1760058), c_List_Olinorder__class_Osorted(_1760058, _1760060), hBOOL(hAPP(c_List_Odistinct(_1760058), _1760060)), c_List_Olinorder__class_Osorted(_1760058, _1760062), hBOOL(hAPP(c_List_Odistinct(_1760058), _1760062)), hAPP(c_List_Oset(_1760058), _1760060) = hAPP(c_List_Oset(_1760058), _1760062), -(_1760060 = _1760062)], (48386 ^ _784416) ^ [_1760441, _1760443, _1760445] : [class_Orderings_Olinorder(_1760441), 48389 ^ _784416 : [(48390 ^ _784416) ^ [] : [c_List_Olinorder__class_Osorted(_1760441, hAPP(hAPP(c_List_Olist_OCons(_1760441), _1760443), _1760445)), 48393 ^ _784416 : [(48394 ^ _784416) ^ [] : [-(c_List_Olinorder__class_Osorted(_1760441, _1760445))], (48396 ^ _784416) ^ [_1760627] : [hBOOL(hAPP(hAPP(c_member(_1760441), _1760627), hAPP(c_List_Oset(_1760441), _1760445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1760441), _1760443), _1760627)))]]], (48402 ^ _784416) ^ [] : [-(c_List_Olinorder__class_Osorted(_1760441, hAPP(hAPP(c_List_Olist_OCons(_1760441), _1760443), _1760445))), c_List_Olinorder__class_Osorted(_1760441, _1760445), 48408 ^ _784416 : [(48409 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760441), 48407 ^ [_1760441, _1760443, _1760445]), hAPP(c_List_Oset(_1760441), _1760445))))], (48411 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1760441), _1760443), 48407 ^ [_1760441, _1760443, _1760445]))]]]]], (48415 ^ _784416) ^ [_1760966, _1760968, _1760970] : [class_Orderings_Olinorder(_1760966), 48418 ^ _784416 : [(48419 ^ _784416) ^ [] : [c_List_Olinorder__class_Osorted(_1760966, hAPP(hAPP(c_List_Oappend(_1760966), _1760968), _1760970)), 48422 ^ _784416 : [(48423 ^ _784416) ^ [] : [-(c_List_Olinorder__class_Osorted(_1760966, _1760968))], (48425 ^ _784416) ^ [] : [-(c_List_Olinorder__class_Osorted(_1760966, _1760970))], (48427 ^ _784416) ^ [_1761202] : [hBOOL(hAPP(hAPP(c_member(_1760966), _1761202), hAPP(c_List_Oset(_1760966), _1760968))), 48430 ^ _784416 : [(48431 ^ _784416) ^ [_1761312] : [hBOOL(hAPP(hAPP(c_member(_1760966), _1761312), hAPP(c_List_Oset(_1760966), _1760970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1760966), _1761202), _1761312)))]]]]], (48437 ^ _784416) ^ [] : [-(c_List_Olinorder__class_Osorted(_1760966, hAPP(hAPP(c_List_Oappend(_1760966), _1760968), _1760970))), c_List_Olinorder__class_Osorted(_1760966, _1760968), c_List_Olinorder__class_Osorted(_1760966, _1760970), 48447 ^ _784416 : [(48448 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760966), 48446 ^ [_1760966, _1760968, _1760970]), hAPP(c_List_Oset(_1760966), _1760968))))], (48451 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760966), 48449 ^ [_1760966, _1760968, _1760970]), hAPP(c_List_Oset(_1760966), _1760970))))], (48453 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1760966), 48446 ^ [_1760966, _1760968, _1760970]), 48449 ^ [_1760966, _1760968, _1760970]))]]]]], (48457 ^ _784416) ^ [_1761814, _1761816, _1761818, _1761820, _1761822, _1761824] : [class_Orderings_Olinorder(_1761814), c_List_Olinorder__class_Osorted(_1761814, hAPP(hAPP(c_List_Omap(_1761816, _1761814), _1761818), _1761820)), hBOOL(hAPP(_1761822, _1761824)), -(hAPP(c_List_Ofilter(_1761816, _1761822), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1761816, _1761814, _1761818), _1761824), _1761820)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1761816, _1761814, _1761818), _1761824), hAPP(c_List_Ofilter(_1761816, _1761822), _1761820)))], (48471 ^ _784416) ^ [_1762103, _1762105, _1762107] : [class_Orderings_Olinorder(_1762103), 48474 ^ _784416 : [(48475 ^ _784416) ^ [] : [c_List_Olinorder__class_Osorted(_1762103, hAPP(hAPP(c_List_Olist_OCons(_1762103), _1762105), _1762107)), 48478 ^ _784416 : [(48485 ^ _784416) ^ [] : [-(c_List_Olinorder__class_Osorted(_1762103, _1762107))], (48479 ^ _784416) ^ [_1762271] : [hBOOL(hAPP(hAPP(c_member(_1762103), _1762271), hAPP(c_List_Oset(_1762103), _1762107))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1762103), _1762105), _1762271)))]]], (48487 ^ _784416) ^ [] : [-(c_List_Olinorder__class_Osorted(_1762103, hAPP(hAPP(c_List_Olist_OCons(_1762103), _1762105), _1762107))), 48491 ^ _784416 : [(48492 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1762103), 48490 ^ [_1762103, _1762105, _1762107]), hAPP(c_List_Oset(_1762103), _1762107))))], (48494 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1762103), _1762105), 48490 ^ [_1762103, _1762105, _1762107]))]], c_List_Olinorder__class_Osorted(_1762103, _1762107)]]], (48500 ^ _784416) ^ [_1762629, _1762631, _1762633] : [class_Orderings_Olinorder(_1762629), hBOOL(hAPP(hAPP(c_member(_1762629), _1762631), hAPP(c_List_Oset(_1762629), _1762633))), -(c_List_Olinorder__class_Oinsort__insert__key(_1762629, _1762629, c_COMBI(_1762629), _1762631, _1762633) = _1762633)], (48510 ^ _784416) ^ [_1762800, _1762802, _1762804] : [class_Orderings_Olinorder(_1762800), -(hAPP(c_List_Oset(_1762800), c_List_Olinorder__class_Oinsort__insert__key(_1762800, _1762800, c_COMBI(_1762800), _1762802, _1762804)) = hAPP(hAPP(c_Set_Oinsert(_1762800), _1762802), hAPP(c_List_Oset(_1762800), _1762804)))], (48516 ^ _784416) ^ [_1762929, _1762931] : [class_Orderings_Olinorder(_1762929), hBOOL(hAPP(c_Finite__Set_Ofinite(_1762929), _1762931)), 48523 ^ _784416 : [(48524 ^ _784416) ^ [] : [-(hAPP(c_List_Oset(_1762929), c_List_Olinorder__class_Osorted__list__of__set(_1762929, _1762931)) = _1762931)], (48526 ^ _784416) ^ [] : [-(c_List_Olinorder__class_Osorted(_1762929, c_List_Olinorder__class_Osorted__list__of__set(_1762929, _1762931)))], (48528 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1762929), c_List_Olinorder__class_Osorted__list__of__set(_1762929, _1762931))))]]], (48530 ^ _784416) ^ [_1763150, _1763152, _1763154] : [class_Orderings_Olinorder(_1763150), hBOOL(hAPP(hAPP(c_member(_1763150), _1763152), hAPP(c_List_Oset(_1763150), _1763154))), c_List_Olinorder__class_Osorted(_1763150, _1763154), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1763150, _1763150, c_COMBI(_1763150)), _1763152), c_List_Oremove1(_1763150, _1763152, _1763154)) = _1763154)], (48544 ^ _784416) ^ [_1763391, _1763393] : [class_Orderings_Olinorder(_1763391), 48547 ^ _784416 : [(48562 ^ _784416) ^ [] : [48564 ^ _784416 : [(48565 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48563 ^ [_1763391, _1763393]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763391)), _1763393))))], (48568 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 48566 ^ [_1763391, _1763393]), 48563 ^ [_1763391, _1763393])))], (48570 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1763391), hAPP(hAPP(c_List_Onth(_1763391), _1763393), 48566 ^ [_1763391, _1763393])), hAPP(hAPP(c_List_Onth(_1763391), _1763393), 48563 ^ [_1763391, _1763393])))]], -(c_List_Olinorder__class_Osorted(_1763391, _1763393))], (48548 ^ _784416) ^ [] : [c_List_Olinorder__class_Osorted(_1763391, _1763393), 48551 ^ _784416 : [(48552 ^ _784416) ^ [_1763562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1763562), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763391)), _1763393))), 48555 ^ _784416 : [(48556 ^ _784416) ^ [_1763679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1763679), _1763562)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1763391), hAPP(hAPP(c_List_Onth(_1763391), _1763393), _1763679)), hAPP(hAPP(c_List_Onth(_1763391), _1763393), _1763562))))]]]]]]], (48574 ^ _784416) ^ [_1764115, _1764117, _1764119, _1764121] : [class_Orderings_Olinorder(_1764115), c_List_Olinorder__class_Osorted(_1764115, _1764117), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1764119), _1764121)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1764121), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1764115)), _1764117))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1764115), hAPP(hAPP(c_List_Onth(_1764115), _1764117), _1764119)), hAPP(hAPP(c_List_Onth(_1764115), _1764117), _1764121))))], (48592 ^ _784416) ^ [_1764442, _1764444, _1764446, _1764448, _1764450] : [class_Orderings_Olinorder(_1764442), c_Fun_Oinj__on(_1764444, _1764442, _1764446, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1764444, tc_HOL_Obool)), hAPP(c_List_Oset(_1764444), _1764448)), hAPP(c_List_Oset(_1764444), _1764450))), c_List_Olinorder__class_Osorted(_1764442, hAPP(hAPP(c_List_Omap(_1764444, _1764442), _1764446), _1764448)), hBOOL(hAPP(c_List_Odistinct(_1764442), hAPP(hAPP(c_List_Omap(_1764444, _1764442), _1764446), _1764448))), c_List_Olinorder__class_Osorted(_1764442, hAPP(hAPP(c_List_Omap(_1764444, _1764442), _1764446), _1764450)), hBOOL(hAPP(c_List_Odistinct(_1764442), hAPP(hAPP(c_List_Omap(_1764444, _1764442), _1764446), _1764450))), hAPP(c_List_Oset(_1764444), _1764448) = hAPP(c_List_Oset(_1764444), _1764450), -(_1764448 = _1764450)], (48622 ^ _784416) ^ [_1765025, _1765027, _1765029, _1765031, _1765033] : [class_Orderings_Olinorder(_1765025), hBOOL(hAPP(hAPP(c_member(_1765025), hAPP(_1765027, _1765029)), hAPP(c_Set_Oimage(_1765031, _1765025, _1765027), hAPP(c_List_Oset(_1765031), _1765033)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1765031, _1765025, _1765027, _1765029, _1765033) = _1765033)], (48632 ^ _784416) ^ [_1765220, _1765222, _1765224] : [class_Orderings_Olinorder(_1765220), -(hBOOL(hAPP(hAPP(c_member(_1765220), _1765222), hAPP(c_List_Oset(_1765220), _1765224)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1765220, _1765220, c_COMBI(_1765220), _1765222, _1765224) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1765220, _1765220, c_COMBI(_1765220)), _1765222), _1765224))], (48642 ^ _784416) ^ [_1765376, _1765378, _1765380] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1765376), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1765376))), _1765378))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1765380), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1765376))), _1765378))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1765376), _1765376), hAPP(hAPP(c_COMBC(tc_List_Olist(_1765376), tc_Nat_Onat, _1765376), c_List_Onth(_1765376)), _1765380)), hAPP(c_List_Ofilter(tc_List_Olist(_1765376), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1765376)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1765380)), c_Nat_Osize__class_Osize(tc_List_Olist(_1765376)))), c_List_Otranspose(_1765376, _1765378))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1765376)), _1765378), _1765380))], (48652 ^ _784416) ^ [_1765703, _1765705, _1765707, _1765709] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1765703), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1765703))), _1765705))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1765707), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1765703))), c_List_Otranspose(_1765703, _1765705)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1765709), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1765703))), hAPP(c_List_Ofilter(tc_List_Olist(_1765703), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1765703)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1765707)), c_Nat_Osize__class_Osize(tc_List_Olist(_1765703)))), _1765705)))), -(hAPP(hAPP(c_List_Onth(_1765703), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1765703)), c_List_Otranspose(_1765703, _1765705)), _1765707)), _1765709) = hAPP(hAPP(c_List_Onth(_1765703), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1765703)), _1765705), _1765709)), _1765707))], (48666 ^ _784416) ^ [_1766126, _1766128] : [-(c_Fun_Oinj__on(tc_List_Olist(_1766126), tc_List_Olist(_1766126), c_List_Orev(_1766126), _1766128))], (48668 ^ _784416) ^ [_1766159, _1766161, _1766163, _1766165, _1766167] : [-(c_List_Ofoldr(_1766159, _1766161, _1766163, _1766165, _1766167) = hAPP(c_List_Ofoldl(_1766161, _1766159, hAPP(c_COMBC(_1766159, _1766161, _1766161), _1766163), _1766167), hAPP(c_List_Orev(_1766159), _1766165)))], (48670 ^ _784416) ^ [_1766216, _1766218, _1766220, _1766222, _1766224] : [-(hAPP(c_List_Ofoldl(_1766216, _1766218, _1766220, _1766222), _1766224) = c_List_Ofoldr(_1766218, _1766216, hAPP(c_COMBC(_1766216, _1766218, _1766216), _1766220), hAPP(c_List_Orev(_1766218), _1766224), _1766222))], (48672 ^ _784416) ^ [_1766273, _1766275, _1766277] : [-(hAPP(c_List_Orev(_1766273), hAPP(hAPP(c_List_Oappend(_1766273), _1766275), _1766277)) = hAPP(hAPP(c_List_Oappend(_1766273), hAPP(c_List_Orev(_1766273), _1766277)), hAPP(c_List_Orev(_1766273), _1766275)))], (48674 ^ _784416) ^ [_1766349, _1766351, _1766353] : [hAPP(hAPP(c_List_Olist_OCons(_1766349), _1766351), c_List_Olist_ONil(_1766349)) = hAPP(c_List_Orev(_1766349), _1766353), -(_1766353 = hAPP(hAPP(c_List_Olist_OCons(_1766349), _1766351), c_List_Olist_ONil(_1766349)))], (48680 ^ _784416) ^ [_1766474, _1766476, _1766478] : [_1766478 = hAPP(hAPP(c_List_Olist_OCons(_1766474), _1766476), c_List_Olist_ONil(_1766474)), -(hAPP(hAPP(c_List_Olist_OCons(_1766474), _1766476), c_List_Olist_ONil(_1766474)) = hAPP(c_List_Orev(_1766474), _1766478))], (48686 ^ _784416) ^ [_1766623, _1766625, _1766627] : [hAPP(c_List_Orev(_1766623), _1766625) = hAPP(hAPP(c_List_Olist_OCons(_1766623), _1766627), c_List_Olist_ONil(_1766623)), -(_1766625 = hAPP(hAPP(c_List_Olist_OCons(_1766623), _1766627), c_List_Olist_ONil(_1766623)))], (48692 ^ _784416) ^ [_1766748, _1766750, _1766752] : [_1766750 = hAPP(hAPP(c_List_Olist_OCons(_1766748), _1766752), c_List_Olist_ONil(_1766748)), -(hAPP(c_List_Orev(_1766748), _1766750) = hAPP(hAPP(c_List_Olist_OCons(_1766748), _1766752), c_List_Olist_ONil(_1766748)))], (48698 ^ _784416) ^ [_1766894, _1766896] : [hBOOL(hAPP(c_List_Odistinct(_1766894), hAPP(c_List_Orev(_1766894), _1766896))), -(hBOOL(hAPP(c_List_Odistinct(_1766894), _1766896)))], (48704 ^ _784416) ^ [_1766993, _1766995] : [hBOOL(hAPP(c_List_Odistinct(_1766993), _1766995)), -(hBOOL(hAPP(c_List_Odistinct(_1766993), hAPP(c_List_Orev(_1766993), _1766995))))], (48710 ^ _784416) ^ [_1767098] : [-(hAPP(c_List_Orev(_1767098), c_List_Olist_ONil(_1767098)) = c_List_Olist_ONil(_1767098))], (48712 ^ _784416) ^ [_1767145, _1767147] : [c_List_Olist_ONil(_1767145) = hAPP(c_List_Orev(_1767145), _1767147), -(_1767147 = c_List_Olist_ONil(_1767145))], (48718 ^ _784416) ^ [_1767236, _1767238] : [_1767238 = c_List_Olist_ONil(_1767236), -(c_List_Olist_ONil(_1767236) = hAPP(c_List_Orev(_1767236), _1767238))], (48724 ^ _784416) ^ [_1767348, _1767350] : [hAPP(c_List_Orev(_1767348), _1767350) = c_List_Olist_ONil(_1767348), -(_1767350 = c_List_Olist_ONil(_1767348))], (48730 ^ _784416) ^ [_1767439, _1767441] : [_1767441 = c_List_Olist_ONil(_1767439), -(hAPP(c_List_Orev(_1767439), _1767441) = c_List_Olist_ONil(_1767439))], (48736 ^ _784416) ^ [_1767536, _1767538] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767536)), hAPP(c_List_Orev(_1767536), _1767538)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1767536)), _1767538))], (48738 ^ _784416) ^ [_1767580, _1767582] : [-(hAPP(c_List_Orev(_1767580), hAPP(c_List_Orev(_1767580), _1767582)) = _1767582)], (48740 ^ _784416) ^ [_1767633, _1767635, _1767637] : [hAPP(c_List_Orev(_1767633), _1767635) = _1767637, -(_1767635 = hAPP(c_List_Orev(_1767633), _1767637))], (48746 ^ _784416) ^ [_1767728, _1767730, _1767732] : [_1767730 = hAPP(c_List_Orev(_1767728), _1767732), -(hAPP(c_List_Orev(_1767728), _1767730) = _1767732)], (48752 ^ _784416) ^ [_1767847, _1767849, _1767851] : [hAPP(c_List_Orev(_1767847), _1767849) = hAPP(c_List_Orev(_1767847), _1767851), -(_1767849 = _1767851)], (48758 ^ _784416) ^ [_1767942, _1767944, _1767946] : [_1767944 = _1767946, -(hAPP(c_List_Orev(_1767942), _1767944) = hAPP(c_List_Orev(_1767942), _1767946))], (48764 ^ _784416) ^ [_1768043, _1768045] : [class_Groups_Ocomm__monoid__add(_1768043), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1768043), hAPP(c_List_Orev(_1768043), _1768045)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1768043), _1768045))], (48770 ^ _784416) ^ [_1768148, _1768150] : [-(hAPP(c_List_Oset(_1768148), hAPP(c_List_Orev(_1768148), _1768150)) = hAPP(c_List_Oset(_1768148), _1768150))], (48772 ^ _784416) ^ [_1768188, _1768190, _1768192, _1768194] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768188)), _1768190) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1768192)), _1768194), -(hAPP(hAPP(c_List_Ozip(_1768188, _1768192), hAPP(c_List_Orev(_1768188), _1768190)), hAPP(c_List_Orev(_1768192), _1768194)) = hAPP(c_List_Orev(tc_prod(_1768188, _1768192)), hAPP(hAPP(c_List_Ozip(_1768188, _1768192), _1768190), _1768194)))], (48778 ^ _784416) ^ [_1768369, _1768371, _1768373] : [-(hAPP(c_List_Orev(_1768369), hAPP(c_List_Ofilter(_1768369, _1768371), _1768373)) = hAPP(c_List_Ofilter(_1768369, _1768371), hAPP(c_List_Orev(_1768369), _1768373)))], (48780 ^ _784416) ^ [_1768418, _1768420] : [-(hAPP(c_List_Orev(_1768418), c_List_Oconcat(_1768418, _1768420)) = c_List_Oconcat(_1768418, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1768418), tc_List_Olist(_1768418)), c_List_Orev(_1768418)), hAPP(c_List_Orev(tc_List_Olist(_1768418)), _1768420))))], (48782 ^ _784416) ^ [_1768476, _1768478, _1768480, _1768482] : [-(hAPP(c_List_Orev(_1768476), hAPP(hAPP(c_List_Omap(_1768478, _1768476), _1768480), _1768482)) = hAPP(hAPP(c_List_Omap(_1768478, _1768476), _1768480), hAPP(c_List_Orev(_1768478), _1768482)))], (48784 ^ _784416) ^ [_1768554, _1768556, _1768558, _1768560] : [hAPP(c_List_Orev(_1768554), _1768556) = hAPP(hAPP(c_List_Olist_OCons(_1768554), _1768558), _1768560), -(_1768556 = hAPP(hAPP(c_List_Oappend(_1768554), hAPP(c_List_Orev(_1768554), _1768560)), hAPP(hAPP(c_List_Olist_OCons(_1768554), _1768558), c_List_Olist_ONil(_1768554))))], (48790 ^ _784416) ^ [_1768703, _1768705, _1768707, _1768709] : [_1768705 = hAPP(hAPP(c_List_Oappend(_1768703), hAPP(c_List_Orev(_1768703), _1768709)), hAPP(hAPP(c_List_Olist_OCons(_1768703), _1768707), c_List_Olist_ONil(_1768703))), -(hAPP(c_List_Orev(_1768703), _1768705) = hAPP(hAPP(c_List_Olist_OCons(_1768703), _1768707), _1768709))], (48796 ^ _784416) ^ [_1768858, _1768860, _1768862] : [-(hAPP(c_List_Orev(_1768858), hAPP(hAPP(c_List_Olist_OCons(_1768858), _1768860), _1768862)) = hAPP(hAPP(c_List_Oappend(_1768858), hAPP(c_List_Orev(_1768858), _1768862)), hAPP(hAPP(c_List_Olist_OCons(_1768858), _1768860), c_List_Olist_ONil(_1768858))))], (48798 ^ _784416) ^ [_1768917, _1768919] : [-(_1768917 = c_List_Olist_ONil(_1768919)), -(hAPP(c_List_Ohd(_1768919), hAPP(c_List_Orev(_1768919), _1768917)) = c_List_Olast(_1768919, _1768917))], (48804 ^ _784416) ^ [_1768964, _1768966] : [-(_1768964 = c_List_Olist_ONil(_1768966)), -(c_List_Olast(_1768966, hAPP(c_List_Orev(_1768966), _1768964)) = hAPP(c_List_Ohd(_1768966), _1768964))], (48810 ^ _784416) ^ [_1769015, _1769017] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1769015), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1769015))), c_List_Otranspose(_1769015, _1769017)))))], (48812 ^ _784416) ^ [_1769061, _1769063] : [-(hAPP(c_List_Orev(_1769061), _1769063) = hAPP(c_List_Ofoldl(tc_List_Olist(_1769061), _1769061, hAPP(c_COMBC(_1769061, tc_List_Olist(_1769061), tc_List_Olist(_1769061)), c_List_Olist_OCons(_1769061)), c_List_Olist_ONil(_1769061)), _1769063))], (48814 ^ _784416) ^ [_1769116, _1769118, _1769120] : [-(hAPP(c_List_Orev(_1769116), hAPP(hAPP(c_List_Odrop(_1769116), _1769118), _1769120)) = hAPP(hAPP(c_List_Otake(_1769116), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769116)), _1769120)), _1769118)), hAPP(c_List_Orev(_1769116), _1769120)))], (48816 ^ _784416) ^ [_1769182, _1769184, _1769186] : [-(hAPP(c_List_Orev(_1769182), hAPP(hAPP(c_List_Otake(_1769182), _1769184), _1769186)) = hAPP(hAPP(c_List_Odrop(_1769182), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769182)), _1769186)), _1769184)), hAPP(c_List_Orev(_1769182), _1769186)))], (48818 ^ _784416) ^ [_1769248, _1769250, _1769252] : [-(hAPP(c_List_Orotate(_1769248, _1769250), hAPP(c_List_Orev(_1769248), _1769252)) = hAPP(c_List_Orev(_1769248), hAPP(c_List_Orotate(_1769248, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769248)), _1769252)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1769250, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769248)), _1769252)))), _1769252)))], (48820 ^ _784416) ^ [_1769321, _1769323, _1769325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1769321), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769323)), _1769325))), -(hAPP(hAPP(c_List_Onth(_1769323), hAPP(c_List_Orev(_1769323), _1769325)), _1769321) = hAPP(hAPP(c_List_Onth(_1769323), _1769325), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769323)), _1769325)), hAPP(c_Nat_OSuc, _1769321))))], (48826 ^ _784416) ^ [_1769498, _1769500, _1769502, _1769504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1769498), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769500)), _1769502))), -(hAPP(c_List_Orev(_1769500), hAPP(hAPP(c_List_Olist__update(_1769500, _1769502), _1769498), _1769504)) = hAPP(hAPP(c_List_Olist__update(_1769500, hAPP(c_List_Orev(_1769500), _1769502)), 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(_1769500)), _1769502)), _1769498)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1769504))], (48832 ^ _784416) ^ [_1769697, _1769699, _1769701, _1769703] : [class_Orderings_Olinorder(_1769697), c_List_Olinorder__class_Osorted(_1769697, hAPP(c_List_Orev(_1769697), _1769699)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1769701), _1769703)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1769703), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1769697)), _1769699))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1769697), hAPP(hAPP(c_List_Onth(_1769697), _1769699), _1769703)), hAPP(hAPP(c_List_Onth(_1769697), _1769699), _1769701))))], (48850 ^ _784416) ^ [_1770034, _1770036, _1770038] : [class_Orderings_Olinorder(_1770034), c_List_Olinorder__class_Osorted(_1770034, hAPP(c_List_Orev(_1770034), _1770036)), 48857 ^ _784416 : [(48858 ^ _784416) ^ [] : [_1770036 = c_List_Olist_ONil(_1770034), -(c_List_Ofoldr(_1770034, _1770034, c_Orderings_Oord__class_Omax(_1770034), _1770036, _1770038) = _1770038)], (48864 ^ _784416) ^ [] : [-(_1770036 = c_List_Olist_ONil(_1770034)), -(c_List_Ofoldr(_1770034, _1770034, c_Orderings_Oord__class_Omax(_1770034), _1770036, _1770038) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1770034), hAPP(hAPP(c_List_Onth(_1770034), _1770036), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1770038))]]], (48870 ^ _784416) ^ [_1770348, _1770350] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1770348), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1770348))), _1770350))), 48873 ^ _784416 : [(48874 ^ _784416) ^ [] : [_1770350 = c_List_Olist_ONil(tc_List_Olist(_1770348)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1770348))), c_List_Otranspose(_1770348, _1770350)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48880 ^ _784416) ^ [] : [-(_1770350 = c_List_Olist_ONil(tc_List_Olist(_1770348))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1770348))), c_List_Otranspose(_1770348, _1770350)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770348)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1770348)), _1770350), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (48886 ^ _784416) ^ [_1770658, _1770660, _1770662] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1770658), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1770658))), _1770660))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1770662), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1770658))), _1770660))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1770658))), hAPP(c_List_Ofilter(tc_List_Olist(_1770658), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1770658)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1770662)), c_Nat_Osize__class_Osize(tc_List_Olist(_1770658)))), c_List_Otranspose(_1770658, _1770660))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770658)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1770658)), _1770660), _1770662)))], (48896 ^ _784416) ^ [_1770967, _1770969] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1770967), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1770967))), _1770969))), -(c_List_Otranspose(_1770967, c_List_Otranspose(_1770967, _1770969)) = c_List_OtakeWhile(tc_List_Olist(_1770967), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1770967)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1770967), tc_List_Olist(_1770967), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1770967))), _1770969))], (48902 ^ _784416) ^ [_1771160, _1771162] : [class_Orderings_Olinorder(_1771160), 48909 ^ _784416 : [(48910 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 48907 ^ [_1771160, _1771162]), 48908 ^ [_1771160, _1771162])))], (48912 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48908 ^ [_1771160, _1771162]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1771160)), _1771162))))], (48914 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1771160), hAPP(hAPP(c_List_Onth(_1771160), _1771162), 48907 ^ [_1771160, _1771162])), hAPP(hAPP(c_List_Onth(_1771160), _1771162), 48908 ^ [_1771160, _1771162])))]], -(c_List_Olinorder__class_Osorted(_1771160, _1771162))], (48918 ^ _784416) ^ [_1771535, _1771537, _1771539] : [class_Orderings_Olinorder(_1771535), c_List_Olinorder__class_Osorted(_1771535, _1771537), -(c_List_Olinorder__class_Osorted(_1771535, c_List_OtakeWhile(_1771535, _1771539, _1771537)))], (48928 ^ _784416) ^ [_1771674, _1771676, _1771678, _1771680, _1771682] : [-(hAPP(hAPP(c_List_Ozip(_1771674, _1771676), _1771678), c_List_OtakeWhile(_1771676, _1771680, _1771682)) = c_List_OtakeWhile(tc_prod(_1771674, _1771676), hAPP(c_Fun_Ocomp(_1771676, tc_HOL_Obool, tc_prod(_1771674, _1771676), _1771680), c_Product__Type_Osnd(_1771674, _1771676)), hAPP(hAPP(c_List_Ozip(_1771674, _1771676), _1771678), _1771682)))], (48930 ^ _784416) ^ [_1771748, _1771750, _1771752, _1771754, _1771756] : [-(hAPP(hAPP(c_List_Ozip(_1771748, _1771750), c_List_OtakeWhile(_1771748, _1771752, _1771754)), _1771756) = c_List_OtakeWhile(tc_prod(_1771748, _1771750), hAPP(c_Fun_Ocomp(_1771748, tc_HOL_Obool, tc_prod(_1771748, _1771750), _1771752), c_Product__Type_Ofst(_1771748, _1771750)), hAPP(hAPP(c_List_Ozip(_1771748, _1771750), _1771754), _1771756)))], (48932 ^ _784416) ^ [_1771822, _1771824, _1771826, _1771828, _1771830] : [-(c_List_OtakeWhile(_1771822, _1771824, hAPP(hAPP(c_List_Omap(_1771826, _1771822), _1771828), _1771830)) = hAPP(hAPP(c_List_Omap(_1771826, _1771822), _1771828), c_List_OtakeWhile(_1771826, hAPP(c_Fun_Ocomp(_1771822, tc_HOL_Obool, _1771826, _1771824), _1771828), _1771830)))], (48944 ^ _784416) ^ [_1772101, _1772103, _1772105] : [48946 ^ _784416 : [(48947 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1772101), 48945 ^ [_1772101, _1772103, _1772105]), hAPP(c_List_Oset(_1772101), _1772105))))], (48949 ^ _784416) ^ [] : [hBOOL(hAPP(_1772103, 48945 ^ [_1772101, _1772103, _1772105]))]], -(c_List_OtakeWhile(_1772101, _1772103, _1772105) = _1772105)], (48934 ^ _784416) ^ [_1771905, _1771907, _1771909] : [c_List_OtakeWhile(_1771905, _1771907, _1771909) = _1771909, 48937 ^ _784416 : [(48938 ^ _784416) ^ [_1771992] : [hBOOL(hAPP(hAPP(c_member(_1771905), _1771992), hAPP(c_List_Oset(_1771905), _1771909))), -(hBOOL(hAPP(_1771907, _1771992)))]]], (48953 ^ _784416) ^ [_1772289, _1772291, _1772293, _1772295] : [hBOOL(hAPP(hAPP(c_member(_1772289), _1772291), hAPP(c_List_Oset(_1772289), c_List_OtakeWhile(_1772289, _1772293, _1772295)))), 48956 ^ _784416 : [(48957 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1772289), _1772291), hAPP(c_List_Oset(_1772289), _1772295))))], (48959 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1772293, _1772291)))]]], (48961 ^ _784416) ^ [_1772456, _1772458, _1772460] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772456)), c_List_OtakeWhile(_1772456, _1772458, _1772460))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772456)), _1772460))))], (48963 ^ _784416) ^ [_1772506, _1772508] : [-(c_List_OtakeWhile(_1772506, _1772508, c_List_Olist_ONil(_1772506)) = c_List_Olist_ONil(_1772506))], (48965 ^ _784416) ^ [_1772539, _1772541, _1772543] : [hBOOL(hAPP(c_List_Odistinct(_1772539), _1772541)), -(hBOOL(hAPP(c_List_Odistinct(_1772539), c_List_OtakeWhile(_1772539, _1772543, _1772541))))], (48971 ^ _784416) ^ [_1772642, _1772644, _1772646] : [-(c_List_OtakeWhile(_1772642, _1772644, _1772646) = hAPP(hAPP(c_List_Otake(_1772642), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772642)), c_List_OtakeWhile(_1772642, _1772644, _1772646))), _1772646))], (48973 ^ _784416) ^ [_1772707, _1772709, _1772711, _1772713] : [hBOOL(hAPP(_1772707, _1772709)), -(c_List_OtakeWhile(_1772711, _1772707, hAPP(hAPP(c_List_Olist_OCons(_1772711), _1772709), _1772713)) = hAPP(hAPP(c_List_Olist_OCons(_1772711), _1772709), c_List_OtakeWhile(_1772711, _1772707, _1772713)))], (48979 ^ _784416) ^ [_1772834, _1772836, _1772838, _1772840] : [-(hBOOL(hAPP(_1772834, _1772836))), -(c_List_OtakeWhile(_1772838, _1772834, hAPP(hAPP(c_List_Olist_OCons(_1772838), _1772836), _1772840)) = c_List_Olist_ONil(_1772838))], (48985 ^ _784416) ^ [_1772888, _1772890, _1772892, _1772894, _1772896] : [-(hBOOL(hAPP(_1772888, _1772890))), -(c_List_OtakeWhile(_1772892, _1772888, hAPP(hAPP(c_List_Oappend(_1772892), _1772894), hAPP(hAPP(c_List_Olist_OCons(_1772892), _1772890), _1772896))) = c_List_OtakeWhile(_1772892, _1772888, _1772894))], (48991 ^ _784416) ^ [_1772956, _1772958, _1772960, _1772962, _1772964] : [hBOOL(hAPP(hAPP(c_member(_1772956), _1772958), hAPP(c_List_Oset(_1772956), _1772960))), -(hBOOL(hAPP(_1772962, _1772958))), -(c_List_OtakeWhile(_1772956, _1772962, hAPP(hAPP(c_List_Oappend(_1772956), _1772960), _1772964)) = c_List_OtakeWhile(_1772956, _1772962, _1772960))], (49001 ^ _784416) ^ [_1773114, _1773116, _1773118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773114)), c_List_OtakeWhile(_1773114, _1773116, _1773118))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773114)), _1773118))), hBOOL(hAPP(_1773116, hAPP(hAPP(c_List_Onth(_1773114), _1773118), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773114)), c_List_OtakeWhile(_1773114, _1773116, _1773118)))))], (49007 ^ _784416) ^ [_1773282, _1773284, _1773286, _1773288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1773282), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773284)), c_List_OtakeWhile(_1773284, _1773286, _1773288)))), -(hAPP(hAPP(c_List_Onth(_1773284), c_List_OtakeWhile(_1773284, _1773286, _1773288)), _1773282) = hAPP(hAPP(c_List_Onth(_1773284), _1773288), _1773282))], (49013 ^ _784416) ^ [_1773435, _1773437, _1773439, _1773441, _1773443] : [-(c_Map_Omap__upds(_1773435, _1773437, _1773439, _1773441, _1773443) = c_Map_Omap__add(_1773435, _1773437, _1773439, hAPP(c_Map_Omap__of(_1773435, _1773437), hAPP(c_List_Orev(tc_prod(_1773435, _1773437)), hAPP(hAPP(c_List_Ozip(_1773435, _1773437), _1773441), _1773443)))))], (49015 ^ _784416) ^ [_1773499, _1773501] : [-(_1773499 = c_List_Olist_ONil(_1773501)), hBOOL(hAPP(c_List_Odistinct(_1773501), _1773499)), -(c_List_OtakeWhile(_1773501, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1773501), c_fNot), hAPP(hAPP(c_COMBC(_1773501, _1773501, tc_HOL_Obool), c_fequal), c_List_Olast(_1773501, _1773499))), _1773499) = c_List_Obutlast(_1773501, _1773499))], (49025 ^ _784416) ^ [_1773696, _1773698, _1773700, _1773702, _1773704] : [class_Orderings_Olinorder(_1773696), c_List_Olinorder__class_Osorted(_1773696, hAPP(c_List_Orev(_1773696), hAPP(hAPP(c_List_Omap(_1773698, _1773696), _1773700), _1773702))), -(hAPP(c_List_Ofilter(_1773698, hAPP(hAPP(c_COMBB(_1773696, tc_HOL_Obool, _1773698), hAPP(c_Orderings_Oord__class_Oless(_1773696), _1773704)), _1773700)), _1773702) = c_List_OtakeWhile(_1773698, hAPP(hAPP(c_COMBB(_1773696, tc_HOL_Obool, _1773698), hAPP(c_Orderings_Oord__class_Oless(_1773696), _1773704)), _1773700), _1773702))], (49035 ^ _784416) ^ [_1773943, _1773945, _1773947] : [hBOOL(hAPP(c_List_Odistinct(_1773943), _1773945)), hBOOL(hAPP(hAPP(c_member(_1773943), _1773947), hAPP(c_List_Oset(_1773943), _1773945))), -(c_List_OtakeWhile(_1773943, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1773943), c_fNot), hAPP(hAPP(c_COMBC(_1773943, _1773943, tc_HOL_Obool), c_fequal), _1773947)), hAPP(c_List_Orev(_1773943), _1773945)) = hAPP(c_List_Orev(_1773943), hAPP(c_List_Otl(_1773943), c_List_OdropWhile(_1773943, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1773943), c_fNot), hAPP(hAPP(c_COMBC(_1773943, _1773943, tc_HOL_Obool), c_fequal), _1773947)), _1773945))))], (49045 ^ _784416) ^ [_1774234, _1774236, _1774238] : [hBOOL(hAPP(c_List_Odistinct(_1774234), _1774236)), hBOOL(hAPP(hAPP(c_member(_1774234), _1774238), hAPP(c_List_Oset(_1774234), _1774236))), -(c_List_OdropWhile(_1774234, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1774234), c_fNot), hAPP(hAPP(c_COMBC(_1774234, _1774234, tc_HOL_Obool), c_fequal), _1774238)), hAPP(c_List_Orev(_1774234), _1774236)) = hAPP(hAPP(c_List_Olist_OCons(_1774234), _1774238), hAPP(c_List_Orev(_1774234), c_List_OtakeWhile(_1774234, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1774234), c_fNot), hAPP(hAPP(c_COMBC(_1774234, _1774234, tc_HOL_Obool), c_fequal), _1774238)), _1774236))))], (49055 ^ _784416) ^ [_1774531, _1774533, _1774535] : [-(hAPP(hAPP(c_List_Oappend(_1774531), c_List_OtakeWhile(_1774531, _1774533, _1774535)), c_List_OdropWhile(_1774531, _1774533, _1774535)) = _1774535)], (49067 ^ _784416) ^ [_1774792, _1774794, _1774796] : [49069 ^ _784416 : [(49070 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1774792), 49068 ^ [_1774792, _1774794, _1774796]), hAPP(c_List_Oset(_1774792), _1774796))))], (49072 ^ _784416) ^ [] : [hBOOL(hAPP(_1774794, 49068 ^ [_1774792, _1774794, _1774796]))]], -(c_List_OdropWhile(_1774792, _1774794, _1774796) = c_List_Olist_ONil(_1774792))], (49057 ^ _784416) ^ [_1774592, _1774594, _1774596] : [c_List_OdropWhile(_1774592, _1774594, _1774596) = c_List_Olist_ONil(_1774592), 49060 ^ _784416 : [(49061 ^ _784416) ^ [_1774683] : [hBOOL(hAPP(hAPP(c_member(_1774592), _1774683), hAPP(c_List_Oset(_1774592), _1774596))), -(hBOOL(hAPP(_1774594, _1774683)))]]], (49076 ^ _784416) ^ [_1774999, _1775001, _1775003, _1775005] : [hBOOL(hAPP(_1774999, _1775001)), -(c_List_OdropWhile(_1775003, _1774999, hAPP(hAPP(c_List_Olist_OCons(_1775003), _1775001), _1775005)) = c_List_OdropWhile(_1775003, _1774999, _1775005))], (49082 ^ _784416) ^ [_1775110, _1775112, _1775114, _1775116] : [-(hBOOL(hAPP(_1775110, _1775112))), -(c_List_OdropWhile(_1775114, _1775110, hAPP(hAPP(c_List_Olist_OCons(_1775114), _1775112), _1775116)) = hAPP(hAPP(c_List_Olist_OCons(_1775114), _1775112), _1775116))], (49088 ^ _784416) ^ [_1775174, _1775176, _1775178] : [hBOOL(hAPP(c_List_Odistinct(_1775174), _1775176)), -(hBOOL(hAPP(c_List_Odistinct(_1775174), c_List_OdropWhile(_1775174, _1775178, _1775176))))], (49094 ^ _784416) ^ [_1775277, _1775279] : [-(c_List_OdropWhile(_1775277, _1775279, c_List_Olist_ONil(_1775277)) = c_List_Olist_ONil(_1775277))], (49096 ^ _784416) ^ [_1775309, _1775311, _1775313] : [-(c_List_OdropWhile(_1775309, _1775311, _1775313) = c_List_Olist_ONil(_1775309)), hBOOL(hAPP(_1775311, hAPP(c_List_Ohd(_1775309), c_List_OdropWhile(_1775309, _1775311, _1775313))))], (49102 ^ _784416) ^ [_1775415, _1775417, _1775419] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775415)), c_List_OdropWhile(_1775415, _1775417, _1775419))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1775415)), _1775419))))], (49104 ^ _784416) ^ [_1775465, _1775467, _1775469] : [class_Orderings_Olinorder(_1775465), c_List_Olinorder__class_Osorted(_1775465, _1775467), -(c_List_Olinorder__class_Osorted(_1775465, c_List_OdropWhile(_1775465, _1775469, _1775467)))], (49114 ^ _784416) ^ [_1775604, _1775606, _1775608, _1775610, _1775612] : [-(c_List_OdropWhile(_1775604, _1775606, hAPP(hAPP(c_List_Omap(_1775608, _1775604), _1775610), _1775612)) = hAPP(hAPP(c_List_Omap(_1775608, _1775604), _1775610), c_List_OdropWhile(_1775608, hAPP(c_Fun_Ocomp(_1775604, tc_HOL_Obool, _1775608, _1775606), _1775610), _1775612)))], (49116 ^ _784416) ^ [_1775669, _1775671, _1775673, _1775675, _1775677] : [hBOOL(hAPP(hAPP(c_member(_1775669), _1775671), hAPP(c_List_Oset(_1775669), _1775673))), -(hBOOL(hAPP(_1775675, _1775671))), -(c_List_OdropWhile(_1775669, _1775675, hAPP(hAPP(c_List_Oappend(_1775669), _1775673), _1775677)) = hAPP(hAPP(c_List_Oappend(_1775669), c_List_OdropWhile(_1775669, _1775675, _1775673)), _1775677))], (49126 ^ _784416) ^ [_1775867, _1775869, _1775871, _1775873, _1775875] : [c_List_OdropWhile(_1775867, _1775869, _1775871) = hAPP(hAPP(c_List_Olist_OCons(_1775867), _1775873), _1775875), 49129 ^ _784416 : [(49130 ^ _784416) ^ [] : [-(_1775871 = hAPP(hAPP(c_List_Oappend(_1775867), c_List_OtakeWhile(_1775867, _1775869, _1775871)), hAPP(hAPP(c_List_Olist_OCons(_1775867), _1775873), _1775875)))], (49132 ^ _784416) ^ [] : [hBOOL(hAPP(_1775869, _1775873))]]], (49134 ^ _784416) ^ [_1776048, _1776050, _1776052, _1776054, _1776056] : [-(c_List_OdropWhile(_1776048, _1776050, _1776052) = hAPP(hAPP(c_List_Olist_OCons(_1776048), _1776054), _1776056)), _1776052 = hAPP(hAPP(c_List_Oappend(_1776048), c_List_OtakeWhile(_1776048, _1776050, _1776052)), hAPP(hAPP(c_List_Olist_OCons(_1776048), _1776054), _1776056)), -(hBOOL(hAPP(_1776050, _1776054)))], (49144 ^ _784416) ^ [_1776262, _1776264, _1776266] : [-(c_List_OdropWhile(_1776262, _1776264, _1776266) = hAPP(hAPP(c_List_Odrop(_1776262), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776262)), c_List_OtakeWhile(_1776262, _1776264, _1776266))), _1776266))], (49146 ^ _784416) ^ [_1776312, _1776314, _1776316, _1776318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1776312), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776314)), c_List_OdropWhile(_1776314, _1776316, _1776318)))), -(hAPP(hAPP(c_List_Onth(_1776314), c_List_OdropWhile(_1776314, _1776316, _1776318)), _1776312) = hAPP(hAPP(c_List_Onth(_1776314), _1776318), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1776312), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776314)), c_List_OtakeWhile(_1776314, _1776316, _1776318)))))], (49152 ^ _784416) ^ [_1776495, _1776497, _1776499] : [49154 ^ _784416 : [(49155 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1776495), 49153 ^ [_1776495, _1776497, _1776499]), hAPP(c_List_Oset(_1776495), c_List_OdropWhile(_1776495, _1776497, _1776499)))))], (49157 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1776497, 49153 ^ [_1776495, _1776497, _1776499])))]], -(c_List_OtakeWhile(_1776495, _1776497, _1776499) = hAPP(c_List_Ofilter(_1776495, _1776497), _1776499))], (49161 ^ _784416) ^ [_1776616, _1776618, _1776620, _1776622] : [49163 ^ _784416 : [(49164 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49162 ^ [_1776616, _1776618, _1776620, _1776622]), _1776616)))], (49166 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49162 ^ [_1776616, _1776618, _1776620, _1776622]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776618)), _1776620))))], (49168 ^ _784416) ^ [] : [hBOOL(hAPP(_1776622, hAPP(hAPP(c_List_Onth(_1776618), _1776620), 49162 ^ [_1776616, _1776618, _1776620, _1776622])))]], 49171 ^ _784416 : [(49172 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1776616), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1776618)), _1776620))))], (49174 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1776622, hAPP(hAPP(c_List_Onth(_1776618), _1776620), _1776616))))]], -(c_List_OtakeWhile(_1776618, _1776622, _1776620) = hAPP(hAPP(c_List_Otake(_1776618), _1776616), _1776620))], (49178 ^ _784416) ^ [_1777020, _1777022, _1777024, _1777026] : [49180 ^ _784416 : [(49181 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49179 ^ [_1777020, _1777022, _1777024, _1777026]), _1777020)))], (49183 ^ _784416) ^ [] : [hBOOL(hAPP(_1777022, hAPP(hAPP(c_List_Onth(_1777024), _1777026), 49179 ^ [_1777020, _1777022, _1777024, _1777026])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1777020), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777024)), _1777026))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1777020), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1777024)), c_List_OtakeWhile(_1777024, _1777022, _1777026)))))], (49191 ^ _784416) ^ [_1777328, _1777330, _1777332, _1777334] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1777328)), _1777330), c_List_Olists(_1777328, _1777332))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1777328)), _1777330), c_List_Olists(_1777328, _1777334))), -(hBOOL(hAPP(c_List_Olistsp(_1777328, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1777328, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1777328, tc_fun(_1777328, tc_HOL_Obool), tc_HOL_Obool), c_member(_1777328)), _1777332)), hAPP(hAPP(c_COMBC(_1777328, tc_fun(_1777328, tc_HOL_Obool), tc_HOL_Obool), c_member(_1777328)), _1777334))), _1777330)))], (49201 ^ _784416) ^ [_1777605, _1777607] : [-(hBOOL(hAPP(c_List_Olistsp(_1777605, _1777607), c_List_Olist_ONil(_1777605))))], (49203 ^ _784416) ^ [_1777658, _1777660, _1777662, _1777664] : [hBOOL(hAPP(c_List_Olistsp(_1777658, _1777660), hAPP(hAPP(c_List_Oappend(_1777658), _1777662), _1777664))), 49206 ^ _784416 : [(49207 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1777658, _1777660), _1777662)))], (49209 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1777658, _1777660), _1777664)))]]], (49211 ^ _784416) ^ [_1777807, _1777809, _1777811, _1777813] : [-(hBOOL(hAPP(c_List_Olistsp(_1777807, _1777809), hAPP(hAPP(c_List_Oappend(_1777807), _1777811), _1777813)))), hBOOL(hAPP(c_List_Olistsp(_1777807, _1777809), _1777811)), hBOOL(hAPP(c_List_Olistsp(_1777807, _1777809), _1777813))], (49221 ^ _784416) ^ [_1778013, _1778015, _1778017, _1778019] : [hBOOL(hAPP(c_List_Olistsp(_1778013, _1778015), hAPP(hAPP(c_List_Olist_OCons(_1778013), _1778017), _1778019))), 49224 ^ _784416 : [(49225 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1778015, _1778017)))], (49227 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1778013, _1778015), _1778019)))]]], (49229 ^ _784416) ^ [_1778156, _1778158, _1778160, _1778162] : [-(hBOOL(hAPP(c_List_Olistsp(_1778156, _1778158), hAPP(hAPP(c_List_Olist_OCons(_1778156), _1778160), _1778162)))), hBOOL(hAPP(_1778158, _1778160)), hBOOL(hAPP(c_List_Olistsp(_1778156, _1778158), _1778162))], (49239 ^ _784416) ^ [_1778335, _1778337] : [-(hBOOL(hAPP(c_List_Olistsp(_1778335, _1778337), c_List_Olist_ONil(_1778335))))], (49241 ^ _784416) ^ [_1778367, _1778369, _1778371] : [-(c_List_Olistsp(_1778367, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1778367, tc_HOL_Obool)), _1778369), _1778371)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1778367), tc_HOL_Obool)), c_List_Olistsp(_1778367, _1778369)), c_List_Olistsp(_1778367, _1778371)))], (49243 ^ _784416) ^ [_1778427, _1778429, _1778431, _1778433] : [hBOOL(hAPP(c_List_Olistsp(_1778427, _1778429), _1778431)), hBOOL(hAPP(c_List_Olistsp(_1778427, _1778433), _1778431)), -(hBOOL(hAPP(c_List_Olistsp(_1778427, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1778427, tc_HOL_Obool)), _1778429), _1778433)), _1778431)))], (49253 ^ _784416) ^ [_1778637, _1778639, _1778641, _1778643] : [hBOOL(hAPP(c_List_Olistsp(_1778637, hAPP(hAPP(c_COMBS(_1778637, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1778637), c_fconj), _1778639)), _1778641)), _1778643)), 49256 ^ _784416 : [(49257 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1778637, _1778639), _1778643)))], (49259 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1778637, _1778641), _1778643)))]]], (49261 ^ _784416) ^ [_1778810, _1778812, _1778814, _1778816] : [-(hBOOL(hAPP(c_List_Olistsp(_1778810, hAPP(hAPP(c_COMBS(_1778810, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1778810), c_fconj), _1778812)), _1778814)), _1778816))), hBOOL(hAPP(c_List_Olistsp(_1778810, _1778812), _1778816)), hBOOL(hAPP(c_List_Olistsp(_1778810, _1778814), _1778816))], (49281 ^ _784416) ^ [_1779235, _1779237, _1779239] : [49283 ^ _784416 : [(49284 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1779235), 49282 ^ [_1779235, _1779237, _1779239]), hAPP(c_List_Oset(_1779235), _1779239))))], (49286 ^ _784416) ^ [] : [hBOOL(hAPP(_1779237, 49282 ^ [_1779235, _1779237, _1779239]))]], -(hBOOL(hAPP(c_List_Olistsp(_1779235, _1779237), _1779239)))], (49271 ^ _784416) ^ [_1779037, _1779039, _1779041] : [hBOOL(hAPP(c_List_Olistsp(_1779037, _1779039), _1779041)), 49274 ^ _784416 : [(49275 ^ _784416) ^ [_1779126] : [hBOOL(hAPP(hAPP(c_member(_1779037), _1779126), hAPP(c_List_Oset(_1779037), _1779041))), -(hBOOL(hAPP(_1779039, _1779126)))]]], (49290 ^ _784416) ^ [_1779425, _1779427, _1779429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1779425, tc_HOL_Obool)), _1779427), _1779429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1779425), tc_HOL_Obool)), c_List_Olistsp(_1779425, _1779427)), c_List_Olistsp(_1779425, _1779429))))], (49296 ^ _784416) ^ [_1779578, _1779580, _1779582] : [hBOOL(hAPP(c_List_Olistsp(_1779578, hAPP(hAPP(c_COMBC(_1779578, tc_fun(_1779578, tc_HOL_Obool), tc_HOL_Obool), c_member(_1779578)), _1779580)), _1779582)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1779578)), _1779582), c_List_Olists(_1779578, _1779580))))], (49302 ^ _784416) ^ [_1779717, _1779719, _1779721] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1779717)), _1779721), c_List_Olists(_1779717, _1779719))), -(hBOOL(hAPP(c_List_Olistsp(_1779717, hAPP(hAPP(c_COMBC(_1779717, tc_fun(_1779717, tc_HOL_Obool), tc_HOL_Obool), c_member(_1779717)), _1779719)), _1779721)))], (49308 ^ _784416) ^ [_1779862, _1779864, _1779866] : [-(c_List_Olistsp(_1779862, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1779862, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1779862, tc_fun(_1779862, tc_HOL_Obool), tc_HOL_Obool), c_member(_1779862)), _1779864)), hAPP(hAPP(c_COMBC(_1779862, tc_fun(_1779862, tc_HOL_Obool), tc_HOL_Obool), c_member(_1779862)), _1779866))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1779862), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1779862), tc_fun(tc_List_Olist(_1779862), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1779862))), c_List_Olists(_1779862, _1779864))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1779862), tc_fun(tc_List_Olist(_1779862), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1779862))), c_List_Olists(_1779862, _1779866))))], (49310 ^ _784416) ^ [_1780018, _1780020, _1780022, _1780024, _1780026] : [c_List_Olist__all2(_1780018, _1780020, _1780022, _1780024, _1780026), 49313 ^ _784416 : [(49314 ^ _784416) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780018)), _1780024) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780020)), _1780026))], (49316 ^ _784416) ^ [_1780184] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780018, _1780020)), _1780184), hAPP(c_List_Oset(tc_prod(_1780018, _1780020)), hAPP(hAPP(c_List_Ozip(_1780018, _1780020), _1780024), _1780026)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1780018, _1780020, tc_HOL_Obool), _1780022), _1780184)))]]], (49322 ^ _784416) ^ [_1780343, _1780345, _1780347, _1780349, _1780351] : [-(c_List_Olist__all2(_1780343, _1780345, _1780347, _1780349, _1780351)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780343)), _1780349) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1780345)), _1780351), 49328 ^ _784416 : [(49329 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780343, _1780345)), 49327 ^ [_1780343, _1780345, _1780347, _1780349, _1780351]), hAPP(c_List_Oset(tc_prod(_1780343, _1780345)), hAPP(hAPP(c_List_Ozip(_1780343, _1780345), _1780349), _1780351)))))], (49331 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1780343, _1780345, tc_HOL_Obool), _1780347), 49327 ^ [_1780343, _1780345, _1780347, _1780349, _1780351]))]]], (49335 ^ _784416) ^ [_1780684, _1780686] : [class_Orderings_Olinorder(_1780684), 49338 ^ _784416 : [(49339 ^ _784416) ^ [] : [c_List_Olinorder__class_Osorted(_1780684, _1780686), -(_1780686 = c_List_Olist_ONil(_1780684)), 49348 ^ _784416 : [(49349 ^ _784416) ^ [] : [-(_1780686 = hAPP(hAPP(c_List_Olist_OCons(_1780684), 49347 ^ [_1780684, _1780686]), 49346 ^ [_1780684, _1780686]))], (49357 ^ _784416) ^ [] : [-(c_List_Olinorder__class_Osorted(_1780684, 49346 ^ [_1780684, _1780686]))], (49351 ^ _784416) ^ [_1781018] : [hBOOL(hAPP(hAPP(c_member(_1780684), _1781018), hAPP(c_List_Oset(_1780684), 49346 ^ [_1780684, _1780686]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1780684), 49347 ^ [_1780684, _1780686]), _1781018)))]]], (49359 ^ _784416) ^ [] : [-(c_List_Olinorder__class_Osorted(_1780684, _1780686)), 49360 ^ _784416 : [(49361 ^ _784416) ^ [] : [_1780686 = c_List_Olist_ONil(_1780684)], (49363 ^ _784416) ^ [_1781244, _1781246] : [_1780686 = hAPP(hAPP(c_List_Olist_OCons(_1780684), _1781244), _1781246), 49369 ^ _784416 : [(49370 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1780684), 49368 ^ [_1780684, _1780686, _1781244, _1781246]), hAPP(c_List_Oset(_1780684), _1781246))))], (49372 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1780684), _1781244), 49368 ^ [_1780684, _1780686, _1781244, _1781246]))]], c_List_Olinorder__class_Osorted(_1780684, _1781246)]]]]], (49378 ^ _784416) ^ [_1781553, _1781555, _1781557, _1781559, _1781561, _1781563, _1781565, _1781567] : [c_List_Olist__all2(_1781553, _1781555, _1781557, _1781559, _1781561), hBOOL(hAPP(hAPP(_1781557, _1781563), _1781565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1781567), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781555)), _1781561))), -(c_List_Olist__all2(_1781553, _1781555, _1781557, hAPP(hAPP(c_List_Olist__update(_1781553, _1781559), _1781567), _1781563), hAPP(hAPP(c_List_Olist__update(_1781555, _1781561), _1781567), _1781565)))], (49392 ^ _784416) ^ [_1781852, _1781854, _1781856, _1781858, _1781860, _1781862, _1781864, _1781866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1781852), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1781854)), _1781856))), c_List_Olist__all2(_1781854, _1781858, _1781860, _1781856, _1781862), hBOOL(hAPP(hAPP(_1781860, _1781864), _1781866)), -(c_List_Olist__all2(_1781854, _1781858, _1781860, hAPP(hAPP(c_List_Olist__update(_1781854, _1781856), _1781852), _1781864), hAPP(hAPP(c_List_Olist__update(_1781858, _1781862), _1781852), _1781866)))], (49406 ^ _784416) ^ [_1782175, _1782177, _1782179, _1782181, _1782183] : [c_List_Olist__all2(_1782175, _1782177, _1782179, _1782181, _1782183), 49409 ^ _784416 : [(49410 ^ _784416) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782175)), _1782181) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782177)), _1782183))], (49412 ^ _784416) ^ [_1782338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1782338), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782175)), _1782181))), -(hBOOL(hAPP(hAPP(_1782179, hAPP(hAPP(c_List_Onth(_1782175), _1782181), _1782338)), hAPP(hAPP(c_List_Onth(_1782177), _1782183), _1782338))))]]], (49418 ^ _784416) ^ [_1782491, _1782493, _1782495, _1782497, _1782499] : [-(c_List_Olist__all2(_1782491, _1782493, _1782495, _1782497, _1782499)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782491)), _1782497) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782493)), _1782499), 49424 ^ _784416 : [(49425 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49423 ^ [_1782491, _1782493, _1782495, _1782497, _1782499]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782491)), _1782497))))], (49427 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1782495, hAPP(hAPP(c_List_Onth(_1782491), _1782497), 49423 ^ [_1782491, _1782493, _1782495, _1782497, _1782499])), hAPP(hAPP(c_List_Onth(_1782493), _1782499), 49423 ^ [_1782491, _1782493, _1782495, _1782497, _1782499])))]]], (49431 ^ _784416) ^ [_1782851, _1782853, _1782855, _1782857, _1782859, _1782861] : [c_List_Olist__all2(_1782851, _1782853, _1782855, _1782857, _1782859), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1782861), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1782851)), _1782857))), -(hBOOL(hAPP(hAPP(_1782855, hAPP(hAPP(c_List_Onth(_1782851), _1782857), _1782861)), hAPP(hAPP(c_List_Onth(_1782853), _1782859), _1782861))))], (49441 ^ _784416) ^ [_1783068, _1783070, _1783072, _1783074, _1783076, _1783078] : [c_List_Olist__all2(_1783068, _1783070, _1783072, _1783074, _1783076), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1783078), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1783070)), _1783076))), -(hBOOL(hAPP(hAPP(_1783072, hAPP(hAPP(c_List_Onth(_1783068), _1783074), _1783078)), hAPP(hAPP(c_List_Onth(_1783070), _1783076), _1783078))))], (49451 ^ _784416) ^ [_1783315, _1783317, _1783319, _1783321, _1783323, _1783325, _1783327] : [c_List_Olist__all2(_1783315, _1783317, _1783319, _1783321, hAPP(hAPP(c_List_Omap(_1783323, _1783317), _1783325), _1783327)), -(c_List_Olist__all2(_1783315, _1783323, hAPP(hAPP(c_COMBC(_1783315, tc_fun(_1783323, _1783317), tc_fun(_1783323, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1783317, tc_HOL_Obool), tc_fun(tc_fun(_1783323, _1783317), tc_fun(_1783323, tc_HOL_Obool)), _1783315), c_COMBB(_1783317, tc_HOL_Obool, _1783323)), _1783319)), _1783325), _1783321, _1783327))], (49457 ^ _784416) ^ [_1783512, _1783514, _1783516, _1783518, _1783520, _1783522, _1783524] : [c_List_Olist__all2(_1783512, _1783520, hAPP(hAPP(c_COMBC(_1783512, tc_fun(_1783520, _1783514), tc_fun(_1783520, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1783514, tc_HOL_Obool), tc_fun(tc_fun(_1783520, _1783514), tc_fun(_1783520, tc_HOL_Obool)), _1783512), c_COMBB(_1783514, tc_HOL_Obool, _1783520)), _1783516)), _1783522), _1783518, _1783524), -(c_List_Olist__all2(_1783512, _1783514, _1783516, _1783518, hAPP(hAPP(c_List_Omap(_1783520, _1783514), _1783522), _1783524)))], (49463 ^ _784416) ^ [_1783745, _1783747, _1783749, _1783751, _1783753, _1783755, _1783757] : [c_List_Olist__all2(_1783745, _1783747, _1783749, hAPP(hAPP(c_List_Omap(_1783751, _1783745), _1783753), _1783755), _1783757), -(c_List_Olist__all2(_1783751, _1783747, hAPP(hAPP(c_COMBB(_1783745, tc_fun(_1783747, tc_HOL_Obool), _1783751), _1783749), _1783753), _1783755, _1783757))], (49469 ^ _784416) ^ [_1783884, _1783886, _1783888, _1783890, _1783892, _1783894, _1783896] : [c_List_Olist__all2(_1783890, _1783886, hAPP(hAPP(c_COMBB(_1783884, tc_fun(_1783886, tc_HOL_Obool), _1783890), _1783888), _1783892), _1783894, _1783896), -(c_List_Olist__all2(_1783884, _1783886, _1783888, hAPP(hAPP(c_List_Omap(_1783890, _1783884), _1783892), _1783894), _1783896))], (49475 ^ _784416) ^ [_1784047, _1784049, _1784051] : [_1784047 = _1784049, -(c_List_Olist__all2(_1784051, _1784051, c_fequal, _1784047, _1784049))], (49481 ^ _784416) ^ [_1784128, _1784130, _1784132] : [c_List_Olist__all2(_1784132, _1784132, c_fequal, _1784128, _1784130), -(_1784128 = _1784130)], (49487 ^ _784416) ^ [_1784215, _1784217, _1784219, _1784221, _1784223] : [c_List_Olist__all2(_1784215, _1784217, _1784219, _1784221, _1784223), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784215)), _1784221) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1784217)), _1784223))], (49493 ^ _784416) ^ [_1784332, _1784334, _1784336, _1784338, _1784340, _1784342] : [c_List_Olist__all2(_1784332, _1784334, _1784336, _1784338, _1784340), -(c_List_Olist__all2(_1784332, _1784334, _1784336, hAPP(hAPP(c_List_Odrop(_1784332), _1784342), _1784338), hAPP(hAPP(c_List_Odrop(_1784334), _1784342), _1784340)))], (49499 ^ _784416) ^ [_1784482, _1784484, _1784486, _1784488] : [c_List_Olist__all2(_1784482, _1784484, _1784486, _1784488, c_List_Olist_ONil(_1784484)), -(_1784488 = c_List_Olist_ONil(_1784482))], (49505 ^ _784416) ^ [_1784573, _1784575, _1784577, _1784579] : [_1784579 = c_List_Olist_ONil(_1784573), -(c_List_Olist__all2(_1784573, _1784575, _1784577, _1784579, c_List_Olist_ONil(_1784575)))], (49511 ^ _784416) ^ [_1784691, _1784693, _1784695, _1784697] : [c_List_Olist__all2(_1784691, _1784693, _1784695, c_List_Olist_ONil(_1784691), _1784697), -(_1784697 = c_List_Olist_ONil(_1784693))], (49517 ^ _784416) ^ [_1784782, _1784784, _1784786, _1784788] : [_1784788 = c_List_Olist_ONil(_1784784), -(c_List_Olist__all2(_1784782, _1784784, _1784786, c_List_Olist_ONil(_1784782), _1784788))], (49523 ^ _784416) ^ [_1784879, _1784881, _1784883, _1784885, _1784887, _1784889] : [c_List_Olist__all2(_1784879, _1784881, _1784883, _1784885, _1784887), -(c_List_Olist__all2(_1784879, _1784881, _1784883, hAPP(hAPP(c_List_Otake(_1784879), _1784889), _1784885), hAPP(hAPP(c_List_Otake(_1784881), _1784889), _1784887)))], (49529 ^ _784416) ^ [_1785038, _1785040, _1785042, _1785044, _1785046, _1785048, _1785050] : [c_List_Olist__all2(_1785038, _1785040, _1785042, hAPP(hAPP(c_List_Olist_OCons(_1785038), _1785044), _1785046), hAPP(hAPP(c_List_Olist_OCons(_1785040), _1785048), _1785050)), 49532 ^ _784416 : [(49533 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(_1785042, _1785044), _1785048)))], (49535 ^ _784416) ^ [] : [-(c_List_Olist__all2(_1785038, _1785040, _1785042, _1785046, _1785050))]]], (49537 ^ _784416) ^ [_1785201, _1785203, _1785205, _1785207, _1785209, _1785211, _1785213] : [-(c_List_Olist__all2(_1785201, _1785203, _1785205, hAPP(hAPP(c_List_Olist_OCons(_1785201), _1785207), _1785209), hAPP(hAPP(c_List_Olist_OCons(_1785203), _1785211), _1785213))), hBOOL(hAPP(hAPP(_1785205, _1785207), _1785211)), c_List_Olist__all2(_1785201, _1785203, _1785205, _1785209, _1785213)], (49547 ^ _784416) ^ [_1785406, _1785408, _1785410, _1785412, _1785414, _1785416, _1785418] : [c_List_Olist__all2(_1785406, _1785408, _1785410, _1785412, _1785414), c_List_Olist__all2(_1785406, _1785408, _1785410, _1785416, _1785418), -(c_List_Olist__all2(_1785406, _1785408, _1785410, hAPP(hAPP(c_List_Oappend(_1785406), _1785412), _1785416), hAPP(hAPP(c_List_Oappend(_1785408), _1785414), _1785418)))], (49557 ^ _784416) ^ [_1785605, _1785607, _1785609, _1785611, _1785613, _1785615, _1785617] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1785605)), _1785607) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1785609)), _1785611), 49560 ^ _784416 : [(49561 ^ _784416) ^ [] : [c_List_Olist__all2(_1785605, _1785609, _1785613, hAPP(hAPP(c_List_Oappend(_1785605), _1785607), _1785615), hAPP(hAPP(c_List_Oappend(_1785609), _1785611), _1785617)), 49564 ^ _784416 : [(49565 ^ _784416) ^ [] : [-(c_List_Olist__all2(_1785605, _1785609, _1785613, _1785607, _1785611))], (49567 ^ _784416) ^ [] : [-(c_List_Olist__all2(_1785605, _1785609, _1785613, _1785615, _1785617))]]], (49569 ^ _784416) ^ [] : [-(c_List_Olist__all2(_1785605, _1785609, _1785613, hAPP(hAPP(c_List_Oappend(_1785605), _1785607), _1785615), hAPP(hAPP(c_List_Oappend(_1785609), _1785611), _1785617))), c_List_Olist__all2(_1785605, _1785609, _1785613, _1785607, _1785611), c_List_Olist__all2(_1785605, _1785609, _1785613, _1785615, _1785617)]]], (49579 ^ _784416) ^ [_1786051, _1786053, _1786055, _1786057, _1786059] : [c_List_Olist__all2(_1786051, _1786053, _1786055, hAPP(c_List_Orev(_1786051), _1786057), hAPP(c_List_Orev(_1786053), _1786059)), -(c_List_Olist__all2(_1786051, _1786053, _1786055, _1786057, _1786059))], (49585 ^ _784416) ^ [_1786162, _1786164, _1786166, _1786168, _1786170] : [c_List_Olist__all2(_1786162, _1786164, _1786166, _1786168, _1786170), -(c_List_Olist__all2(_1786162, _1786164, _1786166, hAPP(c_List_Orev(_1786162), _1786168), hAPP(c_List_Orev(_1786164), _1786170)))], (49591 ^ _784416) ^ [_1786303, _1786305, _1786307, _1786309, _1786311] : [c_List_Olist__all2(_1786303, _1786305, _1786307, hAPP(c_List_Orev(_1786303), _1786309), _1786311), -(c_List_Olist__all2(_1786303, _1786305, _1786307, _1786309, hAPP(c_List_Orev(_1786305), _1786311)))], (49597 ^ _784416) ^ [_1786414, _1786416, _1786418, _1786420, _1786422] : [c_List_Olist__all2(_1786414, _1786416, _1786418, _1786420, hAPP(c_List_Orev(_1786416), _1786422)), -(c_List_Olist__all2(_1786414, _1786416, _1786418, hAPP(c_List_Orev(_1786414), _1786420), _1786422))], (49603 ^ _784416) ^ [_1786531, _1786533, _1786535, _1786537, _1786539] : [49605 ^ _784416 : [(49606 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1786531, _1786533)), 49604 ^ [_1786531, _1786533, _1786535, _1786537, _1786539]), hAPP(c_List_Oset(tc_prod(_1786531, _1786533)), hAPP(hAPP(c_List_Ozip(_1786531, _1786533), _1786535), _1786537)))))], (49608 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1786531, _1786533, tc_HOL_Obool), _1786539), 49604 ^ [_1786531, _1786533, _1786535, _1786537, _1786539]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786531)), _1786535) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786533)), _1786537), -(c_List_Olist__all2(_1786531, _1786533, _1786539, _1786535, _1786537))], (49616 ^ _784416) ^ [_1786870, _1786872, _1786874, _1786876] : [49618 ^ _784416 : [(49619 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49617 ^ [_1786870, _1786872, _1786874, _1786876]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1786870)), _1786872))))], (49621 ^ _784416) ^ [] : [hBOOL(hAPP(_1786874, hAPP(hAPP(c_List_Onth(_1786870), _1786872), 49617 ^ [_1786870, _1786872, _1786874, _1786876])))]], hBOOL(hAPP(hAPP(c_member(_1786870), _1786876), hAPP(c_List_Oset(_1786870), _1786872))), -(hBOOL(hAPP(_1786874, _1786876)))], (49629 ^ _784416) ^ [_1787166, _1787168, _1787170, _1787172, _1787174] : [c_Fun_Oinj__on(_1787166, _1787168, _1787170, hAPP(hAPP(c_Set_Oinsert(_1787166), _1787172), hAPP(c_List_Oset(_1787166), _1787174))), -(hAPP(hAPP(c_List_Omap(_1787166, _1787168), _1787170), hAPP(c_List_OremoveAll(_1787166, _1787172), _1787174)) = hAPP(c_List_OremoveAll(_1787168, hAPP(_1787170, _1787172)), hAPP(hAPP(c_List_Omap(_1787166, _1787168), _1787170), _1787174)))], (49635 ^ _784416) ^ [_1787341, _1787343, _1787345] : [-(hBOOL(hAPP(hAPP(c_member(_1787341), _1787343), hAPP(c_List_Oset(_1787341), _1787345)))), -(c_List_Oinsert(_1787341, _1787343, _1787345) = hAPP(hAPP(c_List_Olist_OCons(_1787341), _1787343), _1787345))], (49641 ^ _784416) ^ [_1787399, _1787401, _1787403] : [-(hBOOL(hAPP(hAPP(c_member(_1787399), _1787401), hAPP(c_List_Oset(_1787399), _1787403)))), -(hAPP(c_List_OremoveAll(_1787399, _1787401), _1787403) = _1787403)], (49647 ^ _784416) ^ [_1787455, _1787457] : [-(c_List_OremoveAll(_1787455, _1787457) = c_List_Ofilter(_1787455, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1787455), c_fNot), hAPP(c_fequal, _1787457))))], (49649 ^ _784416) ^ [_1787495, _1787497, _1787499, _1787501] : [-(hBOOL(hAPP(_1787495, _1787497))), -(hAPP(c_List_OremoveAll(_1787499, _1787497), hAPP(c_List_Ofilter(_1787499, _1787495), _1787501)) = hAPP(c_List_Ofilter(_1787499, _1787495), _1787501))], (49655 ^ _784416) ^ [_1787555, _1787557] : [-(hAPP(c_List_OremoveAll(_1787555, _1787557), c_List_Olist_ONil(_1787555)) = c_List_Olist_ONil(_1787555))], (49657 ^ _784416) ^ [_1787590, _1787592, _1787594] : [hBOOL(hAPP(c_List_Odistinct(_1787590), _1787592)), -(hBOOL(hAPP(c_List_Odistinct(_1787590), c_List_Oinsert(_1787590, _1787594, _1787592))))], (49663 ^ _784416) ^ [_1787693, _1787695, _1787697] : [hBOOL(hAPP(c_List_Odistinct(_1787693), _1787695)), -(hBOOL(hAPP(c_List_Odistinct(_1787693), hAPP(c_List_OremoveAll(_1787693, _1787697), _1787695))))], (49669 ^ _784416) ^ [_1787800, _1787802, _1787804] : [-(c_List_Oinsert(_1787800, _1787802, c_List_Oremdups(_1787800, _1787804)) = c_List_Oremdups(_1787800, c_List_Oinsert(_1787800, _1787802, _1787804)))], (49671 ^ _784416) ^ [_1787856, _1787858, _1787860, _1787862] : [_1787856 = _1787858, -(hAPP(c_List_OremoveAll(_1787860, _1787856), hAPP(hAPP(c_List_Olist_OCons(_1787860), _1787858), _1787862)) = hAPP(c_List_OremoveAll(_1787860, _1787856), _1787862))], (49677 ^ _784416) ^ [_1787971, _1787973, _1787975, _1787977] : [-(_1787971 = _1787973), -(hAPP(c_List_OremoveAll(_1787975, _1787971), hAPP(hAPP(c_List_Olist_OCons(_1787975), _1787973), _1787977)) = hAPP(hAPP(c_List_Olist_OCons(_1787975), _1787973), hAPP(c_List_OremoveAll(_1787975, _1787971), _1787977)))], (49683 ^ _784416) ^ [_1788041, _1788043, _1788045, _1788047] : [-(hAPP(c_List_OremoveAll(_1788041, _1788043), hAPP(hAPP(c_List_Oappend(_1788041), _1788045), _1788047)) = hAPP(hAPP(c_List_Oappend(_1788041), hAPP(c_List_OremoveAll(_1788041, _1788043), _1788045)), hAPP(c_List_OremoveAll(_1788041, _1788043), _1788047)))], (49685 ^ _784416) ^ [_1788104, _1788106, _1788108] : [hBOOL(hAPP(c_List_Odistinct(_1788104), _1788106)), -(c_List_Oremove1(_1788104, _1788108, _1788106) = hAPP(c_List_OremoveAll(_1788104, _1788108), _1788106))], (49691 ^ _784416) ^ [_1788211, _1788213, _1788215] : [hBOOL(hAPP(hAPP(c_member(_1788211), _1788213), hAPP(c_List_Oset(_1788211), _1788215))), -(c_List_Oinsert(_1788211, _1788213, _1788215) = _1788215)], (49697 ^ _784416) ^ [_1788322, _1788324, _1788326] : [-(hAPP(c_List_Oset(_1788322), c_List_Oinsert(_1788322, _1788324, _1788326)) = hAPP(hAPP(c_Set_Oinsert(_1788322), _1788324), hAPP(c_List_Oset(_1788322), _1788326)))], (49699 ^ _784416) ^ [_1788371, _1788373] : [-(c_List_Oinsert(_1788371, _1788373, c_List_Olist_ONil(_1788371)) = hAPP(hAPP(c_List_Olist_OCons(_1788371), _1788373), c_List_Olist_ONil(_1788371)))], (49701 ^ _784416) ^ [_1788412, _1788414, _1788416, _1788418, _1788420] : [c_Fun_Oinj__on(_1788412, _1788414, _1788416, c_Orderings_Otop__class_Otop(tc_fun(_1788412, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1788412, _1788414), _1788416), hAPP(c_List_OremoveAll(_1788412, _1788418), _1788420)) = hAPP(c_List_OremoveAll(_1788414, hAPP(_1788416, _1788418)), hAPP(hAPP(c_List_Omap(_1788412, _1788414), _1788416), _1788420)))], (49707 ^ _784416) ^ [_1788575, _1788577, _1788579] : [-(hAPP(c_List_Oset(_1788575), hAPP(c_List_OremoveAll(_1788575, _1788577), _1788579)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1788575, tc_HOL_Obool)), hAPP(c_List_Oset(_1788575), _1788579)), hAPP(hAPP(c_Set_Oinsert(_1788575), _1788577), c_Orderings_Obot__class_Obot(tc_fun(_1788575, tc_HOL_Obool)))))], (49709 ^ _784416) ^ [_1788654, _1788656, _1788658] : [hBOOL(hAPP(hAPP(c_member(_1788654), _1788656), hAPP(c_List_Oset(_1788654), _1788658))), -(c_List_Oinsert(_1788654, _1788656, _1788658) = _1788658)], (49715 ^ _784416) ^ [_1788759, _1788761, _1788763] : [-(hBOOL(hAPP(hAPP(c_member(_1788759), _1788761), hAPP(c_List_Oset(_1788759), _1788763)))), -(c_List_Oinsert(_1788759, _1788761, _1788763) = hAPP(hAPP(c_List_Olist_OCons(_1788759), _1788761), _1788763))], (49721 ^ _784416) ^ [_1788823, _1788825, _1788827, _1788829] : [-(c_List_Oconcat(_1788823, hAPP(hAPP(c_List_Omap(_1788825, tc_List_Olist(_1788823)), _1788827), _1788829)) = c_List_Omaps(_1788825, _1788823, _1788827, _1788829))], (49723 ^ _784416) ^ [_1788871, _1788873, _1788875, _1788877] : [-(c_List_Omaps(_1788871, _1788873, _1788875, _1788877) = c_List_Oconcat(_1788873, hAPP(hAPP(c_List_Omap(_1788871, tc_List_Olist(_1788873)), _1788875), _1788877)))], (49725 ^ _784416) ^ [_1788919, _1788921, _1788923] : [-(c_List_Omaps(_1788919, _1788921, _1788923, c_List_Olist_ONil(_1788919)) = c_List_Olist_ONil(_1788921))], (49727 ^ _784416) ^ [_1788955, _1788957, _1788959, _1788961, _1788963] : [-(c_List_Omaps(_1788955, _1788957, _1788959, hAPP(hAPP(c_List_Olist_OCons(_1788955), _1788961), _1788963)) = hAPP(hAPP(c_List_Oappend(_1788957), hAPP(_1788959, _1788961)), c_List_Omaps(_1788955, _1788957, _1788959, _1788963)))], (49729 ^ _784416) ^ [_1789015, _1789017] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1789015)), _1789017)), 49735 ^ _784416 : [(49736 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1789015)), 49734 ^ [_1789015, _1789017]), hAPP(c_List_Oset(tc_List_Olist(_1789015)), _1789017))))], (49738 ^ _784416) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1789015), 49734 ^ [_1789015, _1789017]))]], 49742 ^ _784416 : [(49743 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1789015)), 49741 ^ [_1789015, _1789017]), hAPP(c_List_Oset(tc_List_Olist(_1789015)), _1789017))))], (49746 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1789015)), 49744 ^ [_1789015, _1789017]), hAPP(c_List_Oset(tc_List_Olist(_1789015)), _1789017))))], (49748 ^ _784416) ^ [] : [49741 ^ [_1789015, _1789017] = 49744 ^ [_1789015, _1789017]], (49750 ^ _784416) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1789015, tc_HOL_Obool)), hAPP(c_List_Oset(_1789015), 49741 ^ [_1789015, _1789017])), hAPP(c_List_Oset(_1789015), 49744 ^ [_1789015, _1789017])) = c_Orderings_Obot__class_Obot(tc_fun(_1789015, tc_HOL_Obool))]], -(hBOOL(hAPP(c_List_Odistinct(_1789015), c_List_Oconcat(_1789015, _1789017))))], (49754 ^ _784416) ^ [_1789732, _1789734, _1789736, _1789738, _1789740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1789732, _1789734)), hAPP(_1789732, _1789736))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1789738, _1789738)), hAPP(hAPP(c_Product__Type_OPair(_1789738, _1789738), _1789734), _1789736)), c_List_Omeasures(_1789738, _1789740))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1789738, _1789738)), hAPP(hAPP(c_Product__Type_OPair(_1789738, _1789738), _1789734), _1789736)), c_List_Omeasures(_1789738, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1789738, tc_Nat_Onat)), _1789732), _1789740)))))], (49764 ^ _784416) ^ [_1790005, _1790007] : [-(c_Wellfounded_Owf(_1790005, c_List_Omeasures(_1790005, _1790007)))], (49766 ^ _784416) ^ [_1790048, _1790050, _1790052] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1790048, _1790048)), hAPP(hAPP(c_Product__Type_OPair(_1790048, _1790048), _1790050), _1790052)), c_List_Omeasures(_1790048, c_List_Olist_ONil(tc_fun(_1790048, tc_Nat_Onat)))))], (49768 ^ _784416) ^ [_1790102, _1790104] : [-(c_List_Omeasures(_1790102, _1790104) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1790102), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1790102, tc_List_Olist(tc_fun(_1790102, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1790102, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1790102, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1790102), c_List_Omap(tc_fun(_1790102, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1790102, tc_Nat_Onat), _1790102, tc_Nat_Onat), c_COMBI(tc_fun(_1790102, tc_Nat_Onat))))), _1790104)))], (49770 ^ _784416) ^ [_1790199, _1790201, _1790203, _1790205, _1790207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1790199, _1790201)), hAPP(_1790199, _1790203))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1790205, _1790205)), hAPP(hAPP(c_Product__Type_OPair(_1790205, _1790205), _1790201), _1790203)), c_List_Omeasures(_1790205, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1790205, tc_Nat_Onat)), _1790199), _1790207)))))], (49776 ^ _784416) ^ [_1790394, _1790396, _1790398, _1790400, _1790402] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1790394, _1790394)), hAPP(hAPP(c_Product__Type_OPair(_1790394, _1790394), _1790396), _1790398)), c_List_Omeasures(_1790394, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1790394, tc_Nat_Onat)), _1790400), _1790402)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1790400, _1790396)), hAPP(_1790400, _1790398)))), 49783 ^ _784416 : [(49784 ^ _784416) ^ [] : [-(hAPP(_1790400, _1790396) = hAPP(_1790400, _1790398))], (49786 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1790394, _1790394)), hAPP(hAPP(c_Product__Type_OPair(_1790394, _1790394), _1790396), _1790398)), c_List_Omeasures(_1790394, _1790402))))]]], (49788 ^ _784416) ^ [_1790673, _1790675, _1790677, _1790679, _1790681] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1790673, _1790673)), hAPP(hAPP(c_Product__Type_OPair(_1790673, _1790673), _1790675), _1790677)), c_List_Omeasures(_1790673, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1790673, tc_Nat_Onat)), _1790679), _1790681))))), 49789 ^ _784416 : [(49790 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1790679, _1790675)), hAPP(_1790679, _1790677)))], (49792 ^ _784416) ^ [] : [hAPP(_1790679, _1790675) = hAPP(_1790679, _1790677), hBOOL(hAPP(hAPP(c_member(tc_prod(_1790673, _1790673)), hAPP(hAPP(c_Product__Type_OPair(_1790673, _1790673), _1790675), _1790677)), c_List_Omeasures(_1790673, _1790681)))]]], (49800 ^ _784416) ^ [_1790996, _1790998, _1791000, _1791002, _1791004, _1791006, _1791008, _1791010] : [49802 ^ _784416 : [(49803 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1790996), 49801 ^ [_1790996, _1790998, _1791000, _1791002, _1791004, _1791006, _1791008, _1791010]), hAPP(c_List_Oset(_1790996), _1790998))))], (49805 ^ _784416) ^ [] : [hAPP(c_Fun_Ocomp(_1791000, _1791000, _1791002, hAPP(_1791004, 49801 ^ [_1790996, _1790998, _1791000, _1791002, _1791004, _1791006, _1791008, _1791010])), _1791006) = hAPP(c_Fun_Ocomp(_1791002, _1791000, _1791002, _1791006), hAPP(_1791008, 49801 ^ [_1790996, _1790998, _1791000, _1791002, _1791004, _1791006, _1791008, _1791010]))]], -(hAPP(c_List_Ofoldl(_1791000, _1790996, hAPP(c_COMBC(_1790996, _1791000, _1791000), _1791004), hAPP(_1791006, _1791010)), _1790998) = hAPP(_1791006, hAPP(c_List_Ofoldl(_1791002, _1790996, hAPP(c_COMBC(_1790996, _1791002, _1791002), _1791008), _1791010), _1790998)))], (49809 ^ _784416) ^ [_1791365, _1791367, _1791369, _1791371, _1791373] : [49810 ^ _784416 : [(49811 ^ _784416) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791365)), hAPP(hAPP(c_List_Otake(_1791365), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791365)), _1791367)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791369)), _1791371))), _1791367)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791369)), hAPP(hAPP(c_List_Otake(_1791369), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791365)), _1791367)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791369)), _1791371))), _1791371)))], (49813 ^ _784416) ^ [] : [hBOOL(hAPP(_1791373, hAPP(hAPP(c_List_Ozip(_1791365, _1791369), hAPP(hAPP(c_List_Otake(_1791365), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791365)), _1791367)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791369)), _1791371))), _1791367)), hAPP(hAPP(c_List_Otake(_1791369), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791365)), _1791367)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791369)), _1791371))), _1791371))))]], -(hBOOL(hAPP(_1791373, hAPP(hAPP(c_List_Ozip(_1791365, _1791369), _1791367), _1791371))))], (49817 ^ _784416) ^ [_1791777, _1791779, _1791781, _1791783] : [hAPP(c_List_Oset(_1791777), hAPP(hAPP(c_List_Omap(tc_prod(_1791777, _1791779), _1791777), c_Product__Type_Ofst(_1791777, _1791779)), _1791781)) = hAPP(c_List_Oset(_1791777), hAPP(hAPP(c_List_Omap(tc_prod(_1791777, _1791779), _1791777), c_Product__Type_Ofst(_1791777, _1791779)), _1791783)), 49823 ^ _784416 : [(49824 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791777), 49822 ^ [_1791777, _1791779, _1791781, _1791783]), hAPP(c_List_Oset(_1791777), hAPP(hAPP(c_List_Omap(tc_prod(_1791777, _1791779), _1791777), c_Product__Type_Ofst(_1791777, _1791779)), _1791781)))))], (49826 ^ _784416) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1791777, _1791779), _1791781), 49822 ^ [_1791777, _1791779, _1791781, _1791783]) = hAPP(hAPP(c_Map_Omap__of(_1791777, _1791779), _1791783), 49822 ^ [_1791777, _1791779, _1791781, _1791783])]], -(hAPP(c_Map_Omap__of(_1791777, _1791779), _1791781) = hAPP(c_Map_Omap__of(_1791777, _1791779), _1791783))], (49830 ^ _784416) ^ [_1792215, _1792217, _1792219, _1792221] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1792215, _1792217, _1792219, _1792221) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1792215, _1792217), _1792219), _1792221)))], (49832 ^ _784416) ^ [_1792260, _1792262, _1792264, _1792266] : [49834 ^ _784416 : [(49835 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1792260), 49833 ^ [_1792260, _1792262, _1792264, _1792266]), hAPP(c_List_Oset(_1792260), _1792262))))], (49837 ^ _784416) ^ [] : [hBOOL(hAPP(_1792264, 49833 ^ [_1792260, _1792262, _1792264, _1792266]))]], -(c_List_OdropWhile(_1792260, _1792264, hAPP(hAPP(c_List_Oappend(_1792260), _1792262), _1792266)) = c_List_OdropWhile(_1792260, _1792264, _1792266))], (49841 ^ _784416) ^ [_1792478, _1792480, _1792482, _1792484, _1792486] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792478)), _1792480) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792482)), _1792484), 49847 ^ _784416 : [(49848 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49846 ^ [_1792478, _1792480, _1792482, _1792484, _1792486]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792478)), _1792480))))], (49850 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1792486, hAPP(hAPP(c_List_Onth(_1792478), _1792480), 49846 ^ [_1792478, _1792480, _1792482, _1792484, _1792486])), hAPP(hAPP(c_List_Onth(_1792482), _1792484), 49846 ^ [_1792478, _1792480, _1792482, _1792484, _1792486])))]], -(c_List_Olist__all2(_1792478, _1792482, _1792486, _1792480, _1792484))], (49854 ^ _784416) ^ [_1792836, _1792838] : [class_Orderings_Olinorder(_1792836), hBOOL(hAPP(c_Finite__Set_Ofinite(_1792836), _1792838)), 49862 ^ _784416 : [(49863 ^ _784416) ^ [] : [-(hAPP(c_List_Oset(_1792836), 49861 ^ [_1792836, _1792838]) = _1792838)], (49865 ^ _784416) ^ [] : [-(c_List_Olinorder__class_Osorted(_1792836, 49861 ^ [_1792836, _1792838]))], (49867 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1792836), 49861 ^ [_1792836, _1792838])))], (49869 ^ _784416) ^ [_1793162] : [-(_1793162 = 49861 ^ [_1792836, _1792838]), hAPP(c_List_Oset(_1792836), _1793162) = _1792838, c_List_Olinorder__class_Osorted(_1792836, _1793162), hBOOL(hAPP(c_List_Odistinct(_1792836), _1793162))]]], (49883 ^ _784416) ^ [_1793393, _1793395, _1793397, _1793399] : [49885 ^ _784416 : [(49886 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1793393), 49884 ^ [_1793393, _1793395, _1793397, _1793399]), hAPP(c_List_Oset(_1793393), _1793395))))], (49888 ^ _784416) ^ [] : [hBOOL(hAPP(_1793397, 49884 ^ [_1793393, _1793395, _1793397, _1793399]))]], -(c_List_OtakeWhile(_1793393, _1793397, hAPP(hAPP(c_List_Oappend(_1793393), _1793395), _1793399)) = hAPP(hAPP(c_List_Oappend(_1793393), _1793395), c_List_OtakeWhile(_1793393, _1793397, _1793399)))], (49892 ^ _784416) ^ [_1793627, _1793629, _1793631, _1793633, _1793635] : [class_Orderings_Olinorder(_1793627), 49898 ^ _784416 : [(49899 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1793629), 49897 ^ [_1793627, _1793629, _1793631, _1793633, _1793635]), hAPP(c_List_Oset(_1793629), _1793631))))], (49901 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1793627), hAPP(_1793633, _1793635)), hAPP(_1793633, 49897 ^ [_1793627, _1793629, _1793631, _1793633, _1793635])))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1793629, _1793627, _1793633), _1793635), _1793631) = hAPP(hAPP(c_List_Olist_OCons(_1793629), _1793635), _1793631))], (49905 ^ _784416) ^ [_1793970, _1793972, _1793974, _1793976, _1793978] : [hAPP(c_List_Ofilter(_1793970, _1793972), _1793974) = hAPP(hAPP(c_List_Olist_OCons(_1793970), _1793976), _1793978), 49910 ^ _784416 : [(49911 ^ _784416) ^ [] : [-(_1793974 = hAPP(hAPP(c_List_Oappend(_1793970), 49908 ^ [_1793970, _1793972, _1793974, _1793976, _1793978]), hAPP(hAPP(c_List_Olist_OCons(_1793970), _1793976), 49909 ^ [_1793970, _1793972, _1793974, _1793976, _1793978])))], (49919 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1793972, _1793976)))], (49921 ^ _784416) ^ [] : [-(_1793978 = hAPP(c_List_Ofilter(_1793970, _1793972), 49909 ^ [_1793970, _1793972, _1793974, _1793976, _1793978]))], (49913 ^ _784416) ^ [_1794284] : [hBOOL(hAPP(hAPP(c_member(_1793970), _1794284), hAPP(c_List_Oset(_1793970), 49908 ^ [_1793970, _1793972, _1793974, _1793976, _1793978]))), hBOOL(hAPP(_1793972, _1794284))]]], (49923 ^ _784416) ^ [_1794488, _1794490, _1794492, _1794494, _1794496] : [-(hAPP(c_List_Ofilter(_1794488, _1794490), _1794492) = hAPP(hAPP(c_List_Olist_OCons(_1794488), _1794494), _1794496)), 49924 ^ _784416 : [(49925 ^ _784416) ^ [_1794616, _1794618] : [_1794492 = hAPP(hAPP(c_List_Oappend(_1794488), _1794618), hAPP(hAPP(c_List_Olist_OCons(_1794488), _1794494), _1794616)), 49931 ^ _784416 : [(49932 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1794488), 49930 ^ [_1794488, _1794490, _1794492, _1794494, _1794496, _1794616, _1794618]), hAPP(c_List_Oset(_1794488), _1794618))))], (49934 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1794490, 49930 ^ [_1794488, _1794490, _1794492, _1794494, _1794496, _1794616, _1794618])))]], hBOOL(hAPP(_1794490, _1794494)), _1794496 = hAPP(c_List_Ofilter(_1794488, _1794490), _1794616)]]], (49944 ^ _784416) ^ [_1795038, _1795040, _1795042, _1795044, _1795046] : [hAPP(hAPP(c_List_Olist_OCons(_1795038), _1795040), _1795042) = hAPP(c_List_Ofilter(_1795038, _1795044), _1795046), 49949 ^ _784416 : [(49950 ^ _784416) ^ [] : [-(_1795046 = hAPP(hAPP(c_List_Oappend(_1795038), 49947 ^ [_1795038, _1795040, _1795042, _1795044, _1795046]), hAPP(hAPP(c_List_Olist_OCons(_1795038), _1795040), 49948 ^ [_1795038, _1795040, _1795042, _1795044, _1795046])))], (49958 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1795044, _1795040)))], (49960 ^ _784416) ^ [] : [-(_1795042 = hAPP(c_List_Ofilter(_1795038, _1795044), 49948 ^ [_1795038, _1795040, _1795042, _1795044, _1795046]))], (49952 ^ _784416) ^ [_1795352] : [hBOOL(hAPP(hAPP(c_member(_1795038), _1795352), hAPP(c_List_Oset(_1795038), 49947 ^ [_1795038, _1795040, _1795042, _1795044, _1795046]))), hBOOL(hAPP(_1795044, _1795352))]]], (49962 ^ _784416) ^ [_1795556, _1795558, _1795560, _1795562, _1795564] : [-(hAPP(hAPP(c_List_Olist_OCons(_1795556), _1795558), _1795560) = hAPP(c_List_Ofilter(_1795556, _1795562), _1795564)), 49963 ^ _784416 : [(49964 ^ _784416) ^ [_1795684, _1795686] : [_1795564 = hAPP(hAPP(c_List_Oappend(_1795556), _1795686), hAPP(hAPP(c_List_Olist_OCons(_1795556), _1795558), _1795684)), 49970 ^ _784416 : [(49971 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795556), 49969 ^ [_1795556, _1795558, _1795560, _1795562, _1795564, _1795684, _1795686]), hAPP(c_List_Oset(_1795556), _1795686))))], (49973 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1795562, 49969 ^ [_1795556, _1795558, _1795560, _1795562, _1795564, _1795684, _1795686])))]], hBOOL(hAPP(_1795562, _1795558)), _1795560 = hAPP(c_List_Ofilter(_1795556, _1795562), _1795684)]]], (49983 ^ _784416) ^ [_1796082, _1796084, _1796086, _1796088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1796082), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796084)), _1796086))), 49989 ^ _784416 : [(49990 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796084), 49988 ^ [_1796082, _1796084, _1796086, _1796088]), hAPP(c_List_Oset(_1796084), _1796086))))], (49992 ^ _784416) ^ [] : [hBOOL(hAPP(_1796088, 49988 ^ [_1796082, _1796084, _1796086, _1796088]))]], -(hBOOL(hAPP(_1796088, hAPP(hAPP(c_List_Onth(_1796084), _1796086), _1796082))))], (49996 ^ _784416) ^ [_1796368, _1796370, _1796372] : [class_Orderings_Olinorder(_1796368), 50002 ^ _784416 : [(50003 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796368), 50001 ^ [_1796368, _1796370, _1796372]), hAPP(c_List_Oset(_1796368), _1796370))))], (50005 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1796368), _1796372), 50001 ^ [_1796368, _1796370, _1796372]))]], c_List_Olinorder__class_Osorted(_1796368, _1796370), -(c_List_Olinorder__class_Osorted(_1796368, hAPP(hAPP(c_List_Olist_OCons(_1796368), _1796372), _1796370)))], (50013 ^ _784416) ^ [_1796702, _1796704, _1796706] : [c_List_Olist__ex(_1796702, _1796704, _1796706), 50017 ^ _784416 : [(50018 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50016 ^ [_1796702, _1796704, _1796706]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796702)), _1796706))))], (50020 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1796704, hAPP(hAPP(c_List_Onth(_1796702), _1796706), 50016 ^ [_1796702, _1796704, _1796706]))))]]], (50022 ^ _784416) ^ [_1796872, _1796874, _1796876] : [-(c_List_Olist__ex(_1796872, _1796874, _1796876)), 50023 ^ _784416 : [(50024 ^ _784416) ^ [_1796937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1796937), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1796872)), _1796876))), hBOOL(hAPP(_1796874, hAPP(hAPP(c_List_Onth(_1796872), _1796876), _1796937)))]]], (50042 ^ _784416) ^ [_1797227, _1797229, _1797231, _1797233] : [50043 ^ _784416 : [(50044 ^ _784416) ^ [] : [hBOOL(hAPP(_1797229, _1797231))], (50046 ^ _784416) ^ [] : [c_List_Olist__ex(_1797227, _1797229, _1797233)]], -(c_List_Olist__ex(_1797227, _1797229, hAPP(hAPP(c_List_Olist_OCons(_1797227), _1797231), _1797233)))], (50032 ^ _784416) ^ [_1797113, _1797115, _1797117, _1797119] : [c_List_Olist__ex(_1797113, _1797115, hAPP(hAPP(c_List_Olist_OCons(_1797113), _1797117), _1797119)), -(hBOOL(hAPP(_1797115, _1797117))), -(c_List_Olist__ex(_1797113, _1797115, _1797119))], (50050 ^ _784416) ^ [_1797390, _1797392, _1797394] : [c_List_Olist__ex(_1797390, _1797392, hAPP(c_List_Orev(_1797390), _1797394)), -(c_List_Olist__ex(_1797390, _1797392, _1797394))], (50056 ^ _784416) ^ [_1797479, _1797481, _1797483] : [c_List_Olist__ex(_1797479, _1797481, _1797483), -(c_List_Olist__ex(_1797479, _1797481, hAPP(c_List_Orev(_1797479), _1797483)))], (50072 ^ _784416) ^ [_1797707, _1797709, _1797711, _1797713] : [50073 ^ _784416 : [(50074 ^ _784416) ^ [] : [c_List_Olist__ex(_1797707, _1797709, _1797711)], (50076 ^ _784416) ^ [] : [c_List_Olist__ex(_1797707, _1797709, _1797713)]], -(c_List_Olist__ex(_1797707, _1797709, hAPP(hAPP(c_List_Oappend(_1797707), _1797711), _1797713)))], (50062 ^ _784416) ^ [_1797595, _1797597, _1797599, _1797601] : [c_List_Olist__ex(_1797595, _1797597, hAPP(hAPP(c_List_Oappend(_1797595), _1797599), _1797601)), -(c_List_Olist__ex(_1797595, _1797597, _1797599)), -(c_List_Olist__ex(_1797595, _1797597, _1797601))], (50080 ^ _784416) ^ [_1797868, _1797870, _1797872] : [c_List_Olist__ex(_1797868, _1797870, _1797872), 50084 ^ _784416 : [(50085 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1797868), 50083 ^ [_1797868, _1797870, _1797872]), hAPP(c_List_Oset(_1797868), _1797872))))], (50087 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1797870, 50083 ^ [_1797868, _1797870, _1797872])))]]], (50089 ^ _784416) ^ [_1798022, _1798024, _1798026] : [-(c_List_Olist__ex(_1798022, _1798024, _1798026)), 50090 ^ _784416 : [(50091 ^ _784416) ^ [_1798079] : [hBOOL(hAPP(hAPP(c_member(_1798022), _1798079), hAPP(c_List_Oset(_1798022), _1798026))), hBOOL(hAPP(_1798024, _1798079))]]], (50099 ^ _784416) ^ [_1798230, _1798232] : [c_List_Olist__ex(_1798230, _1798232, c_List_Olist_ONil(_1798230))], (50101 ^ _784416) ^ [_1798276, _1798278, _1798280] : [hBOOL(hAPP(hAPP(c_member(_1798276), _1798278), hAPP(c_List_Oset(_1798276), _1798280))), 50106 ^ _784416 : [(50107 ^ _784416) ^ [] : [-(_1798280 = hAPP(hAPP(c_List_Oappend(_1798276), 50104 ^ [_1798276, _1798278, _1798280]), hAPP(hAPP(c_List_Olist_OCons(_1798276), _1798278), 50105 ^ [_1798276, _1798278, _1798280])))], (50109 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1798276), _1798278), hAPP(c_List_Oset(_1798276), 50104 ^ [_1798276, _1798278, _1798280])))]]], (50111 ^ _784416) ^ [_1798531, _1798533, _1798535] : [-(hBOOL(hAPP(hAPP(c_member(_1798531), _1798533), hAPP(c_List_Oset(_1798531), _1798535)))), 50112 ^ _784416 : [(50113 ^ _784416) ^ [_1798620] : [50114 ^ _784416 : [(50115 ^ _784416) ^ [_1798693] : [_1798535 = hAPP(hAPP(c_List_Oappend(_1798531), _1798620), hAPP(hAPP(c_List_Olist_OCons(_1798531), _1798533), _1798693))]], -(hBOOL(hAPP(hAPP(c_member(_1798531), _1798533), hAPP(c_List_Oset(_1798531), _1798620))))]]], (50121 ^ _784416) ^ [_1798832, _1798834, _1798836] : [hBOOL(hAPP(hAPP(c_member(_1798832), _1798834), hAPP(c_List_Oset(_1798832), _1798836))), 50126 ^ _784416 : [(50127 ^ _784416) ^ [] : [-(_1798836 = hAPP(hAPP(c_List_Oappend(_1798832), 50124 ^ [_1798832, _1798834, _1798836]), hAPP(hAPP(c_List_Olist_OCons(_1798832), _1798834), 50125 ^ [_1798832, _1798834, _1798836])))], (50129 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1798832), _1798834), hAPP(c_List_Oset(_1798832), 50125 ^ [_1798832, _1798834, _1798836])))]]], (50131 ^ _784416) ^ [_1799087, _1799089, _1799091] : [-(hBOOL(hAPP(hAPP(c_member(_1799087), _1799089), hAPP(c_List_Oset(_1799087), _1799091)))), 50132 ^ _784416 : [(50133 ^ _784416) ^ [_1799176, _1799178] : [_1799091 = hAPP(hAPP(c_List_Oappend(_1799087), _1799178), hAPP(hAPP(c_List_Olist_OCons(_1799087), _1799089), _1799176)), -(hBOOL(hAPP(hAPP(c_member(_1799087), _1799089), hAPP(c_List_Oset(_1799087), _1799176))))]]], (50141 ^ _784416) ^ [_1799377, _1799379, _1799381] : [hBOOL(hAPP(hAPP(c_member(_1799377), _1799379), hAPP(c_List_Oset(_1799377), _1799381))), -(_1799381 = hAPP(hAPP(c_List_Oappend(_1799377), 50144 ^ [_1799377, _1799379, _1799381]), hAPP(hAPP(c_List_Olist_OCons(_1799377), _1799379), 50145 ^ [_1799377, _1799379, _1799381])))], (50149 ^ _784416) ^ [_1799536, _1799538, _1799540] : [50150 ^ _784416 : [(50151 ^ _784416) ^ [_1799613, _1799615] : [_1799540 = hAPP(hAPP(c_List_Oappend(_1799536), _1799615), hAPP(hAPP(c_List_Olist_OCons(_1799536), _1799538), _1799613))]], -(hBOOL(hAPP(hAPP(c_member(_1799536), _1799538), hAPP(c_List_Oset(_1799536), _1799540))))], (50155 ^ _784416) ^ [_1799696, _1799698, _1799700] : [-(c_Nitpick_Oplus__frac(_1799696, _1799698, _1799700) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1799696), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1799696), _1799698), hAPP(c_Nitpick_Odenom(_1799696), _1799700))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1799696), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1799696), tc_Int_Oint), c_Nitpick_Ofrac(_1799696)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1799696), _1799698))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint)), hAPP(c_Nitpick_Odenom(_1799696), _1799698))))), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1799696), _1799700))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint)), hAPP(c_Nitpick_Odenom(_1799696), _1799700)))))), c_COMBI(tc_Int_Oint))))], (50157 ^ _784416) ^ [_1799827, _1799829, _1799831] : [-(c_Nitpick_Otimes__frac(_1799827, _1799829, _1799831) = hAPP(hAPP(c_Nitpick_Ofrac(_1799827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1799827), _1799829)), hAPP(c_Nitpick_Onum(_1799827), _1799831))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1799827), _1799829)), hAPP(c_Nitpick_Odenom(_1799827), _1799831))))], (50159 ^ _784416) ^ [_1799898, _1799900, _1799902] : [-(c_Nitpick_Oof__frac(_1799900, _1799898, _1799902) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1799898), hAPP(c_Int_Oring__1__class_Oof__int(_1799898), hAPP(c_Nitpick_Onum(_1799900), _1799902))), hAPP(c_Int_Oring__1__class_Oof__int(_1799898), hAPP(c_Nitpick_Odenom(_1799900), _1799902)))), class_Rings_Oinverse(_1799898), class_Rings_Oring__1(_1799898)], (50169 ^ _784416) ^ [_1800091, _1800093] : [-(c_Nitpick_Oinverse__frac(_1800091, _1800093) = hAPP(hAPP(c_Nitpick_Ofrac(_1800091), hAPP(c_Nitpick_Odenom(_1800091), _1800093)), hAPP(c_Nitpick_Onum(_1800091), _1800093)))], (50171 ^ _784416) ^ [_1800137, _1800139] : [-(c_Nitpick_Ouminus__frac(_1800137, _1800139) = c_Nitpick_OAbs__Frac(_1800137, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1800137), _1800139))), hAPP(c_Nitpick_Odenom(_1800137), _1800139))))], (50173 ^ _784416) ^ [_1800205, _1800207, _1800209] : [c_Nitpick_Oless__frac(_1800205, _1800207, _1800209), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1800205), c_Nitpick_Oplus__frac(_1800205, _1800207, c_Nitpick_Ouminus__frac(_1800205, _1800209)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (50179 ^ _784416) ^ [_1800316, _1800318, _1800320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1800316), c_Nitpick_Oplus__frac(_1800316, _1800318, c_Nitpick_Ouminus__frac(_1800316, _1800320)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1800316, _1800318, _1800320))], (50185 ^ _784416) ^ [_1800451, _1800453, _1800455] : [c_Nitpick_Oless__eq__frac(_1800451, _1800453, _1800455), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1800451), c_Nitpick_Oplus__frac(_1800451, _1800453, c_Nitpick_Ouminus__frac(_1800451, _1800455)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (50191 ^ _784416) ^ [_1800562, _1800564, _1800566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1800562), c_Nitpick_Oplus__frac(_1800562, _1800564, c_Nitpick_Ouminus__frac(_1800562, _1800566)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1800562, _1800564, _1800566))], (50197 ^ _784416) ^ [_1800679] : [-(c_Nitpick_Odenom(_1800679) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1800679, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1800679)))], (50199 ^ _784416) ^ [_1800714] : [-(c_Nitpick_Onum(_1800714) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1800714, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1800714)))], (50201 ^ _784416) ^ [_1800749, _1800751, _1800753, _1800755] : [class_Rings_Olinordered__semidom(_1800749), 50207 ^ _784416 : [(50208 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1800751), 50206 ^ [_1800749, _1800751, _1800753, _1800755]), _1800753)))], (50210 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1800749), c_Groups_Ozero__class_Ozero(_1800749)), hAPP(_1800755, 50206 ^ [_1800749, _1800751, _1800753, _1800755])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1800749), c_Groups_Ozero__class_Ozero(_1800749)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1800751, _1800749), _1800755), _1800753))))], (50224 ^ _784416) ^ [_1801277, _1801279, _1801281] : [50226 ^ _784416 : [(50227 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 50225 ^ [_1801277, _1801279, _1801281]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1801277)), _1801281))))], (50229 ^ _784416) ^ [] : [hBOOL(hAPP(_1801279, hAPP(hAPP(c_List_Onth(_1801277), _1801281), 50225 ^ [_1801277, _1801279, _1801281])))]], -(c_List_Olist__all(_1801277, _1801279, _1801281))], (50214 ^ _784416) ^ [_1801063, _1801065, _1801067] : [c_List_Olist__all(_1801063, _1801065, _1801067), 50217 ^ _784416 : [(50218 ^ _784416) ^ [_1801152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1801152), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1801063)), _1801067))), -(hBOOL(hAPP(_1801065, hAPP(hAPP(c_List_Onth(_1801063), _1801067), _1801152))))]]], (50233 ^ _784416) ^ [_1801485, _1801487] : [-(c_List_Olist__all(_1801485, _1801487, c_List_Olist_ONil(_1801485)))], (50245 ^ _784416) ^ [_1801721, _1801723, _1801725] : [50247 ^ _784416 : [(50248 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1801721), 50246 ^ [_1801721, _1801723, _1801725]), hAPP(c_List_Oset(_1801721), _1801725))))], (50250 ^ _784416) ^ [] : [hBOOL(hAPP(_1801723, 50246 ^ [_1801721, _1801723, _1801725]))]], -(c_List_Olist__all(_1801721, _1801723, _1801725))], (50235 ^ _784416) ^ [_1801531, _1801533, _1801535] : [c_List_Olist__all(_1801531, _1801533, _1801535), 50238 ^ _784416 : [(50239 ^ _784416) ^ [_1801612] : [hBOOL(hAPP(hAPP(c_member(_1801531), _1801612), hAPP(c_List_Oset(_1801531), _1801535))), -(hBOOL(hAPP(_1801533, _1801612)))]]], (50254 ^ _784416) ^ [_1801924, _1801926, _1801928, _1801930] : [c_List_Olist__all(_1801924, _1801926, hAPP(hAPP(c_List_Oappend(_1801924), _1801928), _1801930)), 50257 ^ _784416 : [(50258 ^ _784416) ^ [] : [-(c_List_Olist__all(_1801924, _1801926, _1801928))], (50260 ^ _784416) ^ [] : [-(c_List_Olist__all(_1801924, _1801926, _1801930))]]], (50262 ^ _784416) ^ [_1802049, _1802051, _1802053, _1802055] : [-(c_List_Olist__all(_1802049, _1802051, hAPP(hAPP(c_List_Oappend(_1802049), _1802053), _1802055))), c_List_Olist__all(_1802049, _1802051, _1802053), c_List_Olist__all(_1802049, _1802051, _1802055)], (50272 ^ _784416) ^ [_1802228, _1802230, _1802232] : [c_List_Olist__all(_1802228, _1802230, hAPP(c_List_Orev(_1802228), _1802232)), -(c_List_Olist__all(_1802228, _1802230, _1802232))], (50278 ^ _784416) ^ [_1802317, _1802319, _1802321] : [c_List_Olist__all(_1802317, _1802319, _1802321), -(c_List_Olist__all(_1802317, _1802319, hAPP(c_List_Orev(_1802317), _1802321)))], (50284 ^ _784416) ^ [_1802430, _1802432, _1802434] : [50286 ^ _784416 : [(50287 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802430), 50285 ^ [_1802430, _1802432, _1802434]), hAPP(c_List_Oset(_1802430), _1802432))))], (50289 ^ _784416) ^ [] : [hBOOL(hAPP(_1802434, 50285 ^ [_1802430, _1802432, _1802434]))]], -(c_List_Olist__all(_1802430, _1802434, _1802432))], (50293 ^ _784416) ^ [_1802606, _1802608, _1802610] : [c_List_Olist__all(_1802606, _1802610, _1802608), 50296 ^ _784416 : [(50297 ^ _784416) ^ [_1802687] : [hBOOL(hAPP(hAPP(c_member(_1802606), _1802687), hAPP(c_List_Oset(_1802606), _1802608))), -(hBOOL(hAPP(_1802610, _1802687)))]]], (50303 ^ _784416) ^ [_1802823, _1802825, _1802827, _1802829] : [c_List_Olist__all(_1802823, _1802825, hAPP(hAPP(c_List_Olist_OCons(_1802823), _1802827), _1802829)), 50306 ^ _784416 : [(50307 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1802825, _1802827)))], (50309 ^ _784416) ^ [] : [-(c_List_Olist__all(_1802823, _1802825, _1802829))]]], (50311 ^ _784416) ^ [_1802950, _1802952, _1802954, _1802956] : [-(c_List_Olist__all(_1802950, _1802952, hAPP(hAPP(c_List_Olist_OCons(_1802950), _1802954), _1802956))), hBOOL(hAPP(_1802952, _1802954)), c_List_Olist__all(_1802950, _1802952, _1802956)], (50331 ^ _784416) ^ [_1803321, _1803323, _1803325] : [50333 ^ _784416 : [(50334 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1803321), 50332 ^ [_1803321, _1803323, _1803325]), hAPP(c_List_Oset(_1803321), _1803325))))], (50336 ^ _784416) ^ [] : [hBOOL(hAPP(_1803323, 50332 ^ [_1803321, _1803323, _1803325]))]], -(c_List_Olist__all(_1803321, _1803323, _1803325))], (50321 ^ _784416) ^ [_1803131, _1803133, _1803135] : [c_List_Olist__all(_1803131, _1803133, _1803135), 50324 ^ _784416 : [(50325 ^ _784416) ^ [_1803212] : [hBOOL(hAPP(hAPP(c_member(_1803131), _1803212), hAPP(c_List_Oset(_1803131), _1803135))), -(hBOOL(hAPP(_1803133, _1803212)))]]], (50356 ^ _784416) ^ [_1803800, _1803802, _1803804, _1803806] : [-(c_List_Olist__ex1(_1803800, _1803802, hAPP(hAPP(c_List_Olist_OCons(_1803800), _1803804), _1803806))), 50359 ^ _784416 : [(50360 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1803802, _1803804)))], (50362 ^ _784416) ^ [] : [c_List_Olist__all(_1803800, hAPP(hAPP(c_COMBS(_1803800, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1803800), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1803800), c_fNot), _1803802))), hAPP(c_fequal, _1803804)), _1803806)]], 50363 ^ _784416 : [(50364 ^ _784416) ^ [] : [hBOOL(hAPP(_1803802, _1803804))], (50366 ^ _784416) ^ [] : [c_List_Olist__ex1(_1803800, _1803802, _1803806)]]], (50340 ^ _784416) ^ [_1803524, _1803526, _1803528, _1803530] : [c_List_Olist__ex1(_1803524, _1803526, hAPP(hAPP(c_List_Olist_OCons(_1803524), _1803528), _1803530)), 50343 ^ _784416 : [(50344 ^ _784416) ^ [] : [hBOOL(hAPP(_1803526, _1803528)), -(c_List_Olist__all(_1803524, hAPP(hAPP(c_COMBS(_1803524, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1803524), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1803524), c_fNot), _1803526))), hAPP(c_fequal, _1803528)), _1803530))], (50350 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1803526, _1803528))), -(c_List_Olist__ex1(_1803524, _1803526, _1803530))]]], (50370 ^ _784416) ^ [_1804108, _1804110, _1804112] : [-(c_Product__Type_Ointernal__split(_1804108, _1804110, _1804112) = c_Product__Type_Oprod_Oprod__case(_1804108, _1804110, _1804112))], (50372 ^ _784416) ^ [_1804143, _1804145] : [class_Enum_Oenum(_1804143), 50375 ^ _784416 : [(50376 ^ _784416) ^ [] : [-(c_List_Olist__ex1(_1804143, _1804145, c_Enum_Oenum__class_Oenum(_1804143))), 50377 ^ _784416 : [(50378 ^ _784416) ^ [_1804258] : [hBOOL(hAPP(_1804145, _1804258)), 50382 ^ _784416 : [(50383 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1804145, 50381 ^ [_1804143, _1804145, _1804258])))], (50385 ^ _784416) ^ [] : [50381 ^ [_1804143, _1804145, _1804258] = _1804258]]]]], (50389 ^ _784416) ^ [] : [c_List_Olist__ex1(_1804143, _1804145, c_Enum_Oenum__class_Oenum(_1804143)), 50393 ^ _784416 : [(50394 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1804145, 50392 ^ [_1804143, _1804145])))], (50396 ^ _784416) ^ [_1804542] : [hBOOL(hAPP(_1804145, _1804542)), -(_1804542 = 50392 ^ [_1804143, _1804145])]]]]], (50402 ^ _784416) ^ [_1804663, _1804665] : [c_List_Olist__ex1(_1804663, _1804665, c_List_Olist_ONil(_1804663))], (50404 ^ _784416) ^ [_1804691, _1804693, _1804695, _1804697, _1804699, _1804701] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1804691, _1804693, _1804695), _1804697), hAPP(hAPP(c_Product__Type_OPair(_1804691, _1804693), _1804699), _1804701)) = hAPP(hAPP(_1804697, _1804699), _1804701))], (50406 ^ _784416) ^ [_1804767, _1804769, _1804771] : [c_List_Olist__ex1(_1804767, _1804769, _1804771), 50410 ^ _784416 : [(50411 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1804767), 50409 ^ [_1804767, _1804769, _1804771]), hAPP(c_List_Oset(_1804767), _1804771))))], (50413 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1804769, 50409 ^ [_1804767, _1804769, _1804771])))], (50415 ^ _784416) ^ [_1805013] : [-(_1805013 = 50409 ^ [_1804767, _1804769, _1804771]), hBOOL(hAPP(hAPP(c_member(_1804767), _1805013), hAPP(c_List_Oset(_1804767), _1804771))), hBOOL(hAPP(_1804769, _1805013))]]], (50425 ^ _784416) ^ [_1805200, _1805202, _1805204] : [-(c_List_Olist__ex1(_1805200, _1805202, _1805204)), 50426 ^ _784416 : [(50427 ^ _784416) ^ [_1805294] : [hBOOL(hAPP(hAPP(c_member(_1805200), _1805294), hAPP(c_List_Oset(_1805200), _1805204))), hBOOL(hAPP(_1805202, _1805294)), 50435 ^ _784416 : [(50436 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805200), 50434 ^ [_1805200, _1805202, _1805204, _1805294]), hAPP(c_List_Oset(_1805200), _1805204))))], (50438 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1805202, 50434 ^ [_1805200, _1805202, _1805204, _1805294])))], (50440 ^ _784416) ^ [] : [50434 ^ [_1805200, _1805202, _1805204, _1805294] = _1805294]]]]], (50444 ^ _784416) ^ [_1805629, _1805631, _1805633, _1805635] : [class_Rings_Olinordered__semidom(_1805629), 50450 ^ _784416 : [(50451 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805631), 50449 ^ [_1805629, _1805631, _1805633, _1805635]), _1805633)))], (50453 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1805629), c_Groups_Ozero__class_Ozero(_1805629)), hAPP(_1805635, 50449 ^ [_1805629, _1805631, _1805633, _1805635])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1805629), c_Groups_Ozero__class_Ozero(_1805629)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1805631, _1805629), _1805635), _1805633))))], (50457 ^ _784416) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50459 ^ _784416) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50461 ^ _784416) ^ [_1805961, _1805963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50462 ^ [_1805961, _1805963]), hAPP(_1805961, 50462 ^ [_1805961, _1805963]))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), _1805961)), _1805963)))))], (50468 ^ _784416) ^ [_1806121, _1806123, _1806125] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1806121), _1806123)), hBOOL(hAPP(_1806125, c_Orderings_Obot__class_Obot(tc_fun(_1806121, tc_HOL_Obool)))), 50479 ^ _784416 : [(50480 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1806121), 50478 ^ [_1806121, _1806123, _1806125])))], (50482 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1806121), 50477 ^ [_1806121, _1806123, _1806125]), 50478 ^ [_1806121, _1806123, _1806125]))], (50484 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1806125, 50478 ^ [_1806121, _1806123, _1806125])))], (50486 ^ _784416) ^ [] : [hBOOL(hAPP(_1806125, hAPP(hAPP(c_Set_Oinsert(_1806121), 50477 ^ [_1806121, _1806123, _1806125]), 50478 ^ [_1806121, _1806123, _1806125])))]], -(hBOOL(hAPP(_1806125, _1806123)))], (50490 ^ _784416) ^ [] : [-(c_FunDef_Ois__measure(tc_Int_Oint, hAPP(c_Fun_Ocomp(tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, c_Int_Onat), c_Groups_Oabs__class_Oabs(tc_Int_Oint))))], (50492 ^ _784416) ^ [_1806626, _1806628, _1806630, _1806632] : [class_HOL_Oequal(_1806626), class_Enum_Oenum(_1806628), 50499 ^ _784416 : [(50510 ^ _784416) ^ [] : [50512 ^ _784416 : [(50513 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806628), 50511 ^ [_1806626, _1806628, _1806630, _1806632]), hAPP(c_List_Oset(_1806628), c_Enum_Oenum__class_Oenum(_1806628)))))], (50515 ^ _784416) ^ [] : [hAPP(_1806630, 50511 ^ [_1806626, _1806628, _1806630, _1806632]) = hAPP(_1806632, 50511 ^ [_1806626, _1806628, _1806630, _1806632])]], -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(_1806628, _1806626)), _1806630), _1806632)))], (50500 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(_1806628, _1806626)), _1806630), _1806632)), 50503 ^ _784416 : [(50504 ^ _784416) ^ [_1806848] : [hBOOL(hAPP(hAPP(c_member(_1806628), _1806848), hAPP(c_List_Oset(_1806628), c_Enum_Oenum__class_Oenum(_1806628)))), -(hAPP(_1806630, _1806848) = hAPP(_1806632, _1806848))]]]]], (50519 ^ _784416) ^ [_1807163, _1807165, _1807167] : [c_FunDef_Ois__measure(_1807163, _1807165), -(c_FunDef_Ois__measure(tc_prod(_1807167, _1807163), hAPP(hAPP(c_COMBB(_1807163, tc_Nat_Onat, tc_prod(_1807167, _1807163)), _1807165), c_Product__Type_Osnd(_1807167, _1807163))))], (50525 ^ _784416) ^ [_1807280, _1807282, _1807284] : [c_FunDef_Ois__measure(_1807280, _1807282), -(c_FunDef_Ois__measure(tc_prod(_1807280, _1807284), hAPP(hAPP(c_COMBB(_1807280, tc_Nat_Onat, tc_prod(_1807280, _1807284)), _1807282), c_Product__Type_Ofst(_1807280, _1807284))))], (50531 ^ _784416) ^ [_1807397] : [class_Nat_Osize(_1807397), -(c_FunDef_Ois__measure(_1807397, c_Nat_Osize__class_Osize(_1807397)))], (50537 ^ _784416) ^ [_1807474] : [class_HOL_Oequal(_1807474), -(c_fequal = c_HOL_Oequal__class_Oequal(_1807474))], (50543 ^ _784416) ^ [_1807551, _1807553, _1807555] : [class_HOL_Oequal(_1807551), 50546 ^ _784416 : [(50547 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1807551), _1807553), _1807555)), -(_1807553 = _1807555)], (50553 ^ _784416) ^ [] : [_1807553 = _1807555, -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1807551), _1807553), _1807555)))]]], (50559 ^ _784416) ^ [_1807783, _1807785] : [class_HOL_Oequal(_1807783), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1807783), _1807785), _1807785)))], (50565 ^ _784416) ^ [_1807872] : [class_HOL_Oequal(_1807872), -(c_HOL_Oequal__class_Oequal(_1807872) = c_fequal)], (50571 ^ _784416) ^ [_1807949, _1807951] : [-(c_FunDef_Ois__measure(_1807949, _1807951))], (50573 ^ _784416) ^ [_1807974, _1807976] : [-(c_FunDef_Ois__measure(_1807974, _1807976))], (50575 ^ _784416) ^ [_1807999, _1808001] : [-(c_FunDef_Ois__measure(_1807999, _1808001))], (50577 ^ _784416) ^ [] : [-(c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_COMBK(tc_HOL_Obool, tc_Nat_Onat), c_fTrue)))], (50579 ^ _784416) ^ [_1808060, _1808062, _1808064, _1808066, _1808068] : [_1808060 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1808062, _1808064, _1808066, _1808068), _1808060) = c_Lazy__Sequence_Oempty(_1808064))], (50585 ^ _784416) ^ [_1808157, _1808159, _1808161, _1808163, _1808165] : [-(_1808157 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1808159, _1808161, _1808163, _1808165), _1808157) = hAPP(c_Lazy__Sequence_Obind(_1808159, _1808161, hAPP(_1808163, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1808157), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1808159, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1808161)), _1808165), _1808157)))], (50591 ^ _784416) ^ [_1808252, _1808254] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1808252), _1808254)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1808252), _1808254) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (50597 ^ _784416) ^ [_1808347, _1808349] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1808347), _1808349) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1808347), _1808349)))], (50603 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (50605 ^ _784416) ^ [_1808481, _1808483] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1808481)), c_Int_OBit1(_1808483))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1808481), _1808483)))], (50611 ^ _784416) ^ [_1808582, _1808584] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1808582), _1808584)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1808582)), c_Int_OBit1(_1808584))))], (50617 ^ _784416) ^ [_1808704, _1808706] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1808704)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1808706))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1808704), _1808706)))], (50623 ^ _784416) ^ [_1808809, _1808811] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1808809), _1808811)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1808809)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1808811))))], (50629 ^ _784416) ^ [_1808935, _1808937] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1808935)), c_Int_OBit0(_1808937))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1808935), _1808937)))], (50635 ^ _784416) ^ [_1809036, _1809038] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1809036), _1809038)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1809036)), c_Int_OBit0(_1809038))))], (50641 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (50643 ^ _784416) ^ [_1809173, _1809175] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1809173)), c_Int_OBit0(_1809175)))], (50645 ^ _784416) ^ [_1809219, _1809221] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1809219)), c_Int_OBit1(_1809221)))], (50647 ^ _784416) ^ [_1809265] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1809265)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1809265), c_Int_OPls)))], (50653 ^ _784416) ^ [_1809360] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1809360), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1809360)), c_Int_OPls)))], (50659 ^ _784416) ^ [_1809473] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1809473))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1809473)))], (50665 ^ _784416) ^ [_1809556] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1809556)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1809556))))], (50671 ^ _784416) ^ [_1809654] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1809654)), c_Int_OPls))], (50673 ^ _784416) ^ [_1809693] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1809693)))], (50675 ^ _784416) ^ [_1809729] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1809729)), c_Int_OMin))], (50677 ^ _784416) ^ [_1809768] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1809768)))], (50679 ^ _784416) ^ [_1809807] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1809807)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1809807), c_Int_OMin)))], (50685 ^ _784416) ^ [_1809902] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1809902), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1809902)), c_Int_OMin)))], (50691 ^ _784416) ^ [_1810015] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1810015))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1810015)))], (50697 ^ _784416) ^ [_1810098] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1810098)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1810098))))], (50703 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (50705 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OPls))], (50707 ^ _784416) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50709 ^ _784416) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50711 ^ _784416) ^ [_1810271, _1810273, _1810275, _1810277, _1810279, _1810281, _1810283] : [-(c_New__Random__Sequence_Opos__decr__bind(_1810271, _1810273, _1810275, _1810277, _1810279, _1810281, _1810283) = c_New__DSequence_Opos__decr__bind(_1810271, _1810273, hAPP(hAPP(hAPP(_1810275, _1810279), _1810281), _1810283), hAPP(hAPP(c_COMBC(_1810271, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1810273))), hAPP(hAPP(c_COMBC(_1810271, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1810273)))), hAPP(hAPP(c_COMBC(_1810271, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1810273))))), _1810277), _1810279)), _1810281)), _1810283)))], (50713 ^ _784416) ^ [_1810382, _1810384] : [-(hAPP(c_New__DSequence_Opos__empty(_1810382), _1810384) = c_Lazy__Sequence_Oempty(_1810382))], (50715 ^ _784416) ^ [_1810414] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1810414), _1810414)))], (50717 ^ _784416) ^ [_1810442, _1810444, _1810446, _1810448] : [-(c_New__Random__Sequence_Opos__empty(_1810442, _1810444, _1810446, _1810448) = c_New__DSequence_Opos__empty(_1810442))], (50719 ^ _784416) ^ [_1810478, _1810480, _1810482, _1810484, _1810486] : [-(hAPP(c_New__DSequence_Opos__bind(_1810478, _1810480, _1810482, _1810484), _1810486) = hAPP(c_Lazy__Sequence_Obind(_1810478, _1810480, hAPP(_1810482, _1810486)), hAPP(hAPP(c_COMBC(_1810478, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1810480)), _1810484), _1810486)))], (50721 ^ _784416) ^ [_1810539, _1810541, _1810543, _1810545, _1810547, _1810549, _1810551] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1810539, _1810541, _1810543, _1810545), _1810547), _1810549), _1810551) = c_New__DSequence_Opos__bind(_1810539, _1810541, hAPP(hAPP(hAPP(_1810543, _1810547), _1810549), _1810551), hAPP(hAPP(c_COMBC(_1810539, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1810541))), hAPP(hAPP(c_COMBC(_1810539, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1810541)))), hAPP(hAPP(c_COMBC(_1810539, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1810541))))), _1810545), _1810547)), _1810549)), _1810551)))], (50723 ^ _784416) ^ [_1810656, _1810658] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1810656)), _1810658) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1810656, tc_Lazy__Sequence_Olazy__sequence(_1810656)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1810656, tc_Lazy__Sequence_Olazy__sequence(_1810656), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1810656), tc_Nat_Onat), _1810656), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1810656), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1810656)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1810656)))), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), hAPP(c_Lazy__Sequence_Oyield(_1810656), _1810658)))], (50725 ^ _784416) ^ [_1810754, _1810756, _1810758] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1810754, _1810756), _1810758) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1810754, tc_Lazy__Sequence_Olazy__sequence(_1810754)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1810754, tc_Lazy__Sequence_Olazy__sequence(_1810754), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1810754, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1810754), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1810754), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1810754), tc_Nat_Onat)), _1810754), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1810754), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1810754), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1810754), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1810754), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1810754)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1810754, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1810754), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1810754), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1810754), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1810754), tc_Nat_Onat)), _1810754), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1810754))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1810754), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1810756))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1810754, _1810756))))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1810754), _1810758)))], (50727 ^ _784416) ^ [_1810949, _1810951, _1810953, _1810955, _1810957] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1810949, _1810951, _1810953, _1810955, _1810957) = hAPP(c_Option_Ooption_Ooption__case(_1810949, tc_prod(_1810951, tc_Lazy__Sequence_Olazy__sequence(_1810951)), _1810953, hAPP(c_Product__Type_Oprod_Oprod__case(_1810951, tc_Lazy__Sequence_Olazy__sequence(_1810951), _1810949), _1810955)), hAPP(c_Lazy__Sequence_Oyield(_1810951), _1810957)))], (50729 ^ _784416) ^ [_1811013] : [-(c_Lazy__Sequence_Oyieldn(_1811013) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1811013), _1811013, c_Lazy__Sequence_Oyield(_1811013)))], (50731 ^ _784416) ^ [_1811046, _1811048, _1811050, _1811052] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1811046, _1811048), c_Lazy__Sequence_Olazy__sequence_OInsert(_1811046, _1811050, _1811052)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1811048, _1811050)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1811046, _1811048), _1811052))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50733 ^ _784416) ^ [_1811106, _1811108, _1811110, _1811112, _1811114, _1811116] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1811106, _1811108, _1811110, _1811112, c_Lazy__Sequence_Olazy__sequence_OInsert(_1811108, _1811114, _1811116)) = hAPP(hAPP(_1811112, _1811114), _1811116))], (50735 ^ _784416) ^ [_1811179, _1811181, _1811183, _1811185, _1811187] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1811179, _1811181, _1811183) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1811179, _1811185, _1811187), 50738 ^ _784416 : [(50739 ^ _784416) ^ [] : [-(_1811181 = _1811185)], (50741 ^ _784416) ^ [] : [-(_1811183 = _1811187)]]], (50743 ^ _784416) ^ [_1811300, _1811302, _1811304, _1811306, _1811308] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1811300, _1811302, _1811304) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1811300, _1811306, _1811308)), _1811302 = _1811306, _1811304 = _1811308], (50753 ^ _784416) ^ [_1811459, _1811461, _1811463] : [-(hAPP(c_Lazy__Sequence_Oyield(_1811459), c_Lazy__Sequence_Olazy__sequence_OInsert(_1811459, _1811461, _1811463)) = hAPP(c_Option_Ooption_OSome(tc_prod(_1811459, tc_Lazy__Sequence_Olazy__sequence(_1811459))), hAPP(hAPP(c_Product__Type_OPair(_1811459, tc_Lazy__Sequence_Olazy__sequence(_1811459)), _1811461), _1811463)))], (50755 ^ _784416) ^ [_1811516, _1811518, _1811520] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1811516)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1811516, _1811518, _1811520)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1811516)), _1811520)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50757 ^ _784416) ^ [_1811567, _1811569, _1811571, _1811573] : [-(c_New__Random__Sequence_Opos__map(_1811567, _1811569, _1811571, _1811573) = c_New__Random__Sequence_Opos__bind(_1811567, _1811569, _1811573, hAPP(c_Fun_Ocomp(_1811569, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1811569))))), _1811567, c_New__Random__Sequence_Opos__single(_1811569)), _1811571)))], (50759 ^ _784416) ^ [_1811648, _1811650, _1811652, _1811654, _1811656] : [_1811648 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1811650, _1811652, _1811654, _1811656), _1811648) = c_Lazy__Sequence_Ohit__bound(_1811652))], (50765 ^ _784416) ^ [_1811745, _1811747, _1811749, _1811751, _1811753] : [-(_1811745 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1811747, _1811749, _1811751, _1811753), _1811745) = c_Lazy__Sequence_Ohb__bind(_1811747, _1811749, hAPP(_1811751, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1811745), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1811747, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1811749))), _1811753), _1811745)))], (50771 ^ _784416) ^ [_1811825, _1811827, _1811829, _1811831, _1811833, _1811835, _1811837] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1811825, _1811827, _1811829, _1811831, _1811833, _1811835, _1811837) = c_New__DSequence_Oneg__decr__bind(_1811825, _1811827, hAPP(hAPP(hAPP(_1811829, _1811833), _1811835), _1811837), hAPP(hAPP(c_COMBC(_1811825, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1811827)))), hAPP(hAPP(c_COMBC(_1811825, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1811827))))), hAPP(hAPP(c_COMBC(_1811825, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1811827)))))), _1811831), _1811833)), _1811835)), _1811837)))], (50773 ^ _784416) ^ [_1811942, _1811944, _1811946, _1811948, _1811950] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1811942), _1811944), _1811946), _1811948), _1811950) = c_New__DSequence_Opos__single(_1811942, _1811944))], (50775 ^ _784416) ^ [_1811990, _1811992, _1811994] : [-(hAPP(c_New__DSequence_Opos__single(_1811990, _1811992), _1811994) = hAPP(c_Lazy__Sequence_Osingle(_1811990), _1811992))], (50777 ^ _784416) ^ [_1812028, _1812030, _1812032, _1812034, _1812036] : [-(hAPP(c_New__DSequence_Oneg__bind(_1812028, _1812030, _1812032, _1812034), _1812036) = c_Lazy__Sequence_Ohb__bind(_1812028, _1812030, hAPP(_1812032, _1812036), hAPP(hAPP(c_COMBC(_1812028, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1812030))), _1812034), _1812036)))], (50779 ^ _784416) ^ [_1812089, _1812091, _1812093, _1812095, _1812097, _1812099, _1812101] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1812089, _1812091, _1812093, _1812095), _1812097), _1812099), _1812101) = c_New__DSequence_Oneg__bind(_1812089, _1812091, hAPP(hAPP(hAPP(_1812093, _1812097), _1812099), _1812101), hAPP(hAPP(c_COMBC(_1812089, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1812091)))), hAPP(hAPP(c_COMBC(_1812089, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1812091))))), hAPP(hAPP(c_COMBC(_1812089, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1812091)))))), _1812095), _1812097)), _1812099)), _1812101)))], (50781 ^ _784416) ^ [_1812212, _1812214, _1812216, _1812218] : [-(c_Lazy__Sequence_Oproduct(_1812212, _1812214, _1812216, _1812218) = hAPP(c_Lazy__Sequence_Obind(_1812212, tc_prod(_1812212, _1812214), _1812216), hAPP(hAPP(c_COMBB(tc_fun(_1812214, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1812212, _1812214))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1812212, _1812214)), _1812212), c_Lazy__Sequence_Obind(_1812214, tc_prod(_1812212, _1812214), _1812218)), hAPP(hAPP(c_COMBB(tc_fun(_1812214, tc_prod(_1812212, _1812214)), tc_fun(_1812214, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1812212, _1812214))), _1812212), hAPP(c_COMBB(tc_prod(_1812212, _1812214), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1812212, _1812214)), _1812214), c_Lazy__Sequence_Osingle(tc_prod(_1812212, _1812214)))), c_Product__Type_OPair(_1812212, _1812214)))))], (50783 ^ _784416) ^ [_1812333, _1812335, _1812337, _1812339] : [-(c_New__Random__Sequence_Oneg__map(_1812333, _1812335, _1812337, _1812339) = c_New__Random__Sequence_Oneg__bind(_1812333, _1812335, _1812339, hAPP(c_Fun_Ocomp(_1812335, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1812335)))))), _1812333, c_New__Random__Sequence_Oneg__single(_1812335)), _1812337)))], (50785 ^ _784416) ^ [_1812398, _1812400] : [class_Lazy__Sequence_Osmall__lazy(_1812398), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1812398), _1812400) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1812398), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1812398)), c_List_Olist_ONil(_1812398)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1812398))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1812400)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1812398, tc_List_Olist(_1812398)), tc_List_Olist(_1812398), c_Lazy__Sequence_Oproduct(_1812398, tc_List_Olist(_1812398), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1812398, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1812400), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1812398), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1812400), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1812398, tc_List_Olist(_1812398), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1812398))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1812398), tc_List_Olist(_1812398)), tc_fun(tc_List_Olist(_1812398), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1812398))), _1812398), hAPP(c_COMBB(tc_List_Olist(_1812398), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1812398)), tc_List_Olist(_1812398)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1812398)))), c_List_Olist_OCons(_1812398))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1812398)))))], (50791 ^ _784416) ^ [_1812759, _1812761, _1812763] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1812759, _1812761), _1812763) = c_Lazy__Sequence_Oproduct(_1812759, _1812761, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1812759, _1812763), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1812761, _1812763))), class_Lazy__Sequence_Osmall__lazy(_1812759), class_Lazy__Sequence_Osmall__lazy(_1812761)], (50801 ^ _784416) ^ [_1812922, _1812924, _1812926, _1812928] : [-(c_Lazy__Sequence_Oappend(_1812922, c_Lazy__Sequence_Olazy__sequence_OInsert(_1812922, _1812924, _1812926), _1812928) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1812922, _1812924, c_Lazy__Sequence_Oappend(_1812922, _1812926, _1812928)))], (50803 ^ _784416) ^ [_1812967, _1812969, _1812971, _1812973, _1812975] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1812967), _1812969), _1812971), _1812973), _1812975) = c_New__DSequence_Oneg__single(_1812967, _1812969))], (50805 ^ _784416) ^ [_1813015, _1813017, _1813019, _1813021] : [-(hAPP(c_New__DSequence_Opos__union(_1813015, _1813017, _1813019), _1813021) = c_Lazy__Sequence_Oappend(_1813015, hAPP(_1813017, _1813021), hAPP(_1813019, _1813021)))], (50807 ^ _784416) ^ [_1813061, _1813063, _1813065] : [-(hAPP(c_New__DSequence_Oneg__single(_1813061, _1813063), _1813065) = c_Lazy__Sequence_Ohb__single(_1813061, _1813063))], (50809 ^ _784416) ^ [_1813097, _1813099, _1813101, _1813103, _1813105, _1813107] : [-(c_New__Random__Sequence_Opos__union(_1813097, _1813099, _1813101, _1813103, _1813105, _1813107) = c_New__DSequence_Opos__union(_1813097, hAPP(hAPP(hAPP(_1813099, _1813103), _1813105), _1813107), hAPP(hAPP(hAPP(_1813101, _1813103), _1813105), _1813107)))], (50811 ^ _784416) ^ [_1813168, _1813170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1813168), _1813170)), -(c_Lazy__Sequence_Osmall__lazy_H(_1813168, _1813170) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (50817 ^ _784416) ^ [_1813255, _1813257] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1813255), _1813257))), -(c_Lazy__Sequence_Osmall__lazy_H(_1813255, _1813257) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1813257), c_Lazy__Sequence_Osmall__lazy_H(_1813255, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1813257), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50823 ^ _784416) ^ [_1813317, _1813319] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1813317), _1813319))), 50826 ^ _784416 : [(50827 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1813317), _1813319)), -(c_Lazy__Sequence_Osmall__lazy_H(_1813317, _1813319) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (50833 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1813317), _1813319))), -(c_Lazy__Sequence_Osmall__lazy_H(_1813317, _1813319) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1813319), c_Lazy__Sequence_Osmall__lazy_H(_1813317, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1813319), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (50839 ^ _784416) ^ [_1813573] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1813573) = c_Lazy__Sequence_Osmall__lazy_H(_1813573, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1813573)))], (50841 ^ _784416) ^ [_1813605, _1813607, _1813609] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1813605), _1813607))), -(hBOOL(hAPP(hAPP(_1813609, _1813605), _1813607))), 50848 ^ _784416 : [(50849 ^ _784416) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 50846 ^ [_1813605, _1813607, _1813609]), 50847 ^ [_1813605, _1813607, _1813609]))))], (50857 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(_1813609, 50846 ^ [_1813605, _1813607, _1813609]), 50847 ^ [_1813605, _1813607, _1813609]))], (50851 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 50846 ^ [_1813605, _1813607, _1813609]), 50847 ^ [_1813605, _1813607, _1813609]))), -(hBOOL(hAPP(hAPP(_1813609, 50846 ^ [_1813605, _1813607, _1813609]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 50847 ^ [_1813605, _1813607, _1813609]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (50861 ^ _784416) ^ [_1814057, _1814059, _1814061] : [-(c_Lazy__Sequence_Ohb__flat(_1814057, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1814057))), _1814059, _1814061)) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(_1814057), hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1814057)), tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1814057)), c_Lazy__Sequence_Ohit__bound(_1814057), c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1814057)))), _1814059), c_Lazy__Sequence_Ohb__flat(_1814057, _1814061)))], (50863 ^ _784416) ^ [_1814130, _1814132, _1814134, _1814136] : [-(hAPP(c_New__DSequence_Oneg__union(_1814130, _1814132, _1814134), _1814136) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(_1814130), hAPP(_1814132, _1814136), hAPP(_1814134, _1814136)))], (50865 ^ _784416) ^ [_1814178, _1814180, _1814182, _1814184] : [-(c_Lazy__Sequence_Ohb__bind(_1814178, _1814180, _1814182, _1814184) = c_Lazy__Sequence_Ohb__flat(_1814180, c_Lazy__Sequence_Ohb__map(_1814178, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1814180)), _1814184, _1814182)))], (50867 ^ _784416) ^ [_1814224, _1814226, _1814228, _1814230, _1814232] : [-(c_Lazy__Sequence_Ohb__map(_1814224, _1814226, _1814228, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(_1814224), _1814230, _1814232)) = c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(_1814226), hAPP(hAPP(c_Option_Omap(_1814224, _1814226), _1814228), _1814230), c_Lazy__Sequence_Ohb__map(_1814224, _1814226, _1814228, _1814232)))], (50869 ^ _784416) ^ [_1814286, _1814288, _1814290, _1814292, _1814294, _1814296] : [-(c_New__Random__Sequence_Oneg__union(_1814286, _1814288, _1814290, _1814292, _1814294, _1814296) = c_New__DSequence_Oneg__union(_1814286, hAPP(hAPP(hAPP(_1814288, _1814292), _1814294), _1814296), hAPP(hAPP(hAPP(_1814290, _1814292), _1814294), _1814296)))], (50871 ^ _784416) ^ [_1814348, _1814350, _1814352, _1814354, _1814356] : [-(c_New__DSequence_Oneg__map(_1814348, _1814350, _1814352, _1814354, _1814356) = c_Lazy__Sequence_Ohb__map(_1814348, _1814350, _1814352, hAPP(_1814354, _1814356)))], (50873 ^ _784416) ^ [_1814393, _1814395, _1814397] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1814393)), c_List_Osplice(_1814393, _1814395, _1814397)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1814393)), _1814395)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1814393)), _1814397)))], (50875 ^ _784416) ^ [_1814466, _1814468] : [c_Wellfounded_Oacyclic(_1814466, hAPP(c_Set_OCollect(tc_prod(_1814466, _1814466)), hAPP(c_Product__Type_Oprod_Oprod__case(_1814466, _1814466, tc_HOL_Obool), c_Predicate_Oconversep(_1814466, _1814466, _1814468)))), -(c_Wellfounded_Oacyclic(_1814466, hAPP(c_Set_OCollect(tc_prod(_1814466, _1814466)), hAPP(c_Product__Type_Oprod_Oprod__case(_1814466, _1814466, tc_HOL_Obool), _1814468))))], (50881 ^ _784416) ^ [_1814607, _1814609] : [c_Wellfounded_Oacyclic(_1814607, hAPP(c_Set_OCollect(tc_prod(_1814607, _1814607)), hAPP(c_Product__Type_Oprod_Oprod__case(_1814607, _1814607, tc_HOL_Obool), _1814609))), -(c_Wellfounded_Oacyclic(_1814607, hAPP(c_Set_OCollect(tc_prod(_1814607, _1814607)), hAPP(c_Product__Type_Oprod_Oprod__case(_1814607, _1814607, tc_HOL_Obool), c_Predicate_Oconversep(_1814607, _1814607, _1814609)))))], (50887 ^ _784416) ^ [_1814754, _1814756] : [-(c_List_Osplice(_1814754, c_List_Olist_ONil(_1814754), _1814756) = _1814756)], (50889 ^ _784416) ^ [_1814785, _1814787] : [-(c_List_Osplice(_1814785, _1814787, c_List_Olist_ONil(_1814785)) = _1814787)], (50891 ^ _784416) ^ [_1814816, _1814818, _1814820, _1814822, _1814824] : [-(c_Predicate_Oconversep(_1814816, _1814818, c_Predicate_Opred__comp(_1814816, _1814820, _1814818, _1814822, _1814824)) = c_Predicate_Opred__comp(_1814818, _1814820, _1814816, c_Predicate_Oconversep(_1814820, _1814818, _1814824), c_Predicate_Oconversep(_1814816, _1814820, _1814822)))], (50893 ^ _784416) ^ [_1814889, _1814891, _1814893] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1814889, _1814889, hAPP(hAPP(c_COMBB(tc_fun(_1814889, tc_HOL_Obool), tc_fun(_1814889, tc_HOL_Obool), _1814889), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1814889), c_fNot)), c_fequal)), _1814891), _1814893)), _1814891 = _1814893], (50899 ^ _784416) ^ [_1815027, _1815029, _1815031] : [-(_1815029 = _1815031), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1815027, _1815027, hAPP(hAPP(c_COMBB(tc_fun(_1815027, tc_HOL_Obool), tc_fun(_1815027, tc_HOL_Obool), _1815027), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1815027), c_fNot)), c_fequal)), _1815029), _1815031)))], (50905 ^ _784416) ^ [_1815099, _1815101, _1815103, _1815105, _1815107] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1815099, _1815101, _1815103), _1815105), _1815107)), -(hBOOL(hAPP(hAPP(_1815103, _1815107), _1815105)))], (50911 ^ _784416) ^ [_1815210, _1815212, _1815214, _1815216, _1815218] : [hBOOL(hAPP(hAPP(_1815210, _1815212), _1815214)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1815216, _1815218, _1815210), _1815214), _1815212)))], (50917 ^ _784416) ^ [_1815345, _1815347, _1815349, _1815351, _1815353] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1815345, _1815347, _1815349), _1815351), _1815353)), -(hBOOL(hAPP(hAPP(_1815349, _1815353), _1815351)))], (50923 ^ _784416) ^ [_1815452, _1815454, _1815456, _1815458, _1815460] : [hBOOL(hAPP(hAPP(_1815456, _1815460), _1815458)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1815452, _1815454, _1815456), _1815458), _1815460)))], (50929 ^ _784416) ^ [_1815589, _1815591, _1815593, _1815595, _1815597] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1815589, _1815591, _1815593), _1815595), _1815597)), -(hBOOL(hAPP(hAPP(_1815593, _1815597), _1815595)))], (50935 ^ _784416) ^ [_1815696, _1815698, _1815700, _1815702, _1815704] : [hBOOL(hAPP(hAPP(_1815700, _1815704), _1815702)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1815696, _1815698, _1815700), _1815702), _1815704)))], (50941 ^ _784416) ^ [_1815809, _1815811, _1815813] : [-(c_Predicate_Oconversep(_1815809, _1815811, c_Predicate_Oconversep(_1815811, _1815809, _1815813)) = _1815813)], (50943 ^ _784416) ^ [_1815844] : [-(c_Predicate_Oconversep(_1815844, _1815844, c_fequal) = c_fequal)], (50945 ^ _784416) ^ [_1815871, _1815873, _1815875, _1815877] : [-(c_Predicate_Oconversep(_1815871, _1815873, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1815871, tc_fun(_1815873, tc_HOL_Obool))), _1815875), _1815877)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1815873, tc_fun(_1815871, tc_HOL_Obool))), c_Predicate_Oconversep(_1815871, _1815873, _1815875)), c_Predicate_Oconversep(_1815871, _1815873, _1815877)))], (50947 ^ _784416) ^ [_1815940, _1815942, _1815944, _1815946] : [-(c_Predicate_Oconversep(_1815940, _1815942, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1815940, tc_fun(_1815942, tc_HOL_Obool))), _1815944), _1815946)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1815942, tc_fun(_1815940, tc_HOL_Obool))), c_Predicate_Oconversep(_1815940, _1815942, _1815944)), c_Predicate_Oconversep(_1815940, _1815942, _1815946)))], (50949 ^ _784416) ^ [_1816009, _1816011, _1816013, _1816015, _1816017] : [-(c_List_Osplice(_1816009, hAPP(hAPP(c_List_Olist_OCons(_1816009), _1816011), _1816013), hAPP(hAPP(c_List_Olist_OCons(_1816009), _1816015), _1816017)) = hAPP(hAPP(c_List_Olist_OCons(_1816009), _1816011), hAPP(hAPP(c_List_Olist_OCons(_1816009), _1816015), c_List_Osplice(_1816009, _1816013, _1816017))))], (50951 ^ _784416) ^ [_1816104, _1816106, _1816108, _1816110, _1816112] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1816104, _1816106, hAPP(hAPP(c_COMBC(_1816104, tc_fun(tc_prod(_1816104, _1816106), tc_HOL_Obool), tc_fun(_1816106, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1816106, tc_fun(tc_fun(tc_prod(_1816104, _1816106), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1816104, _1816106), tc_HOL_Obool), tc_fun(_1816106, tc_HOL_Obool)), _1816104), c_COMBC(_1816106, tc_fun(tc_prod(_1816104, _1816106), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1816106, tc_prod(_1816104, _1816106)), tc_fun(_1816106, tc_fun(tc_fun(tc_prod(_1816104, _1816106), tc_HOL_Obool), tc_HOL_Obool)), _1816104), hAPP(c_COMBB(tc_prod(_1816104, _1816106), tc_fun(tc_fun(tc_prod(_1816104, _1816106), tc_HOL_Obool), tc_HOL_Obool), _1816106), c_member(tc_prod(_1816104, _1816106)))), c_Product__Type_OPair(_1816104, _1816106)))), _1816108)), _1816110), _1816112)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1816106, _1816104)), hAPP(hAPP(c_Product__Type_OPair(_1816106, _1816104), _1816110), _1816112)), hAPP(c_Relation_Oconverse(_1816104, _1816106), _1816108))))], (50957 ^ _784416) ^ [_1816487, _1816489, _1816491, _1816493, _1816495] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1816489, _1816487)), hAPP(hAPP(c_Product__Type_OPair(_1816489, _1816487), _1816493), _1816495)), hAPP(c_Relation_Oconverse(_1816487, _1816489), _1816491))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1816487, _1816489, hAPP(hAPP(c_COMBC(_1816487, tc_fun(tc_prod(_1816487, _1816489), tc_HOL_Obool), tc_fun(_1816489, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1816489, tc_fun(tc_fun(tc_prod(_1816487, _1816489), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1816487, _1816489), tc_HOL_Obool), tc_fun(_1816489, tc_HOL_Obool)), _1816487), c_COMBC(_1816489, tc_fun(tc_prod(_1816487, _1816489), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1816489, tc_prod(_1816487, _1816489)), tc_fun(_1816489, tc_fun(tc_fun(tc_prod(_1816487, _1816489), tc_HOL_Obool), tc_HOL_Obool)), _1816487), hAPP(c_COMBB(tc_prod(_1816487, _1816489), tc_fun(tc_fun(tc_prod(_1816487, _1816489), tc_HOL_Obool), tc_HOL_Obool), _1816489), c_member(tc_prod(_1816487, _1816489)))), c_Product__Type_OPair(_1816487, _1816489)))), _1816491)), _1816493), _1816495)))], (50963 ^ _784416) ^ [_1816876, _1816878, _1816880] : [-(c_List_Osplice(_1816876, hAPP(hAPP(c_List_Olist_OCons(_1816876), _1816878), _1816880), c_List_Olist_ONil(_1816876)) = hAPP(hAPP(c_List_Olist_OCons(_1816876), _1816878), _1816880))], (50965 ^ _784416) ^ [_1816921, _1816923, _1816925] : [-(_1816921 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1816923), c_List_Oreplicate(_1816923, _1816921, _1816925)) = c_List_Oreplicate(_1816923, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1816921), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1816925))], (50971 ^ _784416) ^ [_1816978, _1816980] : [-(c_Predicate_Opred__comp(_1816978, _1816978, _1816978, c_fequal, c_Predicate_Opred__comp(_1816978, _1816978, _1816978, _1816980, c_fequal)) = _1816980)], (50973 ^ _784416) ^ [_1817015, _1817017, _1817019] : [-(hAPP(hAPP(c_List_Oappend(_1817015), c_List_Oreplicate(_1817015, _1817017, _1817019)), hAPP(hAPP(c_List_Olist_OCons(_1817015), _1817019), c_List_Olist_ONil(_1817015))) = hAPP(hAPP(c_List_Olist_OCons(_1817015), _1817019), c_List_Oreplicate(_1817015, _1817017, _1817019)))], (50975 ^ _784416) ^ [_1817076, _1817078, _1817080, _1817082] : [-(hAPP(hAPP(c_List_Omap(_1817076, _1817078), hAPP(c_COMBK(_1817078, _1817076), _1817080)), _1817082) = c_List_Oreplicate(_1817078, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1817076)), _1817082), _1817080))], (50977 ^ _784416) ^ [_1817131, _1817133, _1817135] : [-(c_List_Oreplicate(_1817131, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1817131)), hAPP(c_List_Ofilter(_1817131, hAPP(c_fequal, _1817133)), _1817135)), _1817133) = hAPP(c_List_Ofilter(_1817131, hAPP(c_fequal, _1817133)), _1817135))], (50979 ^ _784416) ^ [_1817187, _1817189, _1817191] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1817187)), c_List_Oreplicate(_1817187, _1817189, _1817191)) = _1817189)], (50981 ^ _784416) ^ [_1817225, _1817227, _1817229] : [-(c_List_Oreplicate(_1817225, hAPP(c_Nat_OSuc, _1817227), _1817229) = hAPP(hAPP(c_List_Olist_OCons(_1817225), _1817229), c_List_Oreplicate(_1817225, _1817227, _1817229)))], (50983 ^ _784416) ^ [_1817271, _1817273, _1817275, _1817277] : [-(hAPP(hAPP(c_List_Oappend(_1817271), c_List_Oreplicate(_1817271, _1817273, _1817275)), hAPP(hAPP(c_List_Olist_OCons(_1817271), _1817275), _1817277)) = hAPP(hAPP(c_List_Olist_OCons(_1817271), _1817275), hAPP(hAPP(c_List_Oappend(_1817271), c_List_Oreplicate(_1817271, _1817273, _1817275)), _1817277)))], (50985 ^ _784416) ^ [_1817340, _1817342, _1817344] : [-(hAPP(c_List_Orev(_1817340), c_List_Oreplicate(_1817340, _1817342, _1817344)) = c_List_Oreplicate(_1817340, _1817342, _1817344))], (50987 ^ _784416) ^ [_1817380, _1817382, _1817384, _1817386] : [-(c_List_Oreplicate(_1817380, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1817382), _1817384), _1817386) = hAPP(hAPP(c_List_Oappend(_1817380), c_List_Oreplicate(_1817380, _1817382, _1817386)), c_List_Oreplicate(_1817380, _1817384, _1817386)))], (50989 ^ _784416) ^ [_1817435, _1817437, _1817439, _1817441] : [-(hAPP(hAPP(c_List_Oappend(_1817435), c_List_Oreplicate(_1817435, _1817437, _1817439)), c_List_Oreplicate(_1817435, _1817441, _1817439)) = hAPP(hAPP(c_List_Oappend(_1817435), c_List_Oreplicate(_1817435, _1817441, _1817439)), c_List_Oreplicate(_1817435, _1817437, _1817439)))], (50991 ^ _784416) ^ [_1817492, _1817494, _1817496] : [-(_1817492 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1817494, c_List_Oreplicate(_1817494, _1817492, _1817496)) = _1817496)], (50997 ^ _784416) ^ [_1817537, _1817539, _1817541, _1817543] : [-(hAPP(hAPP(c_List_Otake(_1817537), _1817539), c_List_Oreplicate(_1817537, _1817541, _1817543)) = c_List_Oreplicate(_1817537, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1817539), _1817541), _1817543))], (50999 ^ _784416) ^ [_1817584, _1817586, _1817588] : [-(_1817584 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1817586), c_List_Oreplicate(_1817586, _1817584, _1817588)) = _1817588)], (51005 ^ _784416) ^ [_1817631, _1817633, _1817635, _1817637] : [-(hAPP(hAPP(c_List_Odrop(_1817631), _1817633), c_List_Oreplicate(_1817631, _1817635, _1817637)) = c_List_Oreplicate(_1817631, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1817635), _1817633), _1817637))], (51007 ^ _784416) ^ [_1817682, _1817684, _1817686, _1817688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1817682), _1817684)), -(hAPP(hAPP(c_List_Onth(_1817686), c_List_Oreplicate(_1817686, _1817684, _1817688)), _1817682) = _1817688)], (51013 ^ _784416) ^ [_1817821, _1817823, _1817825, _1817827, _1817829] : [c_List_Oreplicate(_1817821, _1817823, _1817825) = c_List_Oreplicate(_1817821, _1817827, _1817829), 51016 ^ _784416 : [(51017 ^ _784416) ^ [] : [-(_1817823 = _1817827)], (51019 ^ _784416) ^ [] : [-(_1817823 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1817825 = _1817829)]]], (51025 ^ _784416) ^ [_1817957, _1817959, _1817961, _1817963, _1817965] : [-(c_List_Oreplicate(_1817957, _1817959, _1817961) = c_List_Oreplicate(_1817957, _1817963, _1817965)), _1817959 = _1817963, 51030 ^ _784416 : [(51031 ^ _784416) ^ [] : [_1817959 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (51033 ^ _784416) ^ [] : [_1817961 = _1817965]]], (51037 ^ _784416) ^ [_1818177, _1818179, _1818181, _1818183] : [51044 ^ _784416 : [(51045 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1818183, _1818181)))], (51047 ^ _784416) ^ [] : [_1818179 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 51038 ^ _784416 : [(51039 ^ _784416) ^ [_1818249] : [hBOOL(hAPP(hAPP(c_member(_1818177), _1818249), hAPP(c_List_Oset(_1818177), c_List_Oreplicate(_1818177, _1818179, _1818181)))), hBOOL(hAPP(_1818183, _1818249))]]], (51049 ^ _784416) ^ [_1818419, _1818421, _1818423, _1818425] : [51057 ^ _784416 : [(51058 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1818419), 51056 ^ [_1818419, _1818421, _1818423, _1818425]), hAPP(c_List_Oset(_1818419), c_List_Oreplicate(_1818419, _1818421, _1818423)))))], (51060 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1818425, 51056 ^ [_1818419, _1818421, _1818423, _1818425])))]], hBOOL(hAPP(_1818425, _1818423)), -(_1818421 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51062 ^ _784416) ^ [_1818675, _1818677, _1818679, _1818681] : [51064 ^ _784416 : [(51065 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1818675), 51063 ^ [_1818675, _1818677, _1818679, _1818681]), hAPP(c_List_Oset(_1818675), c_List_Oreplicate(_1818675, _1818677, _1818679)))))], (51067 ^ _784416) ^ [] : [hBOOL(hAPP(_1818681, 51063 ^ [_1818675, _1818677, _1818679, _1818681]))]], -(hBOOL(hAPP(_1818681, _1818679))), -(_1818677 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51075 ^ _784416) ^ [_1818882, _1818884, _1818886, _1818888] : [51076 ^ _784416 : [(51077 ^ _784416) ^ [] : [hBOOL(hAPP(_1818888, _1818886))], (51079 ^ _784416) ^ [] : [_1818884 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 51080 ^ _784416 : [(51081 ^ _784416) ^ [_1819045] : [hBOOL(hAPP(hAPP(c_member(_1818882), _1819045), hAPP(c_List_Oset(_1818882), c_List_Oreplicate(_1818882, _1818884, _1818886)))), -(hBOOL(hAPP(_1818888, _1819045)))]]], (51087 ^ _784416) ^ [_1819352, _1819354, _1819356, _1819358, _1819360] : [-(hAPP(hAPP(c_List_Omap(_1819352, _1819354), _1819356), c_List_Oreplicate(_1819352, _1819358, _1819360)) = c_List_Oreplicate(_1819354, _1819358, hAPP(_1819356, _1819360)))], (51089 ^ _784416) ^ [_1819530, _1819532, _1819534] : [c_List_Oreplicate(_1819530, _1819532, _1819534) = c_List_Olist_ONil(_1819530), -(_1819532 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51095 ^ _784416) ^ [_1819710, _1819712, _1819714] : [_1819712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1819710, _1819712, _1819714) = c_List_Olist_ONil(_1819710))], (51101 ^ _784416) ^ [_1819983, _1819985, _1819987] : [c_List_Olist_ONil(_1819983) = c_List_Oreplicate(_1819983, _1819985, _1819987), -(_1819985 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51107 ^ _784416) ^ [_1820163, _1820165, _1820167] : [_1820165 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1820163) = c_List_Oreplicate(_1820163, _1820165, _1820167))], (51113 ^ _784416) ^ [_1820378, _1820380] : [-(c_List_Oreplicate(_1820378, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1820380) = c_List_Olist_ONil(_1820378))], (51115 ^ _784416) ^ [_1820478, _1820480] : [-(c_List_Oconcat(_1820478, c_List_Oreplicate(tc_List_Olist(_1820478), _1820480, c_List_Olist_ONil(_1820478))) = c_List_Olist_ONil(_1820478))], (51117 ^ _784416) ^ [_1820648, _1820650, _1820652, _1820654] : [hBOOL(hAPP(_1820648, _1820650)), -(hAPP(c_List_Ofilter(_1820652, _1820648), c_List_Oreplicate(_1820652, _1820654, _1820650)) = c_List_Oreplicate(_1820652, _1820654, _1820650))], (51123 ^ _784416) ^ [_1820854, _1820856, _1820858, _1820860] : [-(hBOOL(hAPP(_1820854, _1820856))), -(hAPP(c_List_Ofilter(_1820858, _1820854), c_List_Oreplicate(_1820858, _1820860, _1820856)) = c_List_Olist_ONil(_1820858))], (51129 ^ _784416) ^ [_1821166, _1821168, _1821170, _1821172] : [hBOOL(hAPP(hAPP(c_member(_1821166), _1821168), hAPP(c_List_Oset(_1821166), c_List_Oreplicate(_1821166, _1821170, _1821172)))), 51132 ^ _784416 : [(51133 ^ _784416) ^ [] : [-(_1821168 = _1821172)], (51135 ^ _784416) ^ [] : [_1821170 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (51137 ^ _784416) ^ [_1821452, _1821454, _1821456, _1821458] : [-(hBOOL(hAPP(hAPP(c_member(_1821452), _1821454), hAPP(c_List_Oset(_1821452), c_List_Oreplicate(_1821452, _1821456, _1821458))))), _1821454 = _1821458, -(_1821456 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51147 ^ _784416) ^ [_1821849, _1821851, _1821853, _1821855, _1821857, _1821859] : [-(hAPP(hAPP(c_List_Ozip(_1821849, _1821851), c_List_Oreplicate(_1821849, _1821853, _1821855)), c_List_Oreplicate(_1821851, _1821857, _1821859)) = c_List_Oreplicate(tc_prod(_1821849, _1821851), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1821853), _1821857), hAPP(hAPP(c_Product__Type_OPair(_1821849, _1821851), _1821855), _1821859)))], (51149 ^ _784416) ^ [_1822004, _1822006, _1822008] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1822004), hAPP(c_COMBK(_1822004, tc_Nat_Onat), _1822006)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1822008)) = c_List_Oreplicate(_1822004, _1822008, _1822006))], (51151 ^ _784416) ^ [_1822171, _1822173, _1822175] : [_1822171 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1822173), c_List_Oreplicate(_1822173, _1822171, _1822175)) = c_Orderings_Obot__class_Obot(tc_fun(_1822173, tc_HOL_Obool)))], (51157 ^ _784416) ^ [_1822367, _1822369, _1822371] : [-(_1822367 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1822369), c_List_Oreplicate(_1822369, _1822367, _1822371)) = hAPP(hAPP(c_Set_Oinsert(_1822369), _1822371), c_Orderings_Obot__class_Obot(tc_fun(_1822369, tc_HOL_Obool))))], (51163 ^ _784416) ^ [_1822646, _1822648, _1822650] : [-(_1822646 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1822648), c_List_Oreplicate(_1822648, _1822646, _1822650)) = hAPP(hAPP(c_Set_Oinsert(_1822648), _1822650), c_Orderings_Obot__class_Obot(tc_fun(_1822648, tc_HOL_Obool))))], (51169 ^ _784416) ^ [_1822908, _1822910, _1822912] : [-(hAPP(c_List_Oset(_1822908), c_List_Oreplicate(_1822908, hAPP(c_Nat_OSuc, _1822910), _1822912)) = hAPP(hAPP(c_Set_Oinsert(_1822908), _1822912), c_Orderings_Obot__class_Obot(tc_fun(_1822908, tc_HOL_Obool))))], (51171 ^ _784416) ^ [_1823058, _1823060, _1823062] : [class_Fields_Olinordered__field(_1823058), 51177 ^ _784416 : [(51178 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1823058), c_Groups_Ozero__class_Ozero(_1823058)), 51176 ^ [_1823058, _1823060, _1823062])))], (51180 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1823058), _1823060), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1823058), _1823062), 51176 ^ [_1823058, _1823060, _1823062])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1823058), _1823060), _1823062)))], (51184 ^ _784416) ^ [_1823648, _1823650, _1823652, _1823654, _1823656] : [51186 ^ _784416 : [(51187 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1823648), 51185 ^ [_1823648, _1823650, _1823652, _1823654, _1823656]), _1823650)))], (51189 ^ _784416) ^ [] : [c_Relation_Orefl__on(_1823652, hAPP(_1823654, 51185 ^ [_1823648, _1823650, _1823652, _1823654, _1823656]), hAPP(_1823656, 51185 ^ [_1823648, _1823650, _1823652, _1823654, _1823656]))]], -(c_Relation_Orefl__on(_1823652, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1823648, tc_fun(_1823652, tc_HOL_Obool)), _1823650), _1823654), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1823648, tc_fun(tc_prod(_1823652, _1823652), tc_HOL_Obool)), _1823650), _1823656)))], (51193 ^ _784416) ^ [_1824205, _1824207, _1824209] : [hBOOL(hAPP(hAPP(c_List_Omember(_1824205), _1824207), _1824209)), -(hBOOL(hAPP(hAPP(c_member(_1824205), _1824209), hAPP(c_List_Oset(_1824205), _1824207))))], (51199 ^ _784416) ^ [_1824411, _1824413, _1824415] : [hBOOL(hAPP(hAPP(c_member(_1824411), _1824415), hAPP(c_List_Oset(_1824411), _1824413))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1824411), _1824413), _1824415)))], (51205 ^ _784416) ^ [_1824710, _1824712, _1824714] : [hBOOL(hAPP(hAPP(c_member(_1824710), _1824712), hAPP(c_List_Oset(_1824710), _1824714))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1824710), _1824714), _1824712)))], (51211 ^ _784416) ^ [_1824916, _1824918, _1824920] : [hBOOL(hAPP(hAPP(c_List_Omember(_1824916), _1824920), _1824918)), -(hBOOL(hAPP(hAPP(c_member(_1824916), _1824918), hAPP(c_List_Oset(_1824916), _1824920))))], (51227 ^ _784416) ^ [_1825545, _1825547, _1825549, _1825551] : [51228 ^ _784416 : [(51229 ^ _784416) ^ [] : [_1825547 = _1825551], (51231 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1825545), _1825549), _1825551))]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1825545), hAPP(hAPP(c_List_Olist_OCons(_1825545), _1825547), _1825549)), _1825551)))], (51217 ^ _784416) ^ [_1825229, _1825231, _1825233, _1825235] : [hBOOL(hAPP(hAPP(c_List_Omember(_1825229), hAPP(hAPP(c_List_Olist_OCons(_1825229), _1825231), _1825233)), _1825235)), -(_1825231 = _1825235), -(hBOOL(hAPP(hAPP(c_List_Omember(_1825229), _1825233), _1825235)))], (51235 ^ _784416) ^ [_1825862] : [-(c_List_Omember(_1825862) = c_List_Oset(_1825862))], (51237 ^ _784416) ^ [_1825957, _1825959] : [hBOOL(hAPP(hAPP(c_List_Omember(_1825957), c_List_Olist_ONil(_1825957)), _1825959))], (51239 ^ _784416) ^ [_1826116, _1826118, _1826120, _1826122, _1826124, _1826126] : [-(c_Nitpick_Opair__box_Opair__box__size(_1826116, _1826118, _1826120, _1826122, c_Nitpick_Opair__box_OPairBox(_1826116, _1826118, _1826124, _1826126)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1826120, _1826124)), hAPP(_1826122, _1826126))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51241 ^ _784416) ^ [_1826305, _1826307, _1826309] : [c_List_Olist__ex1(_1826305, _1826307, _1826309), 51245 ^ _784416 : [(51246 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1826305), 51244 ^ [_1826305, _1826307, _1826309]), hAPP(c_List_Oset(_1826305), _1826309))))], (51248 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1826307, 51244 ^ [_1826305, _1826307, _1826309])))], (51250 ^ _784416) ^ [_1826773] : [-(_1826773 = 51244 ^ [_1826305, _1826307, _1826309]), hBOOL(hAPP(hAPP(c_member(_1826305), _1826773), hAPP(c_List_Oset(_1826305), _1826309))), hBOOL(hAPP(_1826307, _1826773))]]], (51260 ^ _784416) ^ [_1827105, _1827107, _1827109] : [-(c_List_Olist__ex1(_1827105, _1827107, _1827109)), 51261 ^ _784416 : [(51262 ^ _784416) ^ [_1827251] : [hBOOL(hAPP(hAPP(c_member(_1827105), _1827251), hAPP(c_List_Oset(_1827105), _1827109))), hBOOL(hAPP(_1827107, _1827251)), 51270 ^ _784416 : [(51271 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1827105), 51269 ^ [_1827105, _1827107, _1827109, _1827251]), hAPP(c_List_Oset(_1827105), _1827109))))], (51273 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1827107, 51269 ^ [_1827105, _1827107, _1827109, _1827251])))], (51275 ^ _784416) ^ [] : [51269 ^ [_1827105, _1827107, _1827109, _1827251] = _1827251]]]]], (51279 ^ _784416) ^ [_1828048, _1828050, _1828052, _1828054, _1828056, _1828058] : [c_Nitpick_Opair__box_OPairBox(_1828048, _1828050, _1828052, _1828054) = c_Nitpick_Opair__box_OPairBox(_1828048, _1828050, _1828056, _1828058), 51282 ^ _784416 : [(51283 ^ _784416) ^ [] : [-(_1828052 = _1828056)], (51285 ^ _784416) ^ [] : [-(_1828054 = _1828058)]]], (51287 ^ _784416) ^ [_1828337, _1828339, _1828341, _1828343, _1828345, _1828347] : [-(c_Nitpick_Opair__box_OPairBox(_1828337, _1828339, _1828341, _1828343) = c_Nitpick_Opair__box_OPairBox(_1828337, _1828339, _1828345, _1828347)), _1828341 = _1828345, _1828343 = _1828347], (51297 ^ _784416) ^ [_1828711, _1828713, _1828715, _1828717] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1828711, _1828713)), c_Nitpick_Opair__box_OPairBox(_1828711, _1828713, _1828715, _1828717)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51299 ^ _784416) ^ [_1828878, _1828880, _1828882, _1828884, _1828886, _1828888] : [-(c_Nitpick_Opair__box_Opair__box__case(_1828878, _1828880, _1828882, _1828884, c_Nitpick_Opair__box_OPairBox(_1828878, _1828880, _1828886, _1828888)) = hAPP(hAPP(_1828884, _1828886), _1828888))], (51301 ^ _784416) ^ [_1829053, _1829055, _1829057, _1829059, _1829061, _1829063] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1829053, _1829055, _1829057, _1829059, c_Nitpick_Opair__box_OPairBox(_1829053, _1829055, _1829061, _1829063)) = hAPP(hAPP(_1829059, _1829061), _1829063))], (51303 ^ _784416) ^ [_1829221, _1829223, _1829225] : [-(c_FunDef_OTHE__default(_1829223, _1829225, _1829221) = c_HOL_OThe(_1829223, _1829221)), 51304 ^ _784416 : [(51305 ^ _784416) ^ [_1829337] : [hBOOL(hAPP(_1829221, _1829337)), 51309 ^ _784416 : [(51310 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1829221, 51308 ^ [_1829221, _1829223, _1829225, _1829337])))], (51312 ^ _784416) ^ [] : [51308 ^ [_1829221, _1829223, _1829225, _1829337] = _1829337]]]]], (51316 ^ _784416) ^ [_1829751, _1829753, _1829755] : [-(c_FunDef_OTHE__default(_1829753, _1829755, _1829751) = _1829755), 51318 ^ _784416 : [(51319 ^ _784416) ^ [] : [-(hBOOL(hAPP(_1829751, 51317 ^ [_1829751, _1829753, _1829755])))], (51321 ^ _784416) ^ [_1830015] : [hBOOL(hAPP(_1829751, _1830015)), -(_1830015 = 51317 ^ [_1829751, _1829753, _1829755])]]], (51329 ^ _784416) ^ [_1830354, _1830356, _1830358, _1830360] : [class_Groups_Ocomm__monoid__add(_1830354), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1830356, tc_HOL_Obool)), _1830358)), 51339 ^ _784416 : [(51340 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1830356, tc_HOL_Obool)), 51338 ^ [_1830354, _1830356, _1830358, _1830360]), _1830358)))], (51342 ^ _784416) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1830356), 51338 ^ [_1830354, _1830356, _1830358, _1830360]))]], 51346 ^ _784416 : [(51347 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1830356, tc_HOL_Obool)), 51345 ^ [_1830354, _1830356, _1830358, _1830360]), _1830358)))], (51350 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1830356, tc_HOL_Obool)), 51348 ^ [_1830354, _1830356, _1830358, _1830360]), _1830358)))], (51352 ^ _784416) ^ [] : [51345 ^ [_1830354, _1830356, _1830358, _1830360] = 51348 ^ [_1830354, _1830356, _1830358, _1830360]], (51355 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1830356), 51353 ^ [_1830354, _1830356, _1830358, _1830360]), 51345 ^ [_1830354, _1830356, _1830358, _1830360])))], (51357 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1830356), 51353 ^ [_1830354, _1830356, _1830358, _1830360]), 51348 ^ [_1830354, _1830356, _1830358, _1830360])))], (51359 ^ _784416) ^ [] : [hAPP(_1830360, 51353 ^ [_1830354, _1830356, _1830358, _1830360]) = c_Groups_Ozero__class_Ozero(_1830354)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1830356, _1830354), _1830360), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1830356, tc_HOL_Obool), _1830358)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1830356, tc_HOL_Obool), _1830354), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1830356, _1830354), _1830360)), _1830358))], (51363 ^ _784416) ^ [_1832181, _1832183, _1832185, _1832187, _1832189, _1832191, _1832193] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1832181, tc_fun(_1832183, tc_fun(_1832185, tc_HOL_Obool))), _1832187), _1832189), _1832191), _1832193)), 51367 ^ _784416 : [(51368 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1832181), 51366 ^ [_1832181, _1832183, _1832185, _1832187, _1832189, _1832191, _1832193]), _1832187)))], (51370 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1832189, 51366 ^ [_1832181, _1832183, _1832185, _1832187, _1832189, _1832191, _1832193]), _1832191), _1832193)))]]], (51372 ^ _784416) ^ [_1832777, _1832779, _1832781, _1832783, _1832785, _1832787, _1832789] : [51374 ^ _784416 : [(51375 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1832777), 51373 ^ [_1832777, _1832779, _1832781, _1832783, _1832785, _1832787, _1832789]), _1832779)))], (51377 ^ _784416) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1832781, 51373 ^ [_1832777, _1832779, _1832781, _1832783, _1832785, _1832787, _1832789]), _1832783), _1832785))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1832777, tc_fun(_1832787, tc_fun(_1832789, tc_HOL_Obool))), _1832779), _1832781), _1832783), _1832785)))], (51381 ^ _784416) ^ [_1833297, _1833299] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1833297)), _1833299)), 51385 ^ _784416 : [(51386 ^ _784416) ^ [_1833549] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1833297)), _1833549), _1833299)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1833297)), _1833549)), 51384 ^ [_1833297, _1833299])))]]], (51392 ^ _784416) ^ [_1833815, _1833817] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1833815, _1833817), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1833815)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51394 ^ _784416) ^ [_1833931, _1833933, _1833935] : [-(c_Lazy__Sequence_Ohb__map(_1833931, _1833933, _1833935, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(_1833931))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(_1833933)))], (51396 ^ _784416) ^ [_1834053, _1834055, _1834057] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1834053) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1834053, _1834055, _1834057)], (51398 ^ _784416) ^ [_1834168, _1834170, _1834172] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1834168, _1834170, _1834172) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1834168)], (51400 ^ _784416) ^ [_1834270, _1834272] : [-(c_Lazy__Sequence_Oappend(_1834270, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1834270), _1834272) = _1834272)], (51402 ^ _784416) ^ [_1834356] : [-(c_Lazy__Sequence_Ohb__flat(_1834356, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1834356))))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Option_Ooption(_1834356)))], (51404 ^ _784416) ^ [_1834491, _1834493, _1834495, _1834497] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1834491, _1834493, _1834495, _1834497, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1834493)) = _1834495)], (51406 ^ _784416) ^ [_1834583] : [-(hAPP(c_Lazy__Sequence_Oyield(_1834583), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1834583)) = c_Option_Ooption_ONone(tc_prod(_1834583, tc_Lazy__Sequence_Olazy__sequence(_1834583))))], (51408 ^ _784416) ^ [_1834675] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1834675)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1834675)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51410 ^ _784416) ^ [_1834834, _1834836, _1834838] : [c_List_Olist__all(tc_Int_Oint, _1834834, c_List_Oupto(_1834836, _1834838)), -(c_List_Oall__interval__int(_1834834, _1834836, _1834838))], (51416 ^ _784416) ^ [_1835012, _1835014, _1835016] : [c_List_Oall__interval__int(_1835012, _1835014, _1835016), -(c_List_Olist__all(tc_Int_Oint, _1835012, c_List_Oupto(_1835014, _1835016)))], (51422 ^ _784416) ^ [_1835283, _1835285, _1835287] : [c_List_Olist__ex(tc_Int_Oint, _1835283, c_List_Oupto(_1835285, _1835287)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1835283), _1835285, _1835287)], (51428 ^ _784416) ^ [_1835468, _1835470, _1835472] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1835468), _1835470, _1835472)), -(c_List_Olist__ex(tc_Int_Oint, _1835468, c_List_Oupto(_1835470, _1835472)))], (51444 ^ _784416) ^ [_1836109, _1836111, _1836113] : [51446 ^ _784416 : [(51447 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 51445 ^ [_1836109, _1836111, _1836113]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1836111, _1836113))))], (51449 ^ _784416) ^ [] : [hBOOL(hAPP(_1836109, 51445 ^ [_1836109, _1836111, _1836113]))]], -(c_List_Oall__interval__int(_1836109, _1836111, _1836113))], (51434 ^ _784416) ^ [_1835748, _1835750, _1835752] : [c_List_Oall__interval__int(_1835748, _1835750, _1835752), 51437 ^ _784416 : [(51438 ^ _784416) ^ [_1835902] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1835902), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1835750, _1835752))), -(hBOOL(hAPP(_1835748, _1835902)))]]], (51453 ^ _784416) ^ [_1836530, _1836532, _1836534, _1836536] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1836530, _1836532, _1836534, c_Code__Numeral_OSuc__code__numeral(_1836536)) = hAPP(hAPP(_1836534, _1836536), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1836530, _1836532, _1836534, _1836536)))], (51455 ^ _784416) ^ [_1836709, _1836711, _1836713, _1836715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1836709), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1836711, _1836713, _1836709, _1836715) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836711)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1836711)))], (51461 ^ _784416) ^ [_1836939, _1836941, _1836943, _1836945] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1836939), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1836941, _1836943, _1836939, _1836945) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1836941, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm)), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1836943, _1836945)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1836941, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1836941, _1836943, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1836939), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1836945))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1836941, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941))))), tc_prod(_1836941, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1836941)), hAPP(hAPP(c_COMBB(_1836941, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1836941)))), tc_prod(_1836941, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1836941)), c_Product__Type_Ofst(_1836941, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (51467 ^ _784416) ^ [_1837839, _1837841, _1837843] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1837839, _1837841, _1837843, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1837841)], (51469 ^ _784416) ^ [_1837954, _1837956, _1837958] : [-(c_Random__Sequence_Oempty(_1837954, _1837956, _1837958) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1837954)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1837954)))], (51471 ^ _784416) ^ [_1838100, _1838102, _1838104, _1838106] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1838100), _1838102), _1838104), _1838106) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1838100)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1838100), _1838102)))], (51473 ^ _784416) ^ [_1838258, _1838260, _1838262, _1838264] : [-(c_Random__Sequence_Omap(_1838258, _1838260, _1838262, _1838264) = c_Random__Sequence_Obind(_1838258, _1838260, _1838264, hAPP(c_Fun_Ocomp(_1838260, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1838260)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1838258, c_Random__Sequence_Osingle(_1838260)), _1838262)))], (51475 ^ _784416) ^ [_1838468, _1838470, _1838472, _1838474, _1838476, _1838478, _1838480] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1838468), tc_Option_Ooption(_1838470), tc_sum(_1838472, _1838474), hAPP(c_Option_Omap(_1838468, _1838470), _1838476)), c_Sum__Type_Osum_Osum__case(_1838472, tc_Option_Ooption(_1838468), _1838474, _1838478, _1838480)) = c_Sum__Type_Osum_Osum__case(_1838472, tc_Option_Ooption(_1838470), _1838474, hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1838468), tc_Option_Ooption(_1838470), _1838472, hAPP(c_Option_Omap(_1838468, _1838470), _1838476)), _1838478), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1838468), tc_Option_Ooption(_1838470), _1838474, hAPP(c_Option_Omap(_1838468, _1838470), _1838476)), _1838480)))], (51477 ^ _784416) ^ [_1838687, _1838689, _1838691, _1838693, _1838695] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_1838687, _1838689, _1838691, hAPP(c_COMBK(_1838689, _1838687), _1838693), hAPP(c_COMBK(_1838689, _1838691), _1838693)), _1838695) = _1838693)], (51479 ^ _784416) ^ [_1838893, _1838895, _1838897, _1838899, _1838901, _1838903, _1838905] : [c_Sum__Type_Osum_Osum__case(_1838893, _1838895, _1838897, _1838899, _1838901) = c_Sum__Type_Osum_Osum__case(_1838893, _1838895, _1838897, _1838903, _1838905), 51482 ^ _784416 : [(51483 ^ _784416) ^ [] : [-(_1838899 = _1838903)], (51485 ^ _784416) ^ [] : [-(_1838901 = _1838905)]]], (51487 ^ _784416) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (51489 ^ _784416) ^ [_1839299, _1839301] : [class_Lattices_Obounded__lattice(_1839299), -(class_Lattices_Obounded__lattice(tc_fun(_1839301, _1839299)))], (51495 ^ _784416) ^ [_1839511, _1839513] : [class_Complete__Lattice_Ocomplete__lattice(_1839511), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1839513, _1839511)))], (51501 ^ _784416) ^ [_1839723, _1839725] : [class_Lattices_Obounded__lattice(_1839723), -(class_Lattices_Obounded__lattice__top(tc_fun(_1839725, _1839723)))], (51507 ^ _784416) ^ [_1839935, _1839937] : [class_Lattices_Obounded__lattice(_1839935), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1839937, _1839935)))], (51513 ^ _784416) ^ [_1840147, _1840149] : [class_Lattices_Olattice(_1840147), -(class_Lattices_Osemilattice__sup(tc_fun(_1840149, _1840147)))], (51519 ^ _784416) ^ [_1840359, _1840361] : [class_Lattices_Olattice(_1840359), -(class_Lattices_Osemilattice__inf(tc_fun(_1840361, _1840359)))], (51525 ^ _784416) ^ [_1840571, _1840573] : [class_Lattices_Odistrib__lattice(_1840571), -(class_Lattices_Odistrib__lattice(tc_fun(_1840573, _1840571)))], (51531 ^ _784416) ^ [_1840783, _1840785] : [class_Lattices_Oboolean__algebra(_1840783), -(class_Lattices_Oboolean__algebra(tc_fun(_1840785, _1840783)))], (51537 ^ _784416) ^ [_1840995, _1840997] : [class_Orderings_Opreorder(_1840995), -(class_Orderings_Opreorder(tc_fun(_1840997, _1840995)))], (51543 ^ _784416) ^ [_1841207, _1841209] : [-(class_Finite__Set_Ofinite(tc_fun(_1841207, _1841209))), class_Finite__Set_Ofinite(_1841207), class_Finite__Set_Ofinite(_1841209)], (51553 ^ _784416) ^ [_1841506, _1841508] : [class_Lattices_Olattice(_1841506), -(class_Lattices_Olattice(tc_fun(_1841508, _1841506)))], (51559 ^ _784416) ^ [_1841718, _1841720] : [class_Orderings_Oorder(_1841718), -(class_Orderings_Oorder(tc_fun(_1841720, _1841718)))], (51565 ^ _784416) ^ [_1841930, _1841932] : [class_Orderings_Otop(_1841930), -(class_Orderings_Otop(tc_fun(_1841932, _1841930)))], (51571 ^ _784416) ^ [_1842142, _1842144] : [class_Orderings_Oord(_1842142), -(class_Orderings_Oord(tc_fun(_1842144, _1842142)))], (51577 ^ _784416) ^ [_1842354, _1842356] : [class_Orderings_Obot(_1842354), -(class_Orderings_Obot(tc_fun(_1842356, _1842354)))], (51583 ^ _784416) ^ [_1842566, _1842568] : [class_Groups_Ouminus(_1842566), -(class_Groups_Ouminus(tc_fun(_1842568, _1842566)))], (51589 ^ _784416) ^ [_1842778, _1842780] : [class_Groups_Ominus(_1842778), -(class_Groups_Ominus(tc_fun(_1842780, _1842778)))], (51595 ^ _784416) ^ [_1842990, _1842992] : [-(class_HOL_Oequal(tc_fun(_1842990, _1842992))), class_Enum_Oenum(_1842990), class_HOL_Oequal(_1842992)], (51605 ^ _784416) ^ [_1843289, _1843291] : [-(class_Enum_Oenum(tc_fun(_1843289, _1843291))), class_Enum_Oenum(_1843289), class_Enum_Oenum(_1843291)], (51615 ^ _784416) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (51617 ^ _784416) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (51619 ^ _784416) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (51621 ^ _784416) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (51623 ^ _784416) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (51625 ^ _784416) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (51627 ^ _784416) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (51629 ^ _784416) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (51631 ^ _784416) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (51633 ^ _784416) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (51635 ^ _784416) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (51637 ^ _784416) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (51639 ^ _784416) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (51641 ^ _784416) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (51643 ^ _784416) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (51645 ^ _784416) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (51647 ^ _784416) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (51649 ^ _784416) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (51651 ^ _784416) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (51653 ^ _784416) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (51655 ^ _784416) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (51657 ^ _784416) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (51659 ^ _784416) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (51661 ^ _784416) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (51663 ^ _784416) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (51665 ^ _784416) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (51667 ^ _784416) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (51669 ^ _784416) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (51671 ^ _784416) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (51673 ^ _784416) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (51675 ^ _784416) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (51677 ^ _784416) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (51679 ^ _784416) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (51681 ^ _784416) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (51683 ^ _784416) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (51685 ^ _784416) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (51687 ^ _784416) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (51689 ^ _784416) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (51691 ^ _784416) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (51693 ^ _784416) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (51695 ^ _784416) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (51697 ^ _784416) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (51699 ^ _784416) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (51701 ^ _784416) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (51703 ^ _784416) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (51705 ^ _784416) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (51707 ^ _784416) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (51709 ^ _784416) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (51711 ^ _784416) ^ [] : [-(class_Smallcheck_Osmall(tc_Int_Oint))], (51713 ^ _784416) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (51715 ^ _784416) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (51717 ^ _784416) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (51719 ^ _784416) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (51721 ^ _784416) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (51723 ^ _784416) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (51725 ^ _784416) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (51727 ^ _784416) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (51729 ^ _784416) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (51731 ^ _784416) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (51733 ^ _784416) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (51735 ^ _784416) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (51737 ^ _784416) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (51739 ^ _784416) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (51741 ^ _784416) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (51743 ^ _784416) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (51745 ^ _784416) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (51747 ^ _784416) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (51749 ^ _784416) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (51751 ^ _784416) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (51753 ^ _784416) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (51755 ^ _784416) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (51757 ^ _784416) ^ [] : [-(class_HOL_Oequal(tc_Int_Oint))], (51759 ^ _784416) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (51761 ^ _784416) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (51763 ^ _784416) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (51765 ^ _784416) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (51767 ^ _784416) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (51769 ^ _784416) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (51771 ^ _784416) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (51773 ^ _784416) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (51775 ^ _784416) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (51777 ^ _784416) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (51779 ^ _784416) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (51781 ^ _784416) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (51783 ^ _784416) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (51785 ^ _784416) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (51787 ^ _784416) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (51789 ^ _784416) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (51791 ^ _784416) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (51793 ^ _784416) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (51795 ^ _784416) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (51797 ^ _784416) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (51799 ^ _784416) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (51801 ^ _784416) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (51803 ^ _784416) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (51805 ^ _784416) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (51807 ^ _784416) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (51809 ^ _784416) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (51811 ^ _784416) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (51813 ^ _784416) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (51815 ^ _784416) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (51817 ^ _784416) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (51819 ^ _784416) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (51821 ^ _784416) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (51823 ^ _784416) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (51825 ^ _784416) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (51827 ^ _784416) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (51829 ^ _784416) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (51831 ^ _784416) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (51833 ^ _784416) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (51835 ^ _784416) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (51837 ^ _784416) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (51839 ^ _784416) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (51841 ^ _784416) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (51843 ^ _784416) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (51845 ^ _784416) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (51847 ^ _784416) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (51849 ^ _784416) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (51851 ^ _784416) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (51853 ^ _784416) ^ [] : [-(class_HOL_Oequal(tc_Nat_Onat))], (51855 ^ _784416) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (51857 ^ _784416) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (51859 ^ _784416) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (51861 ^ _784416) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (51863 ^ _784416) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (51865 ^ _784416) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (51867 ^ _784416) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (51869 ^ _784416) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (51871 ^ _784416) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (51873 ^ _784416) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (51875 ^ _784416) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (51877 ^ _784416) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (51879 ^ _784416) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (51881 ^ _784416) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (51883 ^ _784416) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (51885 ^ _784416) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (51887 ^ _784416) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (51889 ^ _784416) ^ [] : [-(class_HOL_Oequal(tc_HOL_Obool))], (51891 ^ _784416) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (51893 ^ _784416) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (51895 ^ _784416) ^ [_1850994] : [class_Lazy__Sequence_Osmall__lazy(_1850994), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1850994)))], (51901 ^ _784416) ^ [_1851169] : [-(class_HOL_Oequal(tc_List_Olist(_1851169)))], (51903 ^ _784416) ^ [_1851248] : [-(class_Nat_Osize(tc_List_Olist(_1851248)))], (51905 ^ _784416) ^ [_1851356, _1851358] : [-(class_Finite__Set_Ofinite(tc_sum(_1851356, _1851358))), class_Finite__Set_Ofinite(_1851356), class_Finite__Set_Ofinite(_1851358)], (51915 ^ _784416) ^ [_1851640, _1851642] : [-(class_HOL_Oequal(tc_sum(_1851640, _1851642)))], (51917 ^ _784416) ^ [_1851751, _1851753] : [-(class_Enum_Oenum(tc_sum(_1851751, _1851753))), class_Enum_Oenum(_1851751), class_Enum_Oenum(_1851753)], (51927 ^ _784416) ^ [_1852035, _1852037] : [-(class_Nat_Osize(tc_sum(_1852035, _1852037)))], (51929 ^ _784416) ^ [_1852132] : [class_Finite__Set_Ofinite(_1852132), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1852132)))], (51935 ^ _784416) ^ [_1852307] : [-(class_HOL_Oequal(tc_Option_Ooption(_1852307)))], (51937 ^ _784416) ^ [_1852401] : [class_Enum_Oenum(_1852401), -(class_Enum_Oenum(tc_Option_Ooption(_1852401)))], (51943 ^ _784416) ^ [_1852576] : [-(class_Nat_Osize(tc_Option_Ooption(_1852576)))], (51945 ^ _784416) ^ [_1852669, _1852671] : [-(class_HOL_Oequal(tc_Nitpick_Opair__box(_1852669, _1852671)))], (51947 ^ _784416) ^ [_1852765, _1852767] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1852765, _1852767)))], (51949 ^ _784416) ^ [_1852876, _1852878] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1852876, _1852878))), class_Lazy__Sequence_Osmall__lazy(_1852876), class_Lazy__Sequence_Osmall__lazy(_1852878)], (51959 ^ _784416) ^ [_1853175, _1853177] : [-(class_Finite__Set_Ofinite(tc_prod(_1853175, _1853177))), class_Finite__Set_Ofinite(_1853175), class_Finite__Set_Ofinite(_1853177)], (51969 ^ _784416) ^ [_1853474, _1853476] : [-(class_Smallcheck_Osmall(tc_prod(_1853474, _1853476))), class_Smallcheck_Osmall(_1853474), class_Smallcheck_Osmall(_1853476)], (51979 ^ _784416) ^ [_1853758, _1853760] : [-(class_HOL_Oequal(tc_prod(_1853758, _1853760)))], (51981 ^ _784416) ^ [_1853869, _1853871] : [-(class_Enum_Oenum(tc_prod(_1853869, _1853871))), class_Enum_Oenum(_1853869), class_Enum_Oenum(_1853871)], (51991 ^ _784416) ^ [_1854153, _1854155] : [-(class_Nat_Osize(tc_prod(_1854153, _1854155)))], (51993 ^ _784416) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (51995 ^ _784416) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (51997 ^ _784416) ^ [] : [-(class_Smallcheck_Osmall(tc_Product__Type_Ounit))], (51999 ^ _784416) ^ [] : [-(class_HOL_Oequal(tc_Product__Type_Ounit))], (52001 ^ _784416) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (52003 ^ _784416) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (52005 ^ _784416) ^ [] : [-(class_HOL_Oequal(tc_Code__Evaluation_Oterm))], (52007 ^ _784416) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (52009 ^ _784416) ^ [_1854659] : [-(class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(_1854659)))], (52011 ^ _784416) ^ [_1854738] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1854738)))], (52013 ^ _784416) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52015 ^ _784416) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (52017 ^ _784416) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52019 ^ _784416) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52021 ^ _784416) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52023 ^ _784416) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52025 ^ _784416) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52027 ^ _784416) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52029 ^ _784416) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (52031 ^ _784416) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (52033 ^ _784416) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52035 ^ _784416) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52037 ^ _784416) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (52039 ^ _784416) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (52041 ^ _784416) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (52043 ^ _784416) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52045 ^ _784416) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52047 ^ _784416) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (52049 ^ _784416) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52051 ^ _784416) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (52053 ^ _784416) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (52055 ^ _784416) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (52057 ^ _784416) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (52059 ^ _784416) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (52061 ^ _784416) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (52063 ^ _784416) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (52065 ^ _784416) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (52067 ^ _784416) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (52069 ^ _784416) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (52071 ^ _784416) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (52073 ^ _784416) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (52075 ^ _784416) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (52077 ^ _784416) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (52079 ^ _784416) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (52081 ^ _784416) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (52083 ^ _784416) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (52085 ^ _784416) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (52087 ^ _784416) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (52089 ^ _784416) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (52091 ^ _784416) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (52093 ^ _784416) ^ [] : [-(class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral))], (52095 ^ _784416) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (52097 ^ _784416) ^ [_1857043] : [-(class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(_1857043)))], (52099 ^ _784416) ^ [_1857122] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1857122)))], (52101 ^ _784416) ^ [_1857215, _1857217] : [-(hAPP(c_COMBI(_1857215), _1857217) = _1857217)], (52103 ^ _784416) ^ [_1857342, _1857344, _1857346, _1857348] : [-(hAPP(hAPP(c_COMBK(_1857342, _1857344), _1857346), _1857348) = _1857346)], (52105 ^ _784416) ^ [_1857505, _1857507, _1857509, _1857511, _1857513, _1857515] : [-(hAPP(hAPP(hAPP(c_COMBB(_1857505, _1857507, _1857509), _1857511), _1857513), _1857515) = hAPP(_1857511, hAPP(_1857513, _1857515)))], (52107 ^ _784416) ^ [_1857682, _1857684, _1857686, _1857688, _1857690, _1857692] : [-(hAPP(hAPP(hAPP(c_COMBC(_1857682, _1857684, _1857686), _1857688), _1857690), _1857692) = hAPP(hAPP(_1857688, _1857692), _1857690))], (52109 ^ _784416) ^ [_1857859, _1857861, _1857863, _1857865, _1857867, _1857869] : [-(hAPP(hAPP(hAPP(c_COMBS(_1857859, _1857861, _1857863), _1857865), _1857867), _1857869) = hAPP(hAPP(_1857865, _1857869), hAPP(_1857867, _1857869)))], (52111 ^ _784416) ^ [_1857998, _1858000] : [hBOOL(hAPP(hAPP(c_fequal, _1857998), _1858000)), -(_1857998 = _1858000)], (52117 ^ _784416) ^ [_1858220, _1858222] : [_1858220 = _1858222, -(hBOOL(hAPP(hAPP(c_fequal, _1858220), _1858222)))], (52123 ^ _784416) ^ [] : [hBOOL(c_fFalse)], (52125 ^ _784416) ^ [] : [-(hBOOL(c_fTrue))], (52127 ^ _784416) ^ [_1858533] : [hBOOL(hAPP(c_fNot, _1858533)), hBOOL(_1858533)], (52133 ^ _784416) ^ [_1858728] : [-(hBOOL(_1858728)), -(hBOOL(hAPP(c_fNot, _1858728)))], (52139 ^ _784416) ^ [_1858939, _1858941] : [hBOOL(_1858939), hBOOL(_1858941), -(hBOOL(hAPP(hAPP(c_fconj, _1858939), _1858941)))], (52149 ^ _784416) ^ [_1859248, _1859250] : [hBOOL(hAPP(hAPP(c_fconj, _1859248), _1859250)), -(hBOOL(_1859248))], (52155 ^ _784416) ^ [_1859468, _1859470] : [hBOOL(hAPP(hAPP(c_fconj, _1859468), _1859470)), -(hBOOL(_1859470))], (52161 ^ _784416) ^ [_1859688, _1859690] : [hBOOL(_1859688), -(hBOOL(hAPP(hAPP(c_fdisj, _1859688), _1859690)))], (52167 ^ _784416) ^ [_1859908, _1859910] : [hBOOL(_1859908), -(hBOOL(hAPP(hAPP(c_fdisj, _1859910), _1859908)))], (52173 ^ _784416) ^ [_1860128, _1860130] : [hBOOL(hAPP(hAPP(c_fdisj, _1860128), _1860130)), -(hBOOL(_1860128)), -(hBOOL(_1860130))], (52183 ^ _784416) ^ [_1860436, _1860438] : [-(hBOOL(_1860436)), -(hBOOL(hAPP(hAPP(c_fimplies, _1860436), _1860438)))], (52189 ^ _784416) ^ [_1860655, _1860657] : [hBOOL(_1860655), -(hBOOL(hAPP(hAPP(c_fimplies, _1860657), _1860655)))], (52205 ^ _784416) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)))))], (52207 ^ _784416) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G, v_ts))], (52209 ^ _784416) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G), v_Ga)))], (52211 ^ _784416) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)))))], (52213 ^ _784416) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts))], (52195 ^ _784416) ^ [_1860875, _1860877] : [hBOOL(hAPP(hAPP(c_fimplies, _1860875), _1860877)), hBOOL(_1860875), -(hBOOL(_1860877))]], input).
% 1.62/2.46  ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts))],start(52215 ^ 0)).
% 1.62/2.46  ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), v_ts))), c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts)],extension(5907 ^ 1,bind([[_878076, _878078, _878080, _878082], [t_a, v_Ga, v_t, v_ts]]))).
% 1.62/2.46  ncf('1.1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)), v_t), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)))))],extension(52211 ^ 2)).
% 1.62/2.46  ncf('1.1.2',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts))],extension(52213 ^ 2)).
% 1.62/2.46  %-----------------------------------------------------
% 1.62/2.46  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------